Observed data: Why so many MPECs about TNOs lately?

This is the result of a new way to investigate the images taken by the PanSTARRS survey, see
Weryk et al. 2016.

A second batch of new discoveries was issued on July 26.
This has been planned for several years, and now there's enough data to get useful results.

Note that Gareth Williams from the MPC has currently some technical problems with the most recent MPECs (O360 and higher). If these links don't work for you, it's probably because of that.

For further information, see
the PS1 Science Consortium blog
and Holman et al. 2015.


I am looking for the SKYMAP Api (To create nightsky/star maps)

Those vendors don't need an API, and neither do you.
What their "how it works" pages do talk about are star catalogs and map projections.

The Bright Star Catalog has about 9000 stars down to magnitude 6, as faint as most people can see in a dark sky without optical aid.
The Hipparcos catalog has about 100k stars down to magnitude 9 or 10.
The key data for a star map are equatorial coordinates (right ascension, declination) and V-band apparent magnitude.
For an all-sky map, which typically uses a stereographic projection to plot everything within 90° of the zenith (RA = sidereal time, Dec = geographic latitude), transformation to horizontal coordinates may be a useful intermediate step.

If you like working in Python, either Skyfield or Astropy/Astroquery can help you retrieve and process the data but will not plot the map.


Vertical speed vector at which the sun travels to and from the galactic equator

The Sun moves at about 15-20 km/s with respect to a local standard of rest defined by the general motion of stars in our vicinity around the Galaxy. In three-dimensions, this "peculiar velocity" is $U=10.00 \pm 0.36$ km/s (radially inwards), $V=5.25 \pm 0.62$ km/s (in the direction of Galactic rotation) and $W=7.17 \pm 0.38$ km/s (up and out of the plane).  (Dehnen & Binney 1998). Different authors arrive at velocities that differ by $\sim 1-2$ km/s from these values and so this would probably be a more conservative estimate of the uncertainties.

The Sun executes oscillations around its mean orbit in the Galaxy, periodically crossing the Galactic plane. The Sun is currently above the plane and moving upwards, and each cycle takes about 70 million years with an amplitude of 100 pc; it will be roughly 30 million years before we cross the plane again.


Is there a lower limit for the altitude of orbiting objects?

For really low orbits over an atmosphereless body, the body needs to have a uniform density. Otherwise the gravity field is not symmetric, the orbit changes shape over time, and you end up with a crater.
NASA had trouble with this, lunar Mascons, during the Apollo era. In one case:

  "The Moon has no atmosphere to cause drag or heating on a spacecraft, so you can go really low: Lunar Prospector spent six months orbiting only 20 miles (30 km) above the surface."

In another:

  The orbit of PFS-2 rapidly changed shape and distance from the Moon. In 2-1/2 weeks the satellite was swooping to within a hair-raising 6 miles (10 km) of the lunar surface at closest approach. As the orbit kept changing, PFS-2 backed off again, until it seemed to be a safe 30 miles away. But not for long: inexorably, the subsatellite's orbit carried it back toward the Moon. And on May 29, 1972—only 35 days and 425 orbits after its release—PFS-2 crashed.

Now that the gravity field of the moon is mapped, it turns out that there are some low orbits that are reasonably stable:

  "What counts is an orbit's inclination," that is, the tilt of its plane to the Moon's equatorial plane. "There are actually a number of 'frozen orbits' where a spacecraft can stay in a low lunar orbit indefinitely. They occur at four inclinations: 27º, 50º, 76º, and 86º"—the last one being nearly over the lunar poles.


Why does the background noise in this image of 2020 QG look like corduroy?

I agree that it’s noise in a fixed pattern, but I think it’s unlikely to be related to ADC sensitivity.  Typically if you have multiple ADCs, they read out blocks of the sensor (e.g. one on each corner to read out a quadrant). And sensitivity differences across those amplifiers usually is removed pretty well by flat-fielding.
In my experience, you get things like this from time-variable electronic noise, e.g. 60 Hz noise from surrounding equipment.  (Probably the electronics are well-shielded from 60 Hz because it’s so ubiquitous, but there could be noise at other frequencies.)
Because CCD pixels are read out sequentially (e.g. the classic bucket brigade analogy), then any time-variable noise source that slightly changes a pixel value will manifest itself as a spatially varying pattern, where the exact pattern depends on the relationship of the readout frequency to the noise frequency.  You see the diagonal stripes because the noise signal wasn’t quite at the same phase when pixel 1 of row 2 was read out as it was when pixel 1 of row 1 was read out, and so on.
(Extra points for including an actual image of corduroy in your question, BTW.  )


When it was discovered that the classical planet are not stars?

On p.33 of the "Cambridge Concise History of Astronomy" it states that Hellenistic astronomers interpreted the variation in the brightness of the planets as a sign that they were closer or further away at various points of time. Unfortunately it doesn't have a deeper discussion here.

But on p.45 it discusses Ptolemy's thinking - he thought Mercury was, at its closest point, as close as the Moon and that the fixed stars were at the same distance as Saturn at its furthest point - the latter point suggesting that while the planets were seen as different, they might not have been thought of as being that different beyond the way they wandered.

To back that up further there is, for instance, a copy of an image from the Nuremberg Chronicle of 1493 on p.77 - here the planets are merely shown as wandering stars.


How to get error out of astropy constants

While I'm not familiar with the package, a very quick look at the documentation suggests that you want

In [90]: c.M_sun.uncertainty

instead.  I've just checked and this appears to be correct.

> python -c "from astropy import constants as c ; print c.M_sun.uncertainty"

5e+25


Whats the name of this eye-shaped galaxy?

That is galaxy NGC 1097, a barred spiral galaxy in the constellation Fornax. It has been distorted by interactions with neighbouring galaxies and has a weakly active galactic nucleus, with jets coming from the nucleus. The jets contain stars from a galaxy that has recently (in astronomical terms) been cannibalized. The ring in the centre is a region of star formation, surrounding the nucleus of the galaxy at about 5000 light years.


A new moon occurs 2017/7/23 09:45:34 UTC. Instantly after that it is waxing.

A crescent won't be visible for a few days. It reaches first quarter about 7 days later. The moon will appear to be about half full for maybe a couple of days. Nevertheless, first quarter, full moon, third quarter and new moon are moments in time, not intervals.

It may, sometimes be convenient to refer to "the day that new moon occurs", and in casual use people will say the moon is full while it appears as a circle to the naked eye (usually lasting several nights) These are casually defined for casual use. For precise terminiology say "it is now 3 days 4 hours after New Moon" or similar.


If we lived in a multiverse, what would our universe most likely then be named?

New objects usually get some preliminary name or number according to one or more naming or numbering conventions (e.g. HR numbers for stars). If there aren't too many objects of interest, they are named by the discoverer(s) (e.g. Hubble volume), an institution (e.g. PANSTARRS), an occasional nickname liked by the public (e.g. black hole), or by a majority in a commitee or an election (e.g. Hydra).

For our universe I can only speculate; probably a notion of the respective multiverse theory would become part of the name, e.g. "Herman brane", if we take a brane cosmology as an example.


In 1929, Hubble published his discovery that the sizes of galaxy redshifts and proportional to galaxy distances. That is, nearby galaxies are less redshifted than further away galaxies. This implies that further away galaxies are travelling away from us faster than nearby galaxies, which implies that we live in an expanding universe. We do not expand into anything, but rather, space is stretching. The Earth is not expanding, nor are you, me, or any other matter in the universe. It is space itself that is stretching.


Does a star's rotation always match a planet's orbit?

TL;DR: No, not always, but most of the time.
Well, most planets are in either an equatorial orbit (~0° in relation to the star's rotation vector / equator). Some are in polar orbit (~90° and almost perpendicular to the star's equator/rotation vector), and even fewer are in retrograde or strange (highly eccentric or inclined) orbits. For example, all the major planets in our Solar System orbit the Sun in an equatorial orbit. WASP-79b, a hot Jupiter, orbits in a near polar orbit (deviation of 5°). WASP-17b and HAT-P-7b are both in retrograde and highly inclined orbits to their parent stars. Neptune's moon, Triton, orbits in an inclined, retrograde  orbit, suggesting that Triton may be a captured body (but that is a long story that is unrelated). This means that a planet's orbit does not necessarily, have to align with the parent star's rotation vector.


How to locate nebulas visible through AstroMaster 114 telescope without device assistance?

Those targets are good choices for beginners at the right times of year.
However, in June M42 is a daytime object, and M31 rises in the wee hours, leaving only M13 and Albireo in the evening.
Other good summer targets include:

M8, the Lagoon Nebula
M11, the Wild Duck Cluster
M57, the Ring Nebula

Precise polar alignment is only required if you plan to take long exposure photographs.
Setting circles help when you can't see much of the sky at once, e.g. under an observatory dome or partial cloud cover.
In order to be useful, the right ascension circle must be reset each observing session, or more frequently if your mount isn't motorized.

The Skymaps.com Evening Sky Map can help you find your way around the night sky.
It shows the whole sky as it appears 2-3 hours after sunset, including several deep-sky objects visible with a 100mm or larger telescope.
A multi-page atlas such as the S&T Pocket Sky Atlas provides enough detail to actually get those objects in the telescope's field of view.
A little red light for the maps minimizes the impact on your night vision.

With practice, you can learn to locate any target of interest by triangulation, first among the bright stars, then among the faint stars in between.
For example, M13 is about 60% of the way from Arcturus to Vega and 30% of the way from η Her to ζ Her.
A detailed atlas also shows two 7th magnitude stars each ¼ degree away from M13 in an obtuse triangle.
If the object does not at first appear in the telescope field, carefully sweep the surrounding area.
Some mounts provide fine motion controls to help with this.


How fast would we have to go for the red(/blue)shifts of galaxies ahead of us to differ from those behind us with statistical significance?

First off, I'm not going to calculate an answer to the "significance level of 1%" part. This is more a rule of thumb kind of answer.

We're moving in a spaceship and want to see

  a statistically significant difference between the mean redshifts of galaxies ahead and those behind

In other words, the red- and blueshift due to our motion must exceed the peculiar motion of the individual galaxies. Cosmologists have been dealing with a very similar problem trying to measure the Hubble constant.

I remember from a cosmology class (can't find a source at the moment) that the Coma cluster is the first cluster whose redshift is dominated by the Hubble flow as opposed to peculiar motion. This is mainly due to the fact that the local group is moving towards the nearer Virgo cluster. From the above wikipedia link: Distance ca. $100 \textrm{MPc}$, apparent recession velocity ca. $7000 \textrm{km s}^{-1}$. So, at that speed, you would definitely see a systematic difference in redshift of galaxies ahead of and behind you. How long to get to that speed at constant acceleration of $10 \frac{m}{s^2}$?

\begin{equation}
 a = \frac{v}{t} \Rightarrow t = \frac{v}{a} = \frac{7\cdot 10^6 m s^{-1}}{10 m s^{-2}} = 7 \cdot 10^5 s \simeq 8\, \textrm{days.}
\end{equation}
Note that this is a worst-case scenario. People have used much closer galaxies to determine the Hubble constant. This paper's abstract says

  Due to the linearity of the expansion field the Hubble constant $\textrm{H}_0$ can be found at any distance $>4.5$ Mpc.

This is all very local, so we'll just assume a Hubble constant of $\textrm{H}_0 = 70\textrm{km}\,\textrm{s}^{-1}\,\textrm{MPc}^{-1}$ (Planck says 67.8 and Riess et al. say 73.8) and calculate redshift and hence apparent recession velocity at that distance using the Hubble law

\begin{equation}
 v = \textrm{H}_0 \cdot d = 70\,\textrm{km}\,\textrm{s}^{-1}\,\textrm{MPc}^{-1} \cdot 4.5\, \textrm{MPc} = 315\,\textrm{km}\,\textrm{s}^{-1}\,.
\end{equation}
At constant acceleration of 1g you'd get to that speed in about 9 hours, but you might need more time to do your data analysis on the galaxy spectra you'll have to take.


Are we moving faster than the Cosmic microwave background radiation?

You seem to struggle with a very common thing; the understanding that The Big Bang is not something that happened in space, but rather to space. It could be good for you to read some answers to misconceptions about The Big Bang here, or the answer to a question about it on Physics Stack Exchange. The Big Bang caused everything in the universe to move away from each other; there is no central point from which everything is receding.

For the first few hundred thousand years of our Universe, photons and matter particles were coupled in a photon-particle soup. They were all so close together, that they constantly bumped into each other, not being able to travel far at all before changing directions. As the universe expanded and the temperature of the soup became colder, the photons and matter particles were able to travel further before interacting with each other. When the temperature became low enough for protons and electrons to form hydrogen, the number of matter particles the photons had to interact with became even lower, allowing the photons to travel even further before having to interact with matter particles. It was approximately at this point in time that the CMB originated; the CMB is simply the light of the photons which interacted a very last time around the time photons and matter particles stopped being a photon-particle soup (we call this time the recombination epoch).

The universe was expanding everywhere both at the very start of its existence and during the recombination epoch, as well as now. The release of the CMB photons thus happened everywhere, and the photons of the CMB travelled in all directions. As the universe expands, the photons travel new distances, and we are constantly observing the CMB photons, which simply are reaching us from different places of origin in the universe -- which, for all we know, may be infinitely large, so we may just be seeing these kind of photons until the end of time.


Light beam (1 photon) in the limited universe?

A finite universe is said to have a "closed geometry", or to be "positively curved", meaning that, in principle, you may travel in a straight line and eventually return back to your starting point. In the 2D analogy, the surface of Earth is positively curved, and if you travel 40,000 km straight, you're back where you started.

A finite universe that does not contain dark energy of some sort, however, is bound to collapse, and you can show mathematically that even a photon will not make it back to its starting point before the universe has collapsed. Only if you consider a photon emitted exactly when the universe is created (Big Bang), it will make it back exactly when the universe ends (Big Crunch).

If the universe contains a sufficient amount of dark energy, this may prevent collapse. This may cause it to expand too fast for the photon to "get back", but you could fine-tune its components such that the expansion/collapse is slow enough for the photon to get back.

One such model is "the loitering universe", which gained some interest in the 1960's, as an explanation for an excess of quasars around redshift $z\simeq2$ (e.g. Petrosian et al. 1967). If the deceleration of matter is almost exactly balanced by the acceleration of a cosmological constant, you can have an (arbitrarily long) period of time where the universe is static.

However, observations indicate that our universe is not such a universe (Planck Collaboration et al. 2018).

Note also that since the universe is not empty, a photon may be absorbed on its way, not returning even if the expansion allows it. However, in our universe, photons that were emitted shortly after Big Bang (the so-called CMB photons) have traveled mostly freely through space ever since, with only 5% interacting with matter along its way.


"True" motionlessness - red shifts and CMB

Yes. This is is actually something that is done in the analysis of redshift data. If no correction to the redshifts are made, then the redshifts are known as "geocentric." When you correct for the motion of the Earth around the Sun, the redshifts are known as "heliocentric" (see, for example, the description of data in the 6dFGS database).

Less common is to correct redshifts for the motion of the Milky Way all the way to the cosmic microwave background's (CMB) frame. This is done by applying a shift to a frame where the CMB dipole is zero. There are two reasons why this is less common. First, the CMB dipole was only well measured relatively recently by the WMAP and Planck missions. Second, correcting for the solar system's motion relative to the CMB fixes only half of the problem. The target galaxy will also be moving with respect to the CMB at speeds that are probably comparable to the Milky Way. This fact leads to distortions in when we try to use redshift as a proxy of distance, some of which are called "Finger-of-God" for their tendency to make plots of galaxies appear to contain filaments that point at the observer.


How can the radius of a star be measured using parallax?

Betelgeuse is large and close enough that it's angular diameter can be measured directly (via optical interferometry etc...)

When you have the angular diameter, knowing the distance lets you calculate the radius with simple trigonometry.

The fact that Betelgeuse has such a large angular diameter has actually made parallax measurements more difficult, because you are measuring the relative movement of a disc that's not insignificant in angular diameter compared to its angular parallax movement, instead of a single point.  So the distance to Betelgeuse has been more uncertain than might normally be expected from a relatively nearby star.


What is a typical value for core-to-star efficiency?

From this book it seems you can have $\epsilon_{core}$ values raging from ~$30\%$ (a low value) up to $70\%$ (which is more "usual", i.e., requested by theories).

More information can be found here and here.


What is the difference between the two terms named "Eccentricity" and "Ellipticity"?

Both ellipticity $f$ (also called flattening) and eccentricity $e$ are measures of how elongated an ellipse is, based on the semi-major axis $a$ and the semi-minor axis $b$  (figure from wikipedia).

They are defined respectively as
$$f=\frac{a-b}{a}$$
and
$$e=\sqrt{1-\frac{b^2}{a^2}}$$
For a circle, $a=b$, which implies that $f=e=0$.  In modern orbital mechanics, $e$ is used rather than $f$.  This is due to convention as $e$ is one of the six orbital elements Kepler defined.
Notes:

We can extend the definition of eccentricity to parabolic and hyperbolic orbits: $$e=\sqrt{1+\frac{2\epsilon h^2}{\mu^2}}$$ where $h$ is the angular momentum of the orbiting body relative to the more massive body, $\epsilon$ is the specific orbital energy, and $\mu$ is the standard gravitational parameter.  Then $e=1$ for a parabolic orbit, and $e>1$ for a hyperbolic orbit.

While $e$ is conventionally used to describe orbits, $f$ is still used in astronomy as a factor expressing the oblateness of nearly circular bodies.

Here is a table and plot that illustrates the difference in values by fixing the semi-major axis $a=1$ and varying the semi-minor axis $b$ between 0 and 1.  Eccentricity and ellipticity are only equal when the orbit is either a circle or a line segment (when the orbit has no tangential component of velocity, in free fall towards the more massive body).


How can I calculate the uncertainties in magnitude like the CDS does?

That is because what is measured is a flux and the flux errors are in the DR2 catalogue.
Since magnitudes are based on the logarithm of the flux, then there is no straightforward correspondence (although it matters little if the error bars are less than a few hundredths if a magnitude).
Simple error propagation formulae give
$$|\Delta G| \simeq \frac{2.5}{\ln 10} \left(\frac{\Delta f}{f}\right),$$
where $f$ is the flux in the G band.
This gives $\Delta G= 0.0023(1)$ for your example. Other algorithms give almost the same result, e.g. taking the average of the $\pm \Delta G$ from using $\pm \Delta f$ to calculate the magnitude.
If the difference between the algorithms (they do give differing results when the flux error exceeds $\sim 10$%), or the fact that the true error is asymmetric in magnitude are important, then you shouldn't be using the symmetric magnitude error bar from CDS.


The smoking guns:

The ratio of oxygen isotopes of lunar rocks are almost identical to those of Earth.
Lunar recession due to the tides which causes the Earth's rotation to slow down, means that just after the Earth formed, the Moon was very close to the Earth and the Earth was rotating very fast. This situation can be reached due to an oblique impact that transfers a lot of angular momentum to the Earth.
The formation of the planets is known to have proceeded via small objects growing larger by colliding with each other, this means that the last stages of planet formation would have involved collisions between large objects. It is to be expected that around the time the Earth was taking shape, there could also be a proto-planet at the Lagrange point 60 degrees away from Earth in the same orbit. On the long term this is an unstable situation which ends with a collision that according to simulations is of the sort that typically leads to the formation of the Moon.
The asymmetry in the geology between the far side and the near side of the Moon. (there are many more maria on the near side compared to the far side). If the Moon had indeed been very close to the Earth after it formed, then the near side would have stayed very hot due to the Earth's surface still being molten and the radiant heat affecting the near side of the Moon. An impact on the near side of the Moon would far more easily be able to penetrate the solid crust and cause magma to flow to the surface compared to the far side of the Moon.


How would parallax affect an object at 200-1000 AU (for example, the 9th planet)?

The parallax is found from a triangle with the Earth's orbit at its base. The annual parallax here would then be between 1/200 and 1/1000 radians ($\sim$ 1000 to 200 arcseconds) which is indeed enormous and much bigger than the likely proper motion during a year.


Is there an equivalent of the red shift effect for cosmic rays?

Yes, there is a "retardation of the co-moving velocity" of particles.  It is important to take it into account to understand the time history of peculiar velocities of galaxies and for determining the energy distribution of cosmic rays coming from other galaxies.
Peculiar velocities, the difference between an object's velocity and the local rest velocity with respect to the microwave background, decay as 1/a(t), if there are no forces.  The global scale factor a(t) is the relative size of the universe compared to today.  So there is a "redshift" that applies to particles similar to that of the frequency of light.
The ratio of "observed" velocity to "emitted" velocity is $\frac{v_o}{v_e} = \frac{1}{1 + z}$. (Peebles, Principles of Physical Cosmology). The $z = \frac{1}{a_e}-1$ here is different from the $z$ of the galaxy because the time of the particle's emission is different from the emission time of the light that we see now.


Why is only a narrow chunk of sky darkened in this amazing Curiosity solar eclipse GIF from Mars?

Phobos' shadow on Mars is very narrow -- only about 15 miles across -- and it didn't quite pass across the Sun as viewed from the lander on that particular orbit.  This image (taken by Mars Global Surveyor) gives you an excellent picture of just how small it is:
 Credit: NASA/JPL/Malin Space Science Systems Source

The penumbral shadow of Phobos is visible on the landscape of Mars, as photographed by the Mars Global Surveyor. The center of the shadow was at approximately 10.9°N 49.2°W (Map of area Map zoom) at 04:00:33.3 UTC Earth time.
The image shows western Xanthe Terra on August 26 1999 at about 2:41 p.m. local solar time on Mars. The image covers an area about 250 kilometers across and is illuminated from the left. The dark spots on the crater floors are probably dark sand dunes. None of the craters pictured currently have names. Nanedi Valles is the meandering valley at the bottom right. The picture covers about 7°–15°N vertically and 52°–48°W horizontally. The vertical orientation of the image is 3.01° to the west of north; a north-pointing arrow superimposed on the image would point slightly to the right.

It only can darken a portion of the sky.


Has a gravitational microlensing event ever been predicted? If so, has it been observed?

In the pre-Gaia era, this was effectively impossible to do, since positions and proper motions weren't precise enough for a large enough sample of stars.  With the release of Gaia data, though, it has become an active area of research.
Bramich 2018 predicts 76 events, while Nielsen & Bramich 2018 extend this to predict an additional 27 events using Pan-STaRRS data for very low mass stars as additional lensing objects against Gaia background stars.
Klüter et al. 2018 also predict 3914 events, and there may be other papers as well.
Note that many of the predicted events are for astrometric microlensing, where the position of the background star would be measurably shifted, rather than the usual photometric microlensing, where it gets brighter.  The latter requires closer alignment for a measurable event than the former does. But some of the events would yield measurable brightening as well.
McGill et al. 2020 suggest that many of the predictions are flawed, being due to either binary companions of the lens star (which would be co-moving and thus would not be lensed, since both stars are moving together) or to cases where there is a duplicate detection in the Gaia catalog (i.e. the candidate lens star and background star are both the same object).  They revise the overall list of predictions, but still retain many events.
As far as I can tell none of these events has been observed yet, but the predictions are there.


After a supernova, why don't new stars coalesce with higher heavier element content?

Supernovae are extremely energetic events. The remnants left behind by a supernova are ejected at much greater than escape velocity. Instead of coalescing due to self-gravitation, the remnants disperse and eventually spread throughout vast regions of the galaxy.


What is the farthest object we've been able to bounce signals off of to date?

1977, Arecibo: Galilean Satellites of Jupiter: 12.6-Centimeter Radar Observations Radar echoes.

1973, 12.6 cm: Radar Observations of the rings of Saturn Content is hidden behind Elsevier's paywall, so this might not be radar echoes.

NASA, 2006 implies the limit for radar echoes is at the moons of Saturn:

  Radar astronomy employs the world's most massive dish-shaped antennas, which beam directed microwave signals at their targets, which can be as close as our moon and as far away as the moons of Saturn.

Looked for studies w radar echoes from moons of Uranus and Neptune, as well as Pluto/Charon, none found. The data may be out there.


How to watch at best this week's planet alignement?

All these planets are naked eye objects, and except for Mercury, are easy to see. Venus is also part of this grouping, Meaning that all 5 planets known to ancient astronomers are on the same side of the Earth. (and the sun is on the other)

The planets are not exactly "aligned", just they are all visible in the sky, spread over a wide part of the south eastern sky, a little while before dawn.

Sky and Telescope has some nice guides to what you can expect. Mercury is always the hardest, as it is always in the twilight. Saturn is an easy sight, appearing as a slightly yellow star. Binoculars will show its moon, Titan.

Best time is around the first week of Feb about 45 min before dawn.


"ugriz" is short for U-band, G-band, R-band, I-band, and Z-band, detailed on the Wikipedia article on photometric systems:
$$\begin{array}{|c|c|}
\hline \text{Band}&\text{Effective Wavelength Midpoint }(\lambda_{\text{eff}})\\
\hline \text{U} & \text{365 nm}\\
\hline \text{G} & \sim\text{475 nm}\\
\hline \text{R} & \text{658 nm}\\
\hline \text{I} & \text{806 nm}\\
\hline \text{Z} & \text{900 nm}\\
\hline
\end{array}$$
This $ugriz$ system is slightly different from the $u'g'r'i'z'$ system; conversions can be found here. The starting point is the same (note that $u(\text{2.5m})=u'$), but there are slight vertical and horizontal shifts.

The differences between $ugriz$ and $u'g'r'i'z'$ are much smaller than the differences between $u'g'r'i'z'$ and the $UBV(RI)_C$ system, which was replaced by them both. This older system of filters had large overlaps and did not cover as broad a range. See Fig. 1 from this thesis for a comparison:


Difference between quasar and Active Galactic Nuclei?

All quasars are AGN, but not all AGN are quasars.

AGN is a terminology that comes later than quasars. Quasars is the term applied at the beginning, when the first objects of this type have been discovered. They were radio-loud and point-like (the so-called quasi-stellar radio sources). This characterization still holds nowadays. Another property is that quasars are cosmological, that is they are objects in the distant universe (redshift $z > 1$).

AGN is the most general term we can use to refer to active galaxies. AGN include all of them (Seyfert galaxies, Quasars, Blazars, etc.). In the end, it seems that the difference among various types of AGN is due to a mix of angle-of-sight/epoch-of-observation.


Doesn't the energy conservation law imply, that the universe can't come to a Big Freeze?

The current model ($\Lambda$CDM) predicts that space will expand exponentially, and keep on doing it indefinitely far into the future. The end result, after the stars burn out, galaxies disperse, protons decay and black holes evaporate is a very thin soup of stable particles (see Adams & Laughlin 1997 or their popular book The Five Ages of the Universe).

Since each stable particle finds itself separated by exponentially growing distances due to the expanding space they will not be able to interact. Their density scales as $\rho(t)\sim \rho_0/a(t)^3 = \rho_0 e^{-3t/H_0}$. The probability of a collision over time $dt$ for a particle is roughly $\sigma v \rho(t) dt$, which if we integrate to infinity becomes $\Pr[\text{any  collision}]=\sigma v \rho_0 \int_0^\infty e^{-3t/H_0} dt = \sigma v \rho_0 H_0/3 $ which is finite - there will only be a finite number of interactions for each particle, ever.

At this point temperatures are extremely low since all background radiation has been redshifted to undetectable levels, and only the very cold horizon radiation remains ($\approx 10^{-30}$ K). Particles end up in a equilibrium state with this heat bath, and this is the real heat death of the universe.

This low temperature is still enough to rarely excite the particles, or generate new particles... or Boltzmann brains or entire worlds. Maybe. Eternity is a very long time, so low-probability processes will happen if they are allowed. They will however be so rare that the effects of one will typically dissipate long before anything else happens.


Gravitational red shift vs Doppler redshift: Is the universe really expanding?

Ultimately this is an application of Occam's razor

In order for the light to be gravitationally redshifted, it would have to be coming out of a deep gravitational well. For the red shift observed in galaxies to be gravitational, you would have to suppose several things.

First, that the stars in distant galaxies are somehow much denser: more than neutron star dense. (or possibly that entire galaxies are as dense as neutron stars.) A neutron star has a redshift of about z=0.35 distant galaxies have redshift of more than 7. No known object has a gravitational redshift like that.

Secondly that the density is proportional to distance from us. Placing us at a special position in the universe.

It is much simpler to interpret the redshift as a doppler redshift, and therefore an expanding universe


Historical estimates of the density parameter

I found an article by Wendy L. Freedman Determination of cosmological parameters which contained the following graphics

The corresponding references should be listed in the references of that paper
References

The online article is also published as Invited Review given at the Nobel Symposium, Particle Physics and the Universe, Haga Slott, Sweden, August, 1998. Published in Physica Scripta, Vol. T85, 37-46, 2000.
http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/denpar.html offers a value of 1.02 +/- 0.02 and dates back to the 2000s


Appearance (frequency) ranking of stars?

In general smaller stars are more common than larger, more massive stars.
This is typically described by the Initial Mass Function which describes the number of stars of a given mass which form initially. Moreover, larger, more massive stars burn through hydrogen quickly and live shorter lives, making them even less common as time passes. Thus, to determine the distribution of objects of various types of equal masses, you need to start with an initial mass function, and then use a stellar evolution model to evolve the system to the time of interest.

More generally, a Universal Mass Function, is an attempt to answer the question you pose in terms of mass. That is, are more massive or less massive objects more common in the universe?

The Universal Mass Function provides a description the density of occurrence of objects of various masses per cubic parsec, shown in Figure 3 of Kroupa et al. 2011. As you can see, the more massive something is, the less common its occurrence. Thus, black holes which form from massive stars will be far less common that small low mass stars which become white dwarfs. There are still uncertainties the exact distribution, shown at least partially by the shaded portions of the figure, and it will vary from one region of space to the next.

For more info check out Kroupa et al. and Binggeli and Hascher. 2007. “Is There a Universal Mass Function?”.

Kroupa, Pavel, Carsten Weidner, Jan Pflamm-Altenburg, Ingo Thies, Joerg Dabringhausen, Michael Marks, and Thomas Maschberger. 2011. “The Stellar and Sub-Stellar IMF of Simple and Composite Populations”. ArXiv e-print 1112.3340.


Determination of orbital elements for Trans-Neptunian Objects, how?

You've asked a big question, too big perhaps for a Q&A forum such as this. Your question is the sole subject of graduate level aerospace engineering classes, e.g., University of Colorado ASEN 5070, Introduction to Statistical Orbit Determination, and is the subject of multiple graduate level texts, e.g., Statistical Orbit Determination by Bob Schutz, Byron Tapley and George H. Born. To have a chance in that class, you'll need to already be well-versed in multivariate calculus, linear algebra, probability and statistics, numerical methods, and computer programming.

That said, you might want to look at Bernstein and Khushalani (2000), "Orbit fitting and uncertainties for Kuiper belt objects," The Astronomical Journal, 120.6:3323.

The preferred approach in statistical orbit determination is to collect data over multiple orbits. That's a luxury that is not possible with Trans-Neptunian Objects that have only been seen a handful of times, and only over a small arc of the multi-hundred year long orbits of those objects.

One thing Bernstein and Khushalani did to overcome this was to realize that TNOs are nearly inertial (Newton's first law) objects. Gravitation is but a small perturbation of inertial behavior at such distances. Another thing they did was to take advantage of the fact that for observations separated by a short span of time (e.g., a day or two), almost all of the apparent motion is due to the Earth rather than proper motion of the target object. This gives a good estimate of the distance to the target.

Their approach involves doing some of the regression in Cartesian space, with gravitation being a small perturbation, and then switching to orbital element space to complete the regression. Along the way, they worry about whether they have enough information to do the full orbital element space regression.


Why would the merger of spinning black holes within the accretion disk of a supermassive black hole cause them to "shoot straight up" out of the disk?

Let me see if I can try answering both parts of your question. The key is a combination of two things: 1) Most of the binary BHs in an accretion disk will have their binary orbits in the same plane as the accretion disk, so that "perpendicular to the binary plane" = "perpendicular to the accretion disk"; 2) The most effective form of binary recoil -- in which, as Steve Linton noted, excess linear momentum is carried away by gravitational waves (GWs) -- causes the merged remnant to be kicked in a direction perpendicular to the binary orbital plane.
For the first part, the combination of a gaseous accretion disk and compact, massive objects orbiting within the disk (stars, white dwarfs, neutron stars, black holes) is thought to accelerate the formation of binary objects (including binary black holes) -- but only for objects that are orbiting in the plane of the accretion disk. Since such objects are orbiting about the central SMBH in the same plane, when two such objects form a binary, they will generally end up orbiting each other in the same plane. So you should imagine a population of binaries within this disk, mostly with their own orbital planes aligned with the plane of the accretion disk. (Note that there is no reason to expect the spins of the individual BHs to be aligned with each other, which will be important later.)
Now we consider the gravitational recoil effect. The simplest scenario -- one that's not actually relevant here! -- for binary-BH merger involves two non-spinning BHs. If they are equal in mass, then everything is symmetric and you get no "kick". If they are unequal in mass, then the lower-mass BH has a higher orbital velocity, and will (due to relativistic beaming) give off momentum in the form of GWs in its orbital direction more effectively than is the case for the more massive BH. So the whole system gives off an excess of (linear) momentum in one direction, and the binary recoils to conserve momentum. There would be no net effect if the orbits were circular and unchanging (because then the "jet" of excess momentum in the GWs would just sweep through $360^{\circ}$ as the BHs orbited each other); but because the orbits are decaying due to the emission of GWs, you end up with a net asymmetric emission of momentum in the GWs, matched by a recoil of the merging binary. But this is in the plane of the binary, so it wouldn't produced the perpendicular kick we're interested in. (See this Astrobites article for a nice picture, taken from this article.)
Although the recoil in the case of non-spinning BHs had been studied theoretically for some time, recent simulations (starting around 2007) showed that if the BHs were spinning (as almost all black holes almost certainly are), and had their spins mis-aligned, then there was an additional, much stronger recoil effect -- a "superkick". The key is that this recoil effect causes the merging binary to be kicked in a direction perpendicular to the binary's orbital plane (see this Astrobites article for a discussion, although it doesn't really offer an nice, simple explanation of the underlying cause). Since, as noted above, the orbital plane of the binary is generally aligned with the plane of the accretion disk, the end result is the merger remnant being kicked approximately perpendicular to the accretion disk.


The position of stars in the sky has been used by navigators for a long time. For instance, astrolabs give you the time based on your position (or vice versa). And until GPS came along, airline pilots learned how to determine where they were using the stars. This comes with a few caveats however.

Determining the date and place from just looking at the sky is ambiguous. Since the Earth rotates, the position of stars and planets at a given place and time is indistinguishable from their position a bit later (say a couple hours) and a bit further West (how many miles further West depends on your latitude).
If you know what epoch you are in, you can determine the latitude by looking at the position of Polaris above the horizon. But to know longitude, you must also know the date and time.

Because of precession and nutation, the star that is aligned with the axis of rotation of the Earth will change over long periods of time (roughly 25 000 years). So the position Polaris isn't even enough to know your latitude if you don't know what millennium you are in.


Why are some planets so close to their star?

Big picture:

The reason why there are planets so close to their host star is probably planetary migration. These planets are difficult to explain by in situ formation models (first of all there is not enough material to form that kind of massive objects in these regions). There are different theories to explain planetary migration:

disk-planet interactions: planets form in a protoplanetary disk that still contains lots of gas after planet formation, and that can interact with the formed planets. There are different interactions that can explain migration, mostly depending on the mass of the planet you consider. We distinguish 3 main types of migration processes: Type I (migration of low-mass embedded planets), Type II (migration and gap formation by massive planets) and Type III migration (rapid migration of intermediate mass planet in relatively massive disk).
planet-planet interactions: gravitational scattering can be also a very efficient process to modify planet orbits.
Kozai mechanism: this mechanism happens in a three body problem. One object can be perturbated by an other object orbiting farther out; the object then starts to oscillate around its orbit, and can therefore migrates.
Interaction with planetesimals (also refers as the Nice model for the Solar System): interaction with a remnant planetesimal disk (as the Kuiper disk for the Solar System) can cause migration. Planets can exchange angular momentum with planetesimals in the outer edge of the disk by gravitational interaction, and thus migrating.

Disk-planet interaction:

Some more details about the Type I, II and III migration mechanisms:

Type I: planets are generating density waves propagating in the disk. Due to Keplerian rotation, this density waves become spiral waves, generating a Lindblad torque. The inner spiral arm is pulling the planet forward, the planet gaining angular momentum and migrating outward, whereas the outer spiral arm is is pulling the planet back and drives inward migration. In most cases, the outer Lindblad resonances take over the inner Lindblad resonances because they lie closer to the planet, and therefore drive an inward migration.
Type II: massive planets open gaps in the disk in which they form. The gravitational interactions become stronger and thus the angular momentum transfer to the disk. If angular momentum is deposit locally in the disk, material inside the planet loses angular momentum and material outside gains angular momentum, and therefore it recedes from the planet, opening a gap in the disk. This gap reduces the importance of Lindblad torques, and the planet is then coupled to the viscous evolution of the disk. Since material from the disk is accreted on the star and angular momentum transported away, massive planets are migrating inward.
Type III: if the surface density distribution in the co-orbital region of the planet is asymmetric, it can lead to a large torque that can cause the planet to fall inwards on a short timescale.

Sources:

Kley & Nelson 2012


How to convert sidereal time to local time?

Convert your current local date and time "t" to UTC if necessary.
Use an app to calculate the local sidereal time (LST) for the current date and time t.
Calculate the following equation:

$$local\;time\;for\;13.30\;LST = t+\frac {13.30-LST\;at\;current\;date\;and\;time\;t}{1.0027379}$$

For example, at 3:00 local time (2:00 UTC) on Feb 6, 2019, the LST=11:25:02 (11.4172 hours) at 5 deg 20' 15" east longitude (5.3375 deg). The above formula gives the time for 13.30 hours LST as
$$=3:00+\frac{13.30-11.4172}{1.0027379}$$
which equals 4.8777 hours local time (4:52:40). Plugging that time (converted to UTC if necessary) back into an app confirms the LST is 13:18:00 (13.30 hours).

After you know one date and time, you can calculate the next date and time approximately by adding 23:56:04 to your answer. For a date more than a few weeks in the future, I suggest you repeat the calculation for a the new date.

I was using this online site, but any site should give a similar answer: Calendar Date And Time To Julian Day And Sidereal Times


Mercury mapping attempts before Mariner 10?

It's very hard to see anything on the surface of Mercury. It is always seen against the glare of the sun. It is always low in the sky, so we see it through a lot of atmospheres, the seeing is worse than it would be for an object higher in the sky. With CCD imaging technology you can see some details, by taking very short exposures and combining them(source). You can't do that with conventional photographic plates.

Lowell produced a map at the start of the century showing supposed linear markings that he thought were the result of cooling.

The best that could be done in the middle of the twentieth century, direct observation images from the Pic du Midi telescope

It wasn't until radar-based observations in the 60s that the rotational period was established. There were some mapping attempts at mapping in the 70s https://www.sciencedirect.com/science/article/pii/0019103572900231 (behind paywall)

It would be hard to identify any features on these drawings with know regions or features on the Mariner images.


What's the exact story of jupiter and our earth, not becoming a super-earth?

Your reasoning is wrong: you cannot extrapolate from the outside of a sphere of matter to the inside of an annulus or a shell of matter. The gravitational pull of a uniform annulus of matter is 0 inside that annulus.
See the wikipedia article for more details on that theorem.
So having a disc of matter around you is not the same as having a sphere of matter next to you.


What would the night sky look like from a planet at the centre of a ring galaxy?

It would perhaps be less impressive than you imagine, and not much different from how any spiral galaxy would look from near the centre.

The many stars near the centre would mean that there were lots of foreground stars and dust near the centre would obscure parts of the ring. The stars of the bulge would mean the whole sky was filled with star fields.

The ring itself would be distant and so quite dim, it would look like a "milky way", but without a central bulge. So it might look something like the milky way in Auriga. Nice, but not especially dramatic.


What name was voted for Tau Boötis b by the Name Exoworlds Project?

The statistics for the 2015 vote are available at http://www.nameexoworlds.iau.org/statistics
This indicates that the winning names were "Shri Ram Matt" for the star, and "Bhagavatidevi" for the planet. The rationale given there is as follows:

One of the proposals for tau Bootis fails to comply with the IAU policy for naming exoplanets, explicitly forbidding the use of names of persons that are known to have been involved in political, religious or military activities. The IAU respects the proposed name, and the high number of votes cast in its favor, but decided to annul the vote for tau Bootis.


Can ground based telescopes use a starshade in space?

If the starshade was to stay in place over the ground telescope, it would have to be in a geosynchronous orbit, which puts it almost 36,000 km from Earth's surface. To cover an angular distance of 1 arcsecond (1/3600 of a degree), it would have a size of around 10km. Certainly not impossible, but technologically impractical at the moment. Also, the starshade would only shade a small region of the sky, so it wouldn't be useful from other observing sites.

As for the space telescopes using a starshade in geosynchronous orbit; that would be impossible, at least for scopes orbiting Earth, like Hubble is. The starshade is orbiting Earth at a different distance, and therefore speed, than the telescopes. As far as I can see, it would be near impossible to keep them aligned for anything more than a few minutes. I haven't done any number-crunching on this, though.


From what I can see, you already found what you were looking for. The table you linked is the description of the data available in the Catalog Archive Server (CAS) database. All you have to do now is use those table names (it seems that masses are on different tables, here and here) and then search whatever you want. If you do not have constraints, you could just search by sky regions, but I would recommend you to use the SQL queries as you can manually select columns an even join tables. Just to give you a quick example:
SELECT TOP 10
   p.specObjID, p.ra, p.dec, p.z, p.bpt, p.Flux_NeV_3425
FROM emissionLinesPort as p
WHERE
   p.z BETWEEN 0 AND 2

You will get a table with the first 10 results that have a redshift between 0 an 2. Columns will be ID, right ascension, declination, redshift, classification and flux of [NeV] 3425 (everything described in the table you linked). Note that for masses you would have to change the table by editing emissionLinesPort and using stellarMassStarFormingPort or stellarMassPassivePort instead (as well as change the columns accordingly).


Does Jupiter lose some atmosphere at all?

The phrase you hear is correct! Atmosphere will always be lost, no matter if it is a star or planet. Stars lose their mass via solar wind. Planets lose theirs via the three types of atmospheric loss you mentioned. Frozen planets lost their atmosphere thru sublimation and other things such as ionization. So, yes Jupiter does indeed lose its atmosphere.

You compared the three types of atmospheric loss and how they relate to Jupiter. This is where you assumptions turn out to be wrong. The thermal loss aka Jean's escape affects Jupiter even though it may seem to be not affected in the chart. Periodical or random heat generated by things could excite particles enough to overcome the escape velocity.

The solar wind, even with Jupiter's extensive magnetic field, will reach the atmosphere and neutralize atoms, which in turn will then not be effected by the magnetic field and drift off.

Jupiter is also prone to bombardment from asteroids and comets and other solar system junk. These can range from large sizes such as Comet Shoemaker-Levy 9, to minute small pieces that are barely larger than a pea. These impacts, though they add a considerable amount of stuff into Jupiter, eject mass into space, even with such strong gravitational pull via vertical atmospheric escape, creating a hot plume of material that rises and escapes from a planet. This effect nullifies most material Jupiter gains from the collisions.

Then, will all things added together, we see that Jupiter is gaining mass only via collection of objects, which in turn removes mass from Jupiter via vertical atmospheric escape. This means only a small portion of all mass collected by Jupiter this way is a gain. Now, subtract off thermal and charge exchange escape from the gain, and you will see that Jupiter is not really gaining any material, but rather losing it. Over time, if enough is given, Jupiter will only be a barren core.


Always start with the low magnification (20 mm) eyepiece.
If the target is not in the eyepiece field at first, methodically sweep the surrounding area.
Any sweep pattern that makes sense to you is fine.
When the telescope is pointed near a bright planet, stray light may brighten the background slightly.
After you find and center the target, switch to the high magnification (6 mm) eyepiece if needed.

Of course it's much easier to aim a telescope with a working finder.
If your finder is not repairable, most modern consumer telescopes have a dovetail fitting which makes it easy to install a replacement.


What's the difference of the oldest light and newest light?

There is no measurable difference between an "old" photon and a "new" one. A photon has a wavelength, a polarisation, and a direction of travel. And no other features.

You may ask if it is meaningful to discuss the age of light. It is certainly possible to say that photons were emitted by a certain body 100 years ago, and these photons are being detected now, and so this light is 100 years old. But it is impossible to measure the age as a property of the light.

We don't know of any characteristic that uniquely specifies the "age" of the light, so we just assume it's travelled from as far away as we think the object that generated it is, and call the time to travel that far it's "age".  In the case of the Cosmic microwave background, this was (we think) released when the universe first became transparent, a few hundred thousand years after the "big bang". The light from this far back has been "stretched" by the expansion of the universe, but not changed by time.

This is normally true of many simple objects. They either exist or not. A proton doesn't age. A neutron may decay, but this is an event, not a process. It is only with complex objects made of many particles that they can change with age while maintaining their identity.


What is the meaning of grain opacity and why does it affect the formation time of gas giants?

The cooling of a gas giants outer envelope (which in turn cools the convective interior) is dominated by radiative transport.
The radiative flux at the photospheric boundary is $$F_{rad}\propto- \frac{ T^3}{\rho \kappa_R}\nabla T,$$ where $\kappa_R$ is the Rosseland-mean opacity (for more, see e.g. these open lecture notes, by K. Dullemond, in 5.5.3). This is what is often called 'the' opacity in the context of gas giant formation.
The opacity quantifies how opaque a medium is to the transport of photons. High opacity means low transport of photons, hence low cooling.
Now depending on the exact density and temperature conditions of a gas layer, it can be that either atomic, molecular or dust-grain contributions dominate the opacity (see a more detailed account for the collapse of protostars, a related problem, in Vaytet et al., (2013), particularly their fig. 2). As the outer layers of gas giants, which set $F_{rad}$, can be quite cold (T<2000K) it is the strong continuum opacity of dust grains that sets the cooling rate, therefore the contraction rate of the envelope, and hence the mass accretion into the inner layers of the proto-gas giant. Note, that when talking about $F_{rad}$ it is equivalent to talk about the gas giants cooling luminosity $L$, as they are trivially related via $L=4\pi r^2_{\tau=1}F_{rad, \tau=1}$, i.e. the radiative flux at the  protogiants photosphere.
The actual self-consistent dust-dependent cooling problem was adressed in Movshovitz et al. (2010), while you are probably aware of the seminal work by Pollack et al., (1996).
For 3-D radiative hydrodynamic simulations of this process see e.g. SPH-based in Ayliffe & Bate (2009), long SPH-based in D'Angelo and Bodenheimer (2013) and grid-based simulations in Schulik et al., (2019).


Why do comets come from our local Oort cloud instead of from interstellar sources?

Since most comets are on a predictable orbit that has them circling the sun (several times), then they cannot be from outside the solar system.

Any comet that originates outside the solar system, will pick up enough velocity approaching the sun to be able to leave the solar system. Therefore, we would only see the comet once. It is unlikely that the comet approaches Jupiter (Saturn, Neptune or Uranus) where the trajectory shifts enough so that it will remain in the solar system.

Since the solar system is believe to be formed from the gravitational attraction of interstellar gas and debris, it is very unlikely that comets will be ejected unless their orbits are perturbed.

So, there is a low probability of a comet being ejected from one system, another low probability that the comet will encounter another system (after millions and billions of years) and yet another low probability that the comet gets captured in the system.

Added:
If the object was pushed out to 1 LY and it then returned as a comet, it was still under the influence the sun's gravity and would not be considered as extra-solar. The object would need to come from another system to be called extra-solar. Since the ejected objects are in a nearby orbit to the solar system, they will either return, or travel outward. Think about a satellite with a period of 12 hours. A slight push will put it in orbit 2 meters higher, and will increase the period significantly.

There is a lot of space at Neptune's orbital distance, and the intersection with Neptune's gravity is quite small (ratio of area of influence (0.1g) / surface area = ${8.6\times 10^{-11}}$). The reason the Jupiter captures asteroids is because they are in the same plane and are moving in the same direction. This increases the probability of changing the orbit significantly. It could also take several hundred passes before the orbit changes significantly.

The area of influence is the cross section area where the gravity is greater than 0.1g. The surface area is the spherical surface area of the mean distance to the planet.

Jupiter - ${5.325\times 10^{-8}}$ ~= 0.0000053%
Saturn  - ${4.703\times 10^{-9}}$ ~= 0.00000047%
Uranus  - ${1.791\times 10^{-10}}$ ~= 0.000000018%
Neptune - ${8.605\times 10^{-11}}$ ~= 0.0000000086%


Collapsing gas clouds fragment into multiple cores because the Jeans mass, that determines the minimum mass that becomes gravitationally unstable to collapse, becomes smaller if the cloud is able to contract without heating up too much.  i.e.
$$M_J \propto T^{3/2} \rho^{-1/2},$$
where $\rho$ is the cloud density. Thus if the cloud density can increase but the temperature stays constant(ish), then the Jeans mass shrinks and the cloud becomes unstable to further fragmentation.

Multiple systems with $n>2$ are inherently unstable unless they are hierarchical. i.e. a star in a wide orbit around a close pair can be stable, as could two close binary systems orbiting each other. The condition for stability is roughly that the separation of the wider star must be 5-10 times that of the inner pair ([dependent on mass ratios and eccentricities - Eggleton & Kiseleva 1995). In most other cases, what happens is the ejection of other stars from a multiple system, leaving behind a binary system Durisen et al. (2001).

What makes a binary stable? We'll what would make it unstable? I'm not sure why you think they should spiral in towards each other. This can't happen unless there is some dissipative mechanism, like tidal interactions. Gravitational waves are ineffective in all but close binaries involving compact stellar remnants. They can't "break away" because they are gravitationally bound.

EDIT: Note that it isn't true that most systems are binaries. The majority of "systems" are in fact single stars. The binary frequency for solar-type stars is about 50% - i.e. as many singles as binaries; but the binary frequency for the much more numerous M-dwarfs is probably around 30% and so single stars outnumber binary systems, though it is not clear whether that is true at birth Duchene & Kraus (2013).


The literal answer to your question is "yes". We can see clear astronomical evidence of black holes of a variety of sizes in this and other galaxies. It is possible of course that all that evidence is actually the result of some unknown physical process(es) and not black holes, but it would be a remarkable coincidence that it looks so much like we would expect black holes to look.

So I'll take your question as asking for a way to understand what black holes are. The best answer to that question is basically just equations -- solutions to the governing equations of general relativity that have event horizons, but I'm going to assume that is not what you want here.

So we are left looking for a better intuitive explanation or understanding, bearing in mind that this is at best inexact, and at worst misleading. If you have a lot of matter in a small region of space, and you look at it from the outside you see that the light coming from the surface of the region is red-shifted and (which is basically the same thing) that clocks on the surface seem to run more slowly.  As you pack the matter in more tightly this effect becomes more pronounced. But because the clocks are running more slowly, whatever process is packing the matter in also runs more slowly. Eventually, as seen from the outside the clocks on the surface approach a complete standstill, and you will receive a final few extremely red-shifted photons from the surface and then nothing. What you have is now a black hole. From your point of view it is "frozen" and all you can see of it from the outside is the gravitational field surrounding it (and maybe an electric field as well). No information can ever leave it (I'm ignoring Hawking radiation and quantum mechanics in this answer, which is reasonable for big black holes).

Relativity being relativity, things can look quite different from another point of view. If you are falling freely into the black hole (and it is big enough that tides don't rip you apart) everything seems fine, as in this simulation Light from the rest of the universe is blue-shifted and increasingly distorted by gravity, but locally everything is OK. However, no matter what you do, within a finite time (a few days for the largest black holes we know about) you will reach a singularity -- a place where the equations of general relativity break down, and some other physics must presumably apply. We don't know what happens there, but we do know that no information about it can come back out of the black hole, so we can't send in any kind of probe to tell us about it.


How would Earth's climate differ if it's axis were tilted around 90 degrees like Uranus?

This is a good question, and has been somewhat a topic of study by a few.  So below is some consequences of if Earth had a tilt like that of Uranus (for this explanation, I am disregarding the wobbles in the Earth's current axis, just focussing on the 90 degree axis):

According to the article Not All Habitable Zones Are Created Equal (Moomaw, 1999), each day and night would be 6 months each (including an epically long dusk and dawn), with daytime temperatures reaching up to 80C, but the night time side may not reach freezing - owing to the time to take to cool down from the 6 month day.  Parts of the equatorial regions would be, however, permanently encased in ice.

Pretty much like this diagram of Uranus' rotation (from Source: University of Hawaii:

A major consequence of this according to the author is:

  In such an environment, life could almost certainly still appear, but it would have much more difficulty evolving into forms that could survive such grotesque temperature extremes -- which would greatly slow down its evolution into more complex forms, maybe by billions of years.

A great consequence of this, particularly the 6 month night is that photosynthesis would have been stilted, if it could have started at all.  This has a great consequence on oxygen levels of the atmosphere.

Interestingly, the authors claim that if the Earth had an axial tilt of 90 degrees, but at 210 million km from the sun, then:

  its climate would be positively balmy -- the equator would be 11 deg C (52 deg F), and the poles would never rise above 46 deg C (115 deg F) or fall below 3 deg C (37 deg F). Earth would have no ice anywhere on its surface, except on some of its highest mountains.

According to the article High Planetary Tilt Lowers Odds for Life? (Hadhazy, 2012), has a great way of putting it:

  "Your northern pole will be boiled during part of the year while the equator gets little sunlight," said Heller. Meanwhile, "the southern pole freezes in total darkness." Essentially, the conventional notion of a scorching hell dominates one side of the planet, while an ultra-cold hell like that of Dante's Ninth Circle prevails on the other.

Then, to make matters worse, the hells reverse half a year later. "The hemispheres are cyclically sterilized, either by too strong irradiation or by freezing," Heller said.

They also describe that if life were to evolve, extremophiles (specifically, thermophiles) would be dominant - seasonally.


For me, it looks like Max Wolf discovered the movements of the Wolf 359, see the (German) original publication from 1918 "Zwei Sterne mit großer Eigenbewegung in Leo," but he does not mention which previous observations existed:

Fun fact: The object was observed from Königstuhl, a peak next to the city of Heidelberg, Germany. That was back in the days when light pollution was not an issue yet.


The two most general, publicly available packages for galaxy image fitting (other than GALFIT) are probably
Imfit and
ProFit. (Note that I am the developer of Imfit.)
There is also Lenstronomy, which is specialized for fitting gravitational lenses; this might be more relevant to your particular needs, though I know very little about it.


Could Black holes forge heavier elements that have yet to be discovered?

The heaviest elements known in nature are forged deep within stars.

No, the heaviest elements are made on Earth in scientific laboratories, or in the extreme gravity of a neutron star's crust.

  These elements are made possible by the high densities/temperature/pressures within the stars.

Many of the larger elements can be made in supernovae and neutron star collisions, not in stars. It requires extreme conditions for these elements to form.

  Black holes are known to have a much higher density/temperature/pressure than any known star.

Black holes are actually very cold, they "absorb" any radiation that passes their event horizon.  Outside the event horizon may be some very hot material, but it is not actually so hot compared to the core of a star.

  Black holes are also known to be a phase of stellar evolution - this suggests that the original star's internal process of forging metals would persist within the resultant black hole.

No, inside the black hole everything falls, and reaches a singularity in a short amount of time.

  Scientists have forged synthetic/ephemeral heavy metals under conditions which could hypothetically be sustained within a black hole.

As above, the conditions beyond the event horizon are unlike anything we have on Earth, because there is the unavoidable singularity.

After some matter has crossed the event horizon it will certainly come to the singularity. (in the same way as you will certainly reach tomorrow) And as it gets closer the tidal effects get greater, eventually ripping the atoms apart.  The extreme gravity in a black hole will tend to pull matter apart not fusing it to larger atoms.

There may be nucleosynthesis in the accretion disc around a black hole. While the amount of high mass atoms made here is relatively small, it may be useful for the sake of detecting and distinguishing black holes from neutron stars or white dwarfs.


Transform asteroid rotation to heliocentric ecliptic coordinates

r_ast is a vector that goes from the center of the asteroid to each vertex of the shape model as if you had stuck a set of rods in the center of a potato and pointing along the long axis, to the pole on top and 90 degrees to these to give X,Y,Z directions.

The matrices above that you give then transform these r_ast vectors for the co-ordinates of the surface of the asteroid into the ecliptic plane as a function of time as the asteroid rotates, giving you r_ecl. It says in the Kaasalainen paper (I think) that r_ecl has an origin shifted to the center of the asteroid. If you are wanting a visualization of what the asteroid looks like relative to the Earth or Sun etc, then you will need to calculate the Sun->asteroid vector and the Sun->Earth vector using e.g. JPL HORIZONS and using the Vector Table ephemeris type or a programmatic wrapper to this (e.g. astroquery) or the NAIF SPICE toolkit and getting or generating a SPK kernel file for the asteroid (the normal e.g. de430.bsp JPL planetary ephemeris will handle the Sun->Earth part)


What is a "21cm/mm absorption system" in the context of measuring old photons from quasars?

They have both 21cm and mm-wave observations for those systems.

Caption to Fig.1

  The hollow squares correspond to two 21 cm and molecular absorption systems.

By "system" they are referring to sets of absorption features caused by multiple clouds of material along the line of sight to a single quasar. Each cloud imposes its own set of absorption features. The totality of these absorption features is referred to as a system.


Is it practical to hand grind a convex parabolic or hyperbolic mirror?

If you're asking in regards to testing methods, as indicated in the comments, the simplest setup for interferometrically testing convex conic mirrors is with a Hindle Test, shown below in a figure from the University of Arizona College of Optical Sciences.  This setup can achieve a perfect null after adjusting the reference sphere to be focused at the focus of the test optic - the catch is that the sphere needs to be larger than your test optic, with a hole through it as shown.

In industry, it is much more common to use an aperture-stitching interferometer for small quantities of non-research-level optics.  Larger, more precise, and higher quantity aspheres may use a set of nulling optics, or a diffractive/holographic element to create a null wavefront, as covered in better detail in the link below, which is a slideset from U of Arizona's optical fabrication and testing course.

http://fp.optics.arizona.edu/jcwyant/Short_Courses/SIRA/7-TestingAsphericSurfaces.pdf

If you're feeling especially ambitious, there is a concept for measuring surface form of a mirror by displaying points on a monitor and using an HD camera to see where the reflections come from, thus telling you the angle of the optical surface at that location.  The data is then integrated to form a full surface map.  In theory, this system could be developed at low cost, with relatively high performance.

https://www.osapublishing.org/ao/abstract.cfm?uri=ao-13-11-2693

Hope this (or at least some of it) helps!

-J


According to the article "Minimum planetary size for forming outer Jovian-type planets - Stability of an isothermal atmosphere surrounding a protoplanet" (Sasaki, 1989), not only is this possible, but is suggested to have been an evolutionary stage for the development of Uranus and Neptune.  But there are a few conditions to allow this to happen, primarily due to distance from the sun, hence temperature.

The article's findings suggest that the critical mass for 'atmospheric collapse' is 0.2 of the current mass of the Earth for distances of 5 AU or greater for our solar system (this value of course would vary, depending on the parent star).  This critical mass increases the closer you are to the parent star - the article explicitly states that Mercury and Mars are too small for this to occur.


How does gyrochronology deal with differential rotation and axial tilt?

Gyrochronology uses the rotation periods of stars, caused by rotational modulation by starspots to estimate a stellar age. In the absence of differential rotation, the rotation axis inclination has no effect on this measurement. The doppler broadening of spectral lines plays no role in gyrochronology.

The rotation period of a star is just that. It is the period that is measured from the light curve. So it is some sort of emission-weighted average rotation period that depends on the distribution of starspot latitudes, the stellar inclination and the limb darkening. Sometimes there is evidence of differential rotation because the rotation period of the star changes from epoch to epoch. This can be used to calibrate the uncertainty in an individual rotation period measurement. Differential rotation is a source of uncertainty in gyrochronology, however its effect is limited because (i) at least on the Sun, and maybe other stars too, spots are confined to relatively low latitudes; (ii) spots occur at a range of latitudes over this latitude range. It is likely that younger, faster rotating stars do have spots at higher latitudes, but these stars also appear to have much weaker differential rotation than the Sun ($\Delta P/P =0.05 P^{0.3}$ according to Donahue et al. 1996, where $\Delta P$ characterises the range of measured periods for a typical star of period $P$).

The effect of differential rotation on gyrochronology is discussed at length by Epstein & Pinsonneault (2014) and rather more concisely by Jeffries (2014). It appears that differential rotation probably does set the precision limit of a measured period to be around 10 per cent (though I would argue that it is smaller for younger stars). Because the rotation rate of a star roughly follows the Skumanich-type spin-down law $\Omega \propto t^{-1/2}$, then this leads to an age uncertainty of around 20% in older stars. For younger stars it is the initial spreads in rotation rates which are more important than differential rotation as a source of error.


The Vela Pulsar (PSR J0835-4510 or PSR B0833-45) is a radio, optical, X-ray- and gamma-emitting pulsar associated with the Vela Supernova Remnant in the constellation of Vela.

First line of the Wikipedia entry on the Vela pulsar.
It's obviously much more spread out and diffuse than the Crab nebula because it occurred more than 10 times as long ago.
Here it is as an optical image, roughly 6 degrees across and almost entirely filled by the supernova remnant. (The arrow marks the position of the Vela pulsar, which is distinctly off-centre.)

The first picture on the Wikipedia page is

which shows the pulsar wind nebula around the Vela pulsar. This again has an analogy with the Crab pulsar (and looks similar) and is due to the interaction of relativistic particles emitted by the pulsar with their surroundings and the strong magnetic fields. The picture is taken in X-rays and is only a few arcminutes across.


What about the magnetic field strength inside of an old accreting neutron star?

This turns out to be tricky to answer definitively and is a topic of contemporary research.
The interior fields may be quite high ($\sim 10^{12}$ G) or approaching zero, depending on details of the interior microphysics.
The argument that fields might be close to zero is based on the probable presence of a superconducting, superfluid of protons. The interior of a neutron star cannot be just neutrons, because of the weak decay mechanism into protons, electons and (anti)neutrinos. Neutron star interiors are therefore expected to have an equilibrium concentration of $\sim 1$% protons (and electrons). If temperatures are low enough, and by that we mean $< \sim 10^9$ K, then a long-range interaction between the protons can create bosonic pairs in much the same way that electrons pair up in a low-temperature superconductor. A similar pairing mechanism can create a superfluid of neutrons in the interior.
In neutron stars, despite neutrino cooling being strongly inhibited by the degeneracy of neutrons, protons and electrons, the cooling rate is very rapid because the same degeneracy means neutron stars have an extremely low heat capacities. This means the core cools on timescales of tens of seconds after the supernova, slowing to decades after a year or two. The result is that the interior temperature falls below $10^9$ K and superfluidity (with accompanying superconductivity in the case of protons) will probably set in on timescales of hundreds of years.
When materials make a phase tranition to a superconducting state it is possible for the magnetic flux that threads them to be expelled. This is known as the Meissner effect.
On that basis, one might expect the magnetic field to be expelled from the interior of the neutron star once the protons become superconducting.
However, the superconductive state in a neutron star may be akin to a type II superconductor. This does allow the penetration of magnetic flux tubes (or "fluxoids") into the interior (Baym, Pethick & Pines 1969 - sorry, can't find a free version) if the magnetic field is greater than some critical value.
There seems to be healthy debate about exactly what state the interior of a neutron star is in as a function of time and whether the timescale for magnetic flux expulsion is short enough for the Meissner effect to take place or whether there is effectively a "frozen in" field in older neutron stars (e.g. Wynn et al. 2017).


What does a solar eclipse at 99% totality look like?

At 99% the sun will be reduced to a small sliver. There are simulations on the internet. It will become very notably darker. However, the sun is 400000 times brighter than the full moon, so 1% of the Sun is still 4000 times brighter than the Moon, and so no corona will be visible. You can still damage you eye looking at that sliver.

Since the centre of totality is less than an hour's drive from Portland, if you have a car, and can get out early, you can see totality and the corona (weather permitting)


Pictures of a curious astronomical phenomenon

In your friends picture are more artifacts than the one you showed in the 2nd picture a little bigger. I marked more of them in the picture below (click to enlarge).

They are all in a perfect line to the bright light. So these artifacts are caused by the bright light and the lens of the camera. A lens is not flat it's, well lenticular (it's where the name came from). The main light source is shining from an angle on the lens. When light hits a surface two things happen (at least in most cases ignoring Brewster's angle). The two things are reflection and transmission (or absorption, but we are talking about a lens so I let this one drop here). Every time the light hits the surface of the lens, a part is reflected and another part is transmitted. But the lens has a thickness so when the light that was first transmitted now hits the back of the lens, a part is transmitted to the CCD sensor of your camera and a (smaller) part is reflected back into the lens. This can happen several times. Normally this effect is small enough it will not be noticed. But this picture is not a normal case. Most of the picture (dark sky) emits no light, the picture is very dark. In contrast to this, there is a bright light source dominating everything (related to luminescence). And we have a 7 sec exposure the picture is taken with. 7 sec are enough time for the CCD sensor to capture some light from the effect described above.

If you now want to know why is it green and not white. White light includes all wave lengths (colors) and every wave length is reflected in another angle on the surface of air-lens. The green wave length just had the best angle to be reflected severals time and still reach the CCD sensor.

So the most accurate answer to your question "what is this green thing“ is: It's the flashlight (or what ever this light source is) that is seen in the bottom of the picture.


Does the ratio of daylight change from year to year?

I don't think it's possible to have a change in the ratio of day to night when averaged on a yearly basis.  To do so would require either a nonlinear change in the Earth's rotation or a significant shift in the polar axis tilt within a year.
If the rotation were simply slowing down over time, the year-averaged ratio would be the same every year (only the number of days in a year would change).  Similarly, the only way a polar tilt could cause a change would be if the change in angle occurred at some (sinusoidal) rate not an integral ratio of the orbital period (year).
Either of those putative mechanisms can only change the per-year ratio by producing a day/night ratio in "summer" that is not the inverse of the "winter" ratio, and producing a different non-inverse the following year.  (I'm oversimplifying a bit, since the elliptic orbit produces a repeatable asymmetry in the Sun's zenith pattern).


When and where are Pluto and Neptune closest to each other?

Per page 13 http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1965AJ.....70...10C&defaultprint=YES&filetype=.pdf (it's Harvard, so relatively reliable):

  the closest approach of Pluto to Neptune is locked in near aphelion
  and the minimum distance between the bodies is approximately 18 a.u.

which works out to roughly 1.7 billion miles or 2.7 billion kilometers.

The image from the other answer:

is deceptive if not outright incorrect (tineye shows 15 results, some of which seem reliable, but I couldn't find the originating source).

Notice how much Pluto moves from 1979 to 1989, compared to how much Neptune moves in the same period. It seems that Pluto moved a lot more, but, since Pluto was about the same distance away as Neptune, it should be moving at nearly the same speed, not faster.

As Stellarium shows, Neptune and Pluto are about 40 degrees apart in 1999 (as viewed from the Sun) significantly more than the diagram in the other question indicates (this might be an artifact of the planes being tilted 17 degrees and an unusual perspective view):

(Pluto is invisible but at the center of the cross-- the bright object nearby is 13 Oph, not Pluto).

A perhaps more interesting question: what is the closest approach of the two orbits, even if the planets in question aren't occupying that given point in the orbit.


Astronomical databases for machine learning?

The European Southern Observatory has catalogues with image data available from http://www.eso.org/qi/, you will have to register before you are able to access them.

I'd suggest you look at other observatory's websites for their data. You will have to look past the pages targeted at the general public and find links for data or science, or user portal or something like that. They are sometimes difficult to find.

Ideally you would have a standard annotated data set of images for classification so that you will be able to compare your results with others. Unfortunately I'm not aware of any standard sets.

For literature on using pattern recognition on astronomical images, http://astrometry.net/biblio.html is a good resource. They've created an ML system that is able not only to distinguish stars from other object classes but also able to identify which stars are visible in an image! Very interesting research.

NB For classifying stars in clusters, the problem is likely not classification, but more segmentation.


How is spectroscopy used to deduce what an object is made of?

This is not exclusive to spectroscopy applied to astronomy but general.
Matter can interact with electromagnetic waves spanning a very wide range of frequency (energy). Also matter can emit electromagnetic radiation when in a kind of excited state.
Due to the internal mechanism of absorption/emission it happens that the spectral characteristics can be peculiar to the chemical nature and physical state of the matter under analysis.
This is basically what you are aware of.
Your concern likely arises by over-focusing on colour, that per se in not the most powerful identification tool, or even by thinking that the particular state of the matter does not count, or changes are neglected.
Let me take your example of leaves. The fact that they colour undergoes changes does actually means that their composition changes. This is already an information rather than a problem.
Imagine that observing a planet one detect, say, carbon monoxide, it does not mean that its atmosphere won't change. Eventually different observations would prompt a planetologist to ask himself why, perhaps concluding that a kind of volcanic activity or degassing is ongoing , just to say.
A planet looking green then brown on a regular pattern would certainly suggest the presence of plants or anyway photosynthesis based on chlorophyll, providing that the green spectrum closely resembles that one we know, and does not come from narrow spectral features that would otherwise indicate, for instance, the presence of chlorine.
In other words, probing a sample, in astronomy as well as on a lab bench, leads to information about that sample in that moment. This is quite philosophical rather than a problem in spectroscopy or spectroscopy applied to astronomy. Moreover spectroscopy doesn't come alone and certainly requires considering the scenario.
But at its core is the existence of peculiar features, they can be single lines or more or less complicated spectra, and those are linked to the composition of the sample, elemental or molecular depending on the frequency window used.
I am not sure if this answer your question, but again this passage
"this thing is absorbing this wavelength or colour, therefore it is this substance”
is both correct and wrong. It must be taken with a grain of salt, or things must be analysed in depth.
What is certainly true is that there are specific lines typical of elements, or other spectral features typical of molecules. Explaining why it is so is way more complicated (for me) to be done in few lines here. But the reason resides on the discrete electronic structure of matter, as well as molecular shapes combined with limitations on which transitions can take places. Combining the two leads to a high specificity.
Unfortunately not the best example for astronomy, but consider that a given compound virtually has its own IR vibrational spectrum, different from that of any other compound!
You might want to read about spectroscopy in general, and have a look at Wikipedia's Astronomical spectroscopy; Chemical properties


Do planets have effect on velocity of Earth?

The Milankovitch Cycles which explain the glacial and interglacial phases of the Ice Age include changes in the Earth's orbital eccentricity (which implies a change in the variation of the velocity even if the orbital period remains roughly constant), the primary contribution to which is the gravitational influence of Jupiter and Saturn.
Since our Solar System is much more widely-spaced than the typical Kepler systems, and the planets aren't in resonant orbital configurations, the variations take place over much longer timescales and have relatively small amplitudes.
Planet-planet interactions are also observed for other planets. As an example, Park et al. (2017) list various contributions to the perihelion precession of Mercury, the bulk of which is due to perturbations from the other planets (principally Venus, Jupiter, the Earth and Saturn). The famous contribution from general relativistic effects amounts to about 43″/century out of a total 575″/century.


Yes.

It does not rotate uniformly though, different portions have a different angular velocity (as a body made of plasma, it can get away with this).

Measuring this in theory is pretty easy, we just need to track the motion of the sunspots. This isn't as simple as calculating the changes in relative positions of the sunspots, though, as the Earth is rotating and revolving, which makes the calculations harder. This measurement can be done using the celestial sphere (the field of stars that we see) as a "fixed" reference point and seeing how the Earth and the sunspots move relative to that.

Almost everything in the universe rotates/revolves, at least a little bit, because angular momentum is hard to get rid of. It can be transferred from body to body, but for a body to end up with zero angular momentum, it needs to meet another body with the exact same angular momentum and collide with it in a particular way. Given that this is pretty rare, all celestial bodies rotate.

In addition to that, a non rotating body that is revolving will eventually start spinning due to tidal forces.


Can a binary star optically "orbit" a planet?

Planets don't orbit stars. Stars don't orbit planets.

Whenever there are two bodies bound by gravity, they are both orbiting their common center of mass. For example, both the Earth and the Moon orbit their common center of mass - but that's pretty close to the center of the Earth actually, so it seems like the Moon orbits the Earth.

For a star to seem to orbit a planet, that would mean the planet is much heavier than the star. As far as we know, that's impossible. Their common center of mass would be much closer to the star, so it would seem like the planet is orbiting the star, as usual.

If you have two stars orbiting each other (actually, orbiting their common center of mass) very closely, then you could have a planet circling around both. If the planet is circling around too closely, its orbit would not be stable.

But if the planet's orbit is far enough from the pair of stars, the orbit could be stable a very long time. The minimum distance it at least 2x ... 4x the distance between stars, ideally much bigger. We have discovered such planets. Kepler-47c is a gas giant in the circumbinary habitable zone of the Kepler-47 system.

This wiki page has more details:

https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems

EDIT: If you have a closely-bound binary star, with a planet right in between them, in the barycenter of the two stars, that's not a stable system. Any slight perturbation would pull the planet out of there, and then the net force would be pulling it further out. It would eventually fall into one of the stars. It's not self-stabilizing.

I can't even imagine any conceivable mechanism that would put the planet in there to begin with.


Why the Sun-Jupiter barycentre is outside Sun?

There are three factors that all play into this:

The Jupiter/Sun mass ratio
The Jupiter/Sun distance
The Sun's radius

The barycenter of any pair of orbiting masses lies on the line connecting their centers of mass, and its position depends on the masses of the two objects.

If two objects have the same mass, their barycenter will lie halfway between them.  If one is twice as massive as the other, the center of mass will be 1/3 of the way from the larger mass to the smaller.  The formula is:

DSb=DSP*MP/(MS+MP)

MS and MP are the masses of the Sun and planet, respectively,
DSP is the distance between their centers of mass, and
DSb is the distance from the center of mass of the Sun to the barycenter.

Finally, whether or not the barycenter is inside the Sun depends on the radius of the Sun. How far it is from the center of mass of the Sun is unaffected by the Sun's radius.

For the Earth-Sun pair, MP/(MS+MP) is 3.0×10-6

For the Jupiter-Sun pair, MP/(MS+MP) is 9.5×10-4

So the Earth-Sun barycenter is about 3.0×10-6 of the way from the Center of the Sun to the Earth, or about 279 miles.  The Jupiter-Sun barycenter is about 9.5×10-4 (a number 300 times bigger) times Jupiter's distance (a number 5.2 times bigger) and comes out at 459,000 miles, which is just slightly larger than the Sun's radius of 430,000 miles.

It's outside the Sun because Jupiter is more massive than the Earth and further away from the Sun.  It's just how the numbers work out -- nothing deeper than that.


One plausible way of detecting wormholes (paper) is gravitational microlensing. Light paths are bent by the curved spacetime around the wormhole, similar to what happens near black holes. As a wormhole moves in front of background stars it can cause the brightness to vary in a characteristic way, making it possible to distinguish it from a black hole.

One of the problems is that there are many possible wormhole models, so the light curves can look different. Some can also produce multiple Einstein rings, others none. However, this may in theory be good news for learning what model is right if one sees a really weird light curve. In practice, given noise and lack of observations, multiple explanations will likely be possible for a long time if one sees just one example.


What is the antonym of "closest approach"?

The term "maximum separation" is often used, though maximum separation can also refer to the maximum angle between two bodies in the celestial sphere.
Here is an example from Quintana and Lissaur of the usage referring to distance:

close binary stars with maximum separations $Q_B≤0.2 AU$

and here is an example from Nouh of the usage referring to angle:

In this paper, an efficient algorithm is established for computing the
maximum (minimum) angular separation ρ max(ρ min) [...] of visual
binary stars


There's another answer here claiming that an off-axis aperture mask will improve things. That is a fairly popular meme, but it's entirely incorrect, and makes misleading claims about the effects of the central obstruction. All that does is it hides existing problems with the instrument.

If the off-axis hole appears to improve things, something else is very wrong and you need to fix that first; it's not a solution, it's a symptom pointing at serious issues. More importantly, it reduces precious aperture, therefore capping the resolving power of the instrument in a situation (observing Mars) when you need all the resolving power you can get. Please don't do that. Ignore the off-axis mask altogether.

Now, what to do to get better results with Mars?

Collimation

Make sure your telescope is in perfect collimation. There is no one technique to rule them all. There are many ways to collimate a telescope. Whichever method you choose, make sure you actually use it before observing Mars. Small deviations from perfect collimation will affect results on this difficult target.

Your instrument's manual, or the manufacturer's website should provide some info. Here are some links to get you started:

https://garyseronik.com/a-beginners-guide-to-collimation/

https://www.skyandtelescope.com/astronomy-resources/how-to-align-your-newtonian-reflector-telescope/

Some info about the importance of collimation:

http://www.astrophoto.fr/collim.html

Regarding laser collimators, which are very popular: A laser collimator is very quick and can be very good, but provided the laser itself is perfectly centered. Plug the laser into the focuser, watch the laser spot on the primary mirror, and slowly turn the laser like a knob - if the spot moves in a circle as you turn the laser, then it's not centered. Some lasers can be adjusted until they are centered (2 or 3 adjustment screws on the barrel), others can't. A laser that's not centered will not provide good collimation for your telescope.

There are many other collimation techniques, keep learning.

You don't need to be in perfect collimation every single time - a lot of faint fuzzies (galaxies, etc) don't require any careful collimation. But for Mars and the Moon you better do it right. Don't obsess over it, but try and do a good job. Personally, I at least check collimation every time no matter what, but with practice now it only takes me 5 minutes to fix any deviation, so it's not a chore.

Thermal equilibrium

If your telescope is not at the same temperature as the air, convection vortices will appear inside which will affect performance. Take the instrument outside at least 1 hour before the observation and let it vent out all the heat.

Some reading material:

https://garyseronik.com/beat-the-heat-conquering-newtonian-reflector-thermals-part-1/

https://garyseronik.com/beat-the-heat-conquering-newtonian-reflector-thermals-part-2/

Seeing

This is basically atmospheric turbulence. When it's bad, the image is distorted and fuzzy. When it's good, the image is clear and you can see small details. Basically, Mars is impossible to watch if seeing is not good or very good. Sometimes, spells of bad seeing can last for days or weeks. There's not much you can do except put the scope in the car and drive someplace else where seeing is good at that time.

https://en.wikipedia.org/wiki/Astronomical_seeing

Seeing is basically weather-related, so it can be predicted to some extent. Go on the Clear Dark Sky website, search for a location close to your home, and pull up the chart:

http://www.cleardarksky.com/csk/

Look at the row called Seeing. If it's dark blue for the time when you plan your observation, chances are good that seeing will not get in the way. If it's light blue or white, the forecast is not good.

Opposition

Mars is only worth trying around oppositions, when it's closest to Earth. This happens roughly every two years.

The previous opposition was in July 2018 when Mars had an apparent size of 24 arcsec.

Currently (November 2018) the apparent size of Mars is 11 arcsec, less than half the size at opposition.

The next opposition is in October 2020, when it will be about 22 arcsec.

A few weeks before and after opposition Mars is worth trying.

https://www.wolframalpha.com/input/?i=mars+apparent+size+in+october+13+2020

Focus

Make sure the scope is perfectly focused. Point it at a fixed star (Polaris is quite convenient since it does not move), and adjust the focuser until the image of the star is as small as it can be.

It's pointless to try fine focusing if the scope is not collimated (see above). Collimate first, then you'll be able to achieve a sharper focus.

Also, if there are seeing issues, or thermal issues, a sharp focus will be hard to achieve.

Other factors

Mars is a difficult object to observe. Good quality optics are important. Aperture is important (more is better - please disregard the memes about limiting the aperture). Experience is important - you'll get better in time.