What are Kepler's laws (as he wrote them)?

Short Answer: Kepler expressed his laws with the sun at a foci rather than a barycenter.
Long Answer: In Astronomia Nova (pub. 1609) Kepler presents the first version of something we can recognize as Kepler’s first law:
On page 285 of Astronomia Nova:

CAPVT  LIX.   Demonftratio, quod orbita MARTIS, librati in diametro
epicycli, fiat perfecta ellipfis: Et quod area circuli metiatur fummam
diftantiarum, ellipticae circumferentiae punctorum.

The translation by William H. Donahue New Astronomy is:

Chapter 59 Demonstration that when Mars reciprocates on the diameter
of the epicycle, its orbit becomes a perfect ellipse; and that the
area of the circle measures the sum of the distances of points on the
circumference of the ellipse.

It isn’t immediately clear from Kepler’s own statement of his first law if the sun or the barycenter is the occupied focus.  Indeed, I couldn’t even find a mention of a focus in Astronomia Nova.  The closest I could find is when Kepler says, “a planet is moved less vigorously when it recedes from the point whence the eccentricity is computed.”  Here, it appears that Kepler is referring to the fastest speed of a planet at Perihelion, and the slowest speed at Aphelion.  The point from "whence the eccentricity is computed" is also clearly the focus of the ellipse.  Here is one of Kepler's original woodcuts, and it can be seen that the sun is at the focus. Kepler used the metaphor of a row boat for the planet's motion, and his drawings of oars in the water complement this cutting.

Kepler believes the sun is the center of this system from “Chapter 33 – The power that moves the planets resides in the body of the sun.”  On page 280 of Donahue’s translation, Kepler says that:

Therefore, with the sun belonging in the center of the system, the
source of the motive power, from what has now been demonstrated,
belongs in the sun, since it too has now been found to be in the
center of the world.

Summary: Kepler believed the sun was the center of the solar system, and provided the motive power for the planets.  He used the location of the sun to calculate the eccentricity of Mars's orbit and later extended his findings to the rest of the planets.  While we can't rule out the possibility that Kepler speculated about a barycenter, he certainly didn't express any such speculations in his original formulations of his laws.
Notes:

Lack of explanation of Kepler’s stated 1st law: Kepler’s 1st law as stated in Astronomia Nova isn’t very recognizable as our modern Kepler’s 1st law.  Explaining how they are equivalent gets complicated due to the ancient math and breadth of terminology.  I do not attempt to bridge that gap in this answer, though I would be happy to provide insight, information, and resources on request.  At the end of Chapter 59, in a conclusion of the book, Kepler himself acknowledges the difficulty of reading his book: “If anyone thinks that the obscurity of this presentation arises from the perplexity of my mind, I shall myself only thus acknowledge to him my guilt, that I was unwilling to leave anything untested, no matter how utterly obscure”…  “He will see that there are some matters which no mind, however gifted, can present in such a way as to be understood in a cursory reading.  There is need of meditation, and a close thinking through of what is said.” If you want to understand what Kepler is talking about, you should buy a copy of Donahue's English translation and pack a lunch. I also found this guide quite helpful in my own journey: Tutorial.

Keplers 2nd and 3rd laws: Kepler’s 2nd law is also articulated in Astronomia Nova in 1609, but I didn’t choose to treat it in this response. I think it needlessly distracts from the deep point of the original question, which is whether or not Kepler included barycenters in his laws.  The 3rd law was published in Harmonices Mundi in 1618.  Though all three laws were asked for in the question, I don’t provide them in this answer, making it somewhat incomplete.

First mention of the barycenter:  The first mention of something like a barycenter that I could find is in a translation of Newton’s Principia, published in 1687, proposition 12, theorem 12: https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-Prop2.  This includes the quote that: “the common centre of gravity of Jupiter and the sun will fall upon a point a little without the surface of the sun” which to me demonstrates a clear understanding and articulation of the idea of a barycenter.  Does anyone know an earlier clear reference to a barycenter?

Implications:  The fact that Kepler’s laws didn’t include a barycenter is not just a historical curiosity, but also informs our modern conventions.  A Kepler orbit assumes that a less massive body orbits around a more massive one in an ellipse, with the more massive body at one of the foci of that ellipse.  Though Kepler’s laws can be generalized to replace the sun with the barycenter, they are no longer recognizable as Kepler’s laws and will no longer conform to convention. All the orbital elements would be different.  For example, the periapsis and apoapsis are always measured from the central body, rather than the barycenter.  Here is a diagram from wikipedia:


Why do comets appear to have a continuous supply of dust?

The rate of loss of mass from a comet is perhaps surprisingly low. A paper The calculation of $Af\rho$ and mass loss rate for comets gives a rate for a "typical" comet at 1.29AU as 153kg/s. A typical comet has a mass of about $10^{13}kg$. Even if the comet is constantly active (and they are not) it would have enough material for over 2000 years.

In fact comets are only active when the are near perihelion, and they are only near perihelion for a small fraction of their orbit. Put it together and you have the potential for an active life of hundreds of thousands of years.

Eventually, however, comets do run out of volatile substances, at which point they become inactive, and appear as small dark asteroids. An example of which is the object 2015 TB145, which passed the Earth on Halloween 2015.

Note: not "oxidising", but "vaporising", the ices in the comet are changing into gas, but there is no burning.


How does the Grand Tack Hypothesis explain how Jupiter formed inside the frost line?

A direct cribbing of the wiki's page for the frost line:

  In astronomy or planetary science, the frost line, also known as the snow line or ice line, is the particular distance in the solar nebula from the central protostar where it is cold enough for volatile compounds such as water, ammonia, methane, carbon dioxide, carbon monoxide to condense into solid ice grains. This condensation temperature depends on the volatile substance and the partial pressure of vapor in the protostar nebula. The actual temperature and distance for the snow line of water ice depend on the physical model used to calculate it:

  170 K at 2.7 AU (Hayashi, 1981)
  143 K at 3.2 AU to 150 K at 3 AU (Podolak and Zucker, 2010)
  3.1 AU (Martin and Livio, 2012)

  Occasionally, the term snow line is also used to represent the present distance at which water ice can be stable (even under direct sunlight). This current snow line distance is different from the formation snow line distance during the formation of Solar System, and approximately equals 5 AU. The reason for the difference is that during the formation of Solar System, the solar nebula was an opaque cloud where temperature were lower close to the Sun,[citation needed] and the Sun itself was less energetic. After formation, the ice got buried by infalling dust and it has remained stable a few meters below the surface. If ice within 5 AU is exposed, e.g. by a crater, then it sublimates on short timescales. However, out of direct sunlight ice can remain stable on the surface of asteroids (and the Moon) if it is located in permanently shadowed craters, where temperature may remain very low over the age of the Solar System (e.g. 30–40 K on the Moon).

  Observations of the asteroid belt, located between Mars and Jupiter, suggest that the water snow line during formation of Solar System was located within this region. The outer asteroids are icy C-class objects (e.g. Abe et al. 2000; Morbidelli et al. 2000) whereas the inner asteroid belt is largely devoid of water. This implies that when planetesimal formation occurred the snow line was located at around $R_{snow} = 2.7$ AU from the Sun.

So in all of the three listed models, as well as the snow line inferred from asteroid properties, it seems that the 3.5 AU starting distance for Jupiter in the Grand Tack hypothesis remains comfortably behind the snow line (for water, at least, which is still an advantage over the inner planets).

Since it ultimately fell well within the snow line for a time, one would expect any exposed ices to rapidly sublimate.  I would guess that it made up for this by accreting the rockier planetesimals found in the inner parts of the Solar System, which could then shield the remaining ices.

This site offers a pretty good detailing of the basic structure of the Grand Tack Hypothesis.  The most digestible piece of information is at the very bottom, in the form of an AVI file that models the first few million years of the solar system.  The short answer to your question is "Jupiter is assumed to have already formed some fundamental core at the start of the hypothesis, then moves around accreting and scattering things through the inner solar system, until returning to the outer solar system to finish growing".  The initial inward migration is caused by interactions with the relatively thick gaseous disc (the majority of it will never become part of any planet), which creates drag on the planets/planetesimals and causes them to lose velocity and fall inward.

But the video's pretty cool, so I'm going to link it and talk about it just for its own sake.

Get the video, as produced by the paper Walsh et. al., 2011

You may find it best to run this at half speed or slower to really see what's going on.

Here's how it starts out.

The solid black orbits are the gas giant orbits, with Jupiter being the innermost one, and Saturn the one after that.  The dashed circle represents a 2 AU distance from the sun (modern day Mars is currently at about 1.5 AU, and the modern asteroid belt stretches roughly 2.2-3 AU).  This is noteworthy since the model is trying to explain why Mars is so small, and why there is so little material (relatively speaking) in the asteroid belt.  The numerous small blue dots are the icy comets/planetesimals that form right around the point Jupiter starts out, and points beyond.  The numerous red dots are the rocky asteroids/planetesimals characteristic of the inner solar system.

For the first several seconds we see Jupiter creep in towards the inner solar system.  You'll notice a lot of rocky planetesimals get scattered out into the outer solar system, while some of the icy ones are scattered to the inner solar system.  Indeed, it seems to be a general feature of this model that the total amount of material within approximately 1 AU undergoes a net increase.

Saturn is also slowly moving in, but not nearly as quicky as Jupiter is (Neptune/Uranus seem pretty stable, but do "pulse" in and out a bit).

In this image we see that Jupiter hits the 2 AU mark at ~3 seconds in, corresponding to a model time of about 68,000 years.  At this point you can see a dashed circle at about the 3.5 AU distance, corresponding to Jupiter's starting distance.  Saturn is about 4 AU out now, having started at over 5.

The third through fourth second are fairly stable-looking, with Jupiter moving in to about 1.5 AU but the other outer planets staying mostly put.

But in the 5th second (~94,000 years model time)...

We see Saturn make a very rapid move inwards.  This is the main reason I suggest playing it slowly, as you can very easily miss it and lose track of where each solid black orbit has come from.  By model time 98,000 years (still in the 5th second of the video time), Saturn has already come to within about 2 AU of the Sun; Jupiter is still about 1.5 AU, and there is a thick concentration of mostly rocky planetesimals within 1 AU.

By model time of about 120,000 years, Saturn and Jupiter are rebounding back out into the outer solar system, to much the same distances we see today, scattering most of the planetesimals that remained in the areas that would become Mars and the asteroid belt.  This leaves a fairly dense disc of material for Earth, Venus, and Mercury to form and grow from, while leaving significantly less for Mars, and lesser still for the asteroid belt.

The whole 10 second movie covers a model time of 600,000 years.

Walsh, K. J., Morbidelli, A., Raymond, S. N., O’Brien, D. P., Mandell, A. M. (2011). A low mass for Mars from Jupiter’s early gas-driven migration. Nature 475, 206-209.

Walsh, K. J., Morbidelli, A., Raymond, S. N., O’Brien, D. P., Mandell, A. M. (2012). Populating the asteroid belt from two parent source regions due to the migration of giant planets – ”The Grand Tack”. Meteoritics & Planetary Science 47(12), 1941-1947.


Is the rate of gravitational wave detection roughly what was expected?

I’d have to dig more to find some references, but the existence of $M > 30\ M_{\rm Sun}$ black holes was a big surprise. So a bunch of the events that have been detected are from a class of objects that wasn’t predicted at all.  Originally I believe that neutron star - neutron star mergers were expected to be the main class of events.   I don’t know how that NS-NS merger rate has stacked up against expectations.


How does a galaxy in Abell 2261 exist without a black hole in the center?

The Brightest Cluster Galaxy (BCG) in Abell 2261 ("Abell 2261-BCG") is a massive elliptical; these almost always seem to have supermassive black holes in their centers. In addition, the center of the galaxy has a large region of relatively low stellar density (a "core"), something usually thought to be produced by the merger of two SMBHs into one, an event which follows the merger of two massive galaxies to form one massive elliptical. (As part of the merger, the two SMBHs form a binary; stars near the center of the merged galaxy can gravitationally interact with this binary, with the usual result being a shrinking of the binary and the ejection of the star to a larger radius; thus, stars get preferentially kicked out of the center into the intermediate or outer parts of the galaxy, and the density of stars in the center gets lower. Eventually, the SMBH binary becomes so small that gravitational radiation shrinks it even further, to the point that the two SMBHs merge to become one in the center of the galaxy.)
The actual paper (Gültekin et al.) behind that article is about looking for X-ray emission from an accretion disk around the possible SMBH in the center of the BCG (and also in a few other locations near the center). Since they don't detect any X-rays, they conclude "there is either no $10^{10} M_{\odot}$ black hole in the core of A2261-BCG, or it is accreting at a low level." So there are really two possibilities:

There is a SMBH in the galaxy center, but it's quiescent (not accreting enough gas to produce a lot of X-rays).

There isn't a SMBH in the galaxy center, which is more exciting because it's unexpected.

Now, there actually is a theoretical mechanism which might occasionally eject a SMBH from the center of a galaxy. When two SMBHs merge to form one SMBH (see above), there can be a "kick" which causes the merged SMBH to be ejected from the galaxy center (the magnitude of this kick depends on things like the mass ratio between the two SMBHs, how fast the individual SMBHs were spinning before the merged, and what the directionw of those spins were relative to the orbit of the binary before the merger). In most cases, the ejected SMBH will fall back into the center of the galaxy -- possibly oscillating in and out a few times before dynamical friction slows its motion down and it settles back in the center of the galaxy. In extreme cases, it might be ejected fast enough so that it escapes the galaxy entirely. This whole process will eject a number of stars from the center of the galaxy, too, which might help explain why its low-density core is so big (i.e., a combination of the SMBH-binary-merger process and a resulting SMBH ejection).
So it's possible something like this happened in Abell 2261-BCG, and the SMBH is currently somewhere outside the galaxy center. (Or it's sitting the center and just doesn't show up in X-rays.) Of course, they didn't find any evidence for an X-ray-emitting SMBH outside the galaxy nucleus, either, so we really don't know -- and I wouldn't be surprised if there is a (quiescent) SMBH in the center after all.
(Rory Alsop is correct that not all galaxies have SMBHs -- for example, the local small spiral galaxy Messier 33 has been studied with the Hubble Space Telescope (Gebhardt et al. 2001, and the modeling of stellar velocities in its center suggests an upper limit of about 1500 $M_{\odot}$ for any possible black hole there. But every massive elliptical that's been studied carefully enough seems to have one, so we would expect Abell 2261-BCG to have one, too.)


Have we Observed Continuum Emission from Neutron Stars?

Yes - quite a few isolated neutron stars have been observed, where any magnetospheric emission or accretion-related emission is either negligible or has been otherwise separated.

As you suspect, this emission is thermal in nature. Neutron stars are roughly approximated by black bodies but, like "normal" stars, they do have atmospheres and strong magnetic fields that modify the black body spectrum considerably. If the neutron star is isolated then the only reason that you might be able to detect thermal emission from the surface is that it is very young (less than about a million years after formation) and still hot. The difficulty is in ruling out any residual, pulsed magnetospheric component or a contribution from accretion of the interstellar medium itself.

A couple of examples to look at in the optical part of the spectrum would be Kulkarni & van Kerwijk (1998) who detected optical radiation from the counterpart to RX0720.4-3125; and Walter & Matthews (1997) who claimed a detection of thermal optical emission detection from the isolated neutron star RXJ185635-3754 (and see picture below).

There are several more examples of thermal emission detected at X-ray wavelengths from young, isolated neutron stars - the so-called X-ray dim neutron stars (see review by Mereghetti 2010).

Of course if you are extending your definition of continuum emission to include non-thermal (but not accretion-related) processes, then continuum emission is detected from all isolated pulsars. Synchrotron radiation is a continuum process and has been detected right across the electromagnetic spectrum in many pulsars.

A visible band HST image of the isolated neutron star RXJ185635-3754, attributable to Walter & Matthews 1997.


How can I determine if a typical low-end telescope is a refractor or reflector?

There is a wide variety of telescopes, so it's a bit difficult to give a general answer, but here are some pointers:

If there is an open-end, it likely is a reflector telescope (perhaps a Newton). In this case, you can see the secondary mirror attached inside.

When you look through the place where you set the eyepiece, are you facing the same direction as the telescope? If not, it is a reflector.

Look into the part that you would normally point towards what you are trying to observe. If you can see a mirror at the opposite end, it is a reflector.

On certain reflectors, there is a lens on the side that you point towards what you want to observe. In this case, there also is a smaller mirror attached to the inside of this lens. You can't see the reflective part of this smaller mirror, but there should be a couple of screws on the back, that can be used to align the mirror with the rest of the telescope.

On a refractor, the part that you point towards what you want to observe is a lens that should have a rather round surface (as opposed to flat). This lens usually is not at the end of the tube, but rather there is a part to protect from stray light.

It the tube tapers a bit, it most likely is a refractor.


Why does the Sun deviate from a typical blackbody spectrum in the S band?

There are other ways of getting emissions than just direct thermal radiation. Most of it happens through plasma interactions in the solar corona and atmosphere than in the chromosphere. This review paper names bremsstrahlung, gyroresonance, cyclotronmaser, and plasma radiation as sources, each with their own brightness temperature way above 6000 K. (See also these lecture slides for a bit more in depth math of the sources).
My own summary would be that there is plenty of energy in the magnetic field and plasma, and this can be released through various wave modes producing radio signals. Further, fast charged particles are spinning around field lines or colliding, producing electromagnetic emissions of various types. None of these are blackbody sources, but they add to the blackbody spectrum to produce the observed curve.


Do we know what's "behind the Milky Way"?

The short answer is that we know a little bit about what is beyond the center of the Milky Way, but a lot is still unknown.
The bands of obscuring dust in the galactic plane are only a few degrees of arch wide as seen from Earth.  Thus we can see for millions and billions of light years in directions which are only a few degrees "above" or "below" the plane of the Milky Way, even in the direction of the galactic center.
A number of external galaxies have been discovered which are nearly in the plane of the Milky Way and which are heavily obscured by dust clouds.
In 1967 Paolo Maffei discovered galaxies Maffei I and Maffei II though the galactic plane by their infrared emissions.
Maffei I is a giant elliptical galaxy which is part of the IC 342/Maffei group of galaxies about ten to twenty million light years away.
Maffei 2 is a spiral galaxy thought to be a member of the IC 342/Maffei group of galaxies about 10 million light years away.
I think that Maffei 1 & 2 are about 90 degrees from the direction to the center of the galaxy.
And it is possible that other distant galaxies have been observed through the dust of the Milky Way in directions closer to the galactic center.


What is the minimum meteor size to see a falling star?

The International Meteor Organization (IMO) defines a meteoroid as "a solid object moving in interplanetary space, of a size considerably smaller than a asteroid and considerably larger than an atom or molecule." This definition is further refined by Rubin and Grossman, who state "a meteoroid is a $10$-$\mathrm{\mu m}$ to $1$-$\mathrm{m}$-size natural solid object moving in interplanetary space." Additionally, the same authors consider a defintion for a micrometeoroid, which they define as "a meteoroid $10\hspace{2pt}\mathrm{\mu m}$ to $2\hspace{2pt}\mathrm{mm}$ in size."

According to astronomer Karen Masters from Cornell, the typical meteor has a mass of a few milligrams. The American Meteor Society (AMS) also states that the most-commonly observed meteors are roughly the size of a grain of sand. This would seem to imply that many meteors are smaller. In fact, this is also implied by the various statements by many groups, including the AMS, IMO, and IAU, that micrometeoroids commonly cause meteors. Because of this, I would argue that a meteoroid with a volume of $1$ $\mathrm{mm}^3$ would easily cause a relatively bright meteor. Statements surrounding the frequency with which micrometeoroids cause meteors would seem to imply that, on average, any body larger than $10$ $\mathrm{\mu m}$ will be observable as a meteor. These figures will vary largely depending on the entrance velocity of the object.


How many stars and galaxies can be seen by the naked eye?

In the best sky conditions, the naked eye (with effort) can see objects with an apparent magnitude of 8.0. This reveals about 43,197 objects in the sky.
There are 9 galaxies visible to the naked eye that you might see when observing the sky, and there are about 13 nebulae that you might see.
Sources:

The Bortle Dark-Sky Scale - John E. Bortle
How many stars are in the sky? - NASA
Naked-eye galaxies - Wikipedia
List of planetary nebulae - Wikipedia
List of diffuse nebulae - Wikipedia


Is there an oxide layer on aluminum reflectors for telescopes?

The aluminum oxide layer forms as soon as oxygen comes in contact with the mirror surface.

Aluminum oxide is tough, firmly attached and transparent;  it serves to protect the aluminum surface.  Rubies and sapphires are slightly impure aluminum oxide


What would this moving point of light be?

This sounds like a satelite to me. Satelites can also "dissapear" right above you, since the sun no longer reaches them and they fade into darkness.

Also 2 minutes is very well possible for a satelites to be visible that is in earths orbit.

You should also know, that there are hunderds of other satelites that can be as bright when observed from earth as the ISS is.


It can't. If we find a star that's "older" than the universe, then either the measurements of the star's age are incorrect, or the measurements of the universe's age are incorrect.


Converting Earth Moon Barycenter coordinate to Geocentric coordinate

How to convert it to Geocentric?

You don't. That's the position and velocity of the Earth-Moon barycenter with respect to the center of the Sun. Converting that to geocentric (a) doesn't make sense, and (b) even if it did, can't be done without knowing the location of the Earth-Moon barycenter in geocentric coordinates.

The position of the Earth-Moon barycenter plus the geocentric inertial position of the Moon expressed in the J2000 ecliptic frame plus the Earth-Moon mass ratio lets you compute the position of the Earth with respect to the Sun (or the position of the Sun with respect to the Earth). Add information about the positions of other planets with respect to the Sun and you can compute the positions of those other planets with respect to the Earth.

You cannot do the above with VSOP2013 alone because VSOP2013 does not contain information about the position of the Moon with respect to the Earth. You'll need a separate lunar ephemeris for that.


What is the largest recorded solar flare?

A spike in Carbon-14 content was recorded from tree rings in Japan, possibly due to a solar flare 20 times more energetic than the 1859 Carrington Event (the largest definitively recorded solar storm). This event has been dated to 774 AD. I think this could be the most energetic (tentatively) recorded solar flare.

Such a solar storm would be far more devastating today than it was back then, in the sense that we rely so much on technology that the EM interference would cost trillions of dollars in damage to power grids and communications.

A flare would need to be disastrously large, I think, to give us on Earth radiation poisoning. Certainly, animals that use Earth's magnetic field for navigation and would get rather confused. But our atmosphere and magnetic field are adequate protection when we're on Earth.

Here is a good write-up of the situation, with a couple of Nature papers if you have access.

If you're going to delve into considering the effects of solar storms on human health (i.e. the effects of magnetic field perturbations), put your tinfoil hat on first. There's a lot of pseudoscience and little substantive research.


How could a 20 inch space telescope "be able to make out Earth-size planets" orbiting Alpha Centauri?

I'm not familiar with the design of the ProjectBlue telescope, but I think you have answered your own question.

The habitable zones for Alpha Cen A and B, are approximately centred at 1.25au and 0.7au. Both are at a distance of 4.37 light years.

1au at 4.37 light years, subtends an angle of 0.74 arcseconds. If working at blue wavelengths (the aim appears to be to find a pale blue dot, so let's say 400nm), an Airy disk of 0.74 arcsec is achieved with a telescope with a diameter of just 13cm. To stand a chance of resolving planets in the habitable zone, you would need a telescope a little bigger than this.

However, a bigger problem is separating the signal from the star and planets when they are barely resolved. The Airy disc is just the first minimum in the diffraction pattern. If the star is around 10 billion times as bright as the planet (ball park figure) then it would still swamp a planet that was just resolved.

Thus you need to build a bigger telescope to increase the angular resolution. And you need to build superb optics and a coronagraph to stop the light from the star swamping your detector. But this costs more money, the telescope has more mass, needs a bigger launch vehicle etc. So I guess a 50cm telescope is their compromise.

Is it achievable? I don't know. The best telescopes on Earth achieve almost diffraction-limited angular resolution using adaptive optics. However the contrast they can obtain for exoplanet imaging is compromised by the atmosphere to some extent. If you are looking for a "pale blue dot", then this can't be done from the ground because adaptive optics systems do not currently work at such wavelengths.

It is quite possible that Earth-like planets in the habitable zone of Alpha Cen could be discovered from the ground in the next few years using improved radial velocity measurements, but not by imaging.

An interesting question is why this can't be done now with HST? The proposed telescope will spend two years doing this. Even if HST could cut this to months, I am not convinced that detecting a faint smudge around the nearest star has the necessary science pay off to get the time, especially as there is a fair chance of failure. There may not be planets in the habitable zone or there may be sufficient zodiacal dust in the system to make the measurements impossible due to scattered light.

Further research suggests that the coronagraph on the HST ACS camera would only give around 7-8 magnitudes (factors of a thousand) contrast at angular separations of an arcsecond. So nowhere near what is required. This new telescope must have radically improved optics and a more advanced coronagraph.


Charge is a conserved quantity. If you add a net charge to an object, then it becomes charged.


The solution to the Friedmann equation in a flat universe is
$$H^2 = \frac{8\pi G}{3}\rho + \frac{\Lambda}{3},$$
where $\rho$ is the matter density (including dark matter) and $\Lambda$ is the cosmological constant.

As the universe expands, $\rho$ of course decreases, but $\Lambda$ remains constant.

Thus the Hubble "constant" actually decreases from its current value $H_0$ and asymptotically tends towards $ H = \sqrt{\Lambda/3}$ as time tends towards infinity.

As $\Lambda = 3H_0^{2} \Omega_\Lambda$, and measurements suggest that $\Omega_{\Lambda} \simeq 2/3$, then $\Lambda \simeq 2H_0^2$, and the Hubble parameter will therefore decrease to approximately $\sqrt{2/3}$ of its present value if the cosmological constant stays constant.

Of course if $\Lambda = \Lambda(t)$, (ie not the basic $\Lambda$-CDM model) then the behaviour will be different.

EDIT: Another useful form of the solution (for the case of a constant vacuum energy density) is

$$H^2 = H_0^2 \left(  \frac{\Omega_r}{a^4} + \frac{\Omega_M}{a^3} + \frac{\Omega_k}{a^2} + \Omega_{\Lambda}\right),$$
where $H_0$ is the Hubble parameter now, $a(t)$ is the scale factor of the universe, $\Omega_r$ is the current (i.e. $a=1$) ratio of the radiation density to the critical density and $\Omega_M$, $\Omega_k$ and $\Omega_{\Lambda}$ are the equivalent densities for the matter (baryonic and dark), curvature and (constant) vacuum energy densities.

As $a$ increases you can see that all three of the leading terms get smaller and the Hubble parameter decreases at all times. When $a$ is very large, $H$ approaches $\sqrt{\Omega_{\Lambda}} H_0$ as before.


Krotanix : nobody really knows the answer to this. We have good evidence that the universe is expanding, and we extrapolate this back to the big bang. Then some people say the universe was once the size of a grapefruit. See for example this. Since WMAP evidence in 2013 suggested the universe is flat, some people have started saying the observable universe was once the size of a grapefruit. And that the universe was always infinite. But this is a non-sequitur, and a non-answer.

Yes,  it looks as if 13.8 billion years space had a much higher density and started expanding. And it may have had a certain volume, so space may have already existed. But nobody knows for sure.

Re your follow-on question, nobody has discovered hollowness or emptiness anywhere in the centre of the universe. The expansion is thought to be like that of a raisin cake rising in an oven. There's no big hole in the middle.


How much of an effect does the moon have on Earth's liquid mantle?

Interesting question. I would say from an energy standpoint, it almost certainly it has no effect.

Of course, the extreme case is Io, one of the Galilean moons whose heat source comes from the gravitational tidal stretching as it orbits very closely to the planet Jupiter. The heat that sustains the core of the Earth, however, is left over from its formation and also comes from radioactive decay of heavy elements.

The differential potential energy (and hence the tidal force) over the planet Io due to Jupiter, which is approximately 1300 times more massive than the Earth, is much larger than that of the Earth due to the moon. The relationship between force and differential potential energy is:
$$ F = - \nabla U $$
At a given location on the potential energy curve, the strength of the force is determined by its steepness (derivative) at that same location. Below is a quick plot I've generated for the Earth-Moon system, where the vertical red line represents the average Earth-Moon distance over a one-year period. As you can see it doesn't appear to be very 'steep', though keep the scales of the x- and y-axes in mind.

Admittedly this isn't that exciting of a plot. But, for comparison one could be made for the Jupiter-Io system, and numerical derivatives could be taken for both to calculate the magnitude of the tidal force in each situation.

To answer the question:

If the difference in the gravitational potential energy of object A on B over the scale of B is comparable to the self-gravitational energy of object B, then tidal forces will become important. This self-gravitational energy is the amount required to completely pull apart all massive particles infinitely far away. Formally, this limit is called the Roche Limit.


In the closest stars, can you see the stellar corona?

Stars other than the Sun do not have photospheres or coronae that can be directly imaged (the exception would be the red giant Betelgeuse that can just be resolved from the HST). They "appear larger than they are" as you put it because of the limitations of physical optics or turbulence in the atmosphere. There is a minimum-sized "point spread function" image that will be convolved with the intrinsic image of a star, whatever its size. Thus even a point-like source will appear to have a finite size when viewed with a telescope with a finite aperture. Images of very bright objects may also be affected by "saturation" of the detector - the counts in saturated pixels can "bleed" into surrounding pixels. All stars (bar Betelgeuse) are too small and far away to be anything but intrinsically "point-like", even when observed with space telescopes.

The image of Sirius in your question is the saturated image of a very bright, point-like object blurred by the imperfect optics (and perhaps a turbulent atmosphere) on a telescope of finite aperture. Any "corona" you see on this picture is the extended wings of the telescope point spread function. The size of Sirius cannot be directly inferred from this picture. (It is also the case that Sirius, an A-type star, does not have a corona like the Sun's, because it lacks the magnetic dynamo and strong magnetic fields that are responsible for heating the solar corona, and it lacks the very strong winds that shock heat coronae in much hotter stars).

That said, there are clever, interferometric techniques to synthesise a large telescope using extended baselines between multiple telescopes. These are capable of directly measuring the angular diameters of stars.  The assumption is that what is being measured is the angular diameter of the photosphere, since this is what dominates the light at optical and near-infrared wavelengths from most stars. In particular, the corona - a regions of tenuous, optically thin, ionised gas - emits hardly any visible/infrared light (it is of order a billion times less bright than the solar disk and due mainly to Thomson scattering of photospheric light from free electrons and dust scattering) and can safely be neglected. That is why the optical/infrared corona of the Sun can only be seen during total solar eclipses on Earth or from spacecraft with occulting disks that can totally block out the dominant light from the photosphere.

Distant stars are too far away for this occultation technique to work. The presence of any coronae around them can only be inferred from the X-ray emission due to the hot coronal gas. In some cases it has been indirectly argued that the coronal gas can extend several radii or more above the stellar surfaces (e.g. by analysing the fall and rise times of stellar X-ray flares or from the lack of X-ray eclipses in some eclipsing binary systems).


It's roughly like this:

set limit 100
format object form1 "%IDLIST(1) : %OTYPE(S)"
query sample (otypes = '*i*') & (bibcode='2009MNRAS.394.1338B')

To get the list of the bibcodes choose
"Other" / "Catalogue collection"
from the menue bar.
The screen should look like

Then click the icon "Click to display the menu" at the left border:

Here you find the bibcode:


Is there going to be a really bad Solar Storm in 2014?

Is it true?

Solar storms are like Earth storms: unpredictable until they are quite near.

  What will happen?

If there is a massive solar storm, we will experience power outages in long lines (e.g. U.S.A. mainland, Russia), communications disruption on satellite links (and again in long copper lines), and very nice auroras.


How are stellar elemental abundances quoted?

First of all, your first question.

This source clearly state that Values are given in the usual logarithmic (dex) scale, for the same formula that you quoted (similar job).
It is a bit tricky as the article "explains" the values, but you have to pay attention to the exact definition.

I think it is better to work out with an example. Let's take the He.

Good enough, you can better read the paper from here.

From the table, we have $A_{el}=10.93$. This is the abundance of He relative to H (in logarithmic scale).
From this you find out that $\frac{N_{el}}{N_H}=0.08 = 8\%$.
Indeed the work confirms this value (see the last page).

What you quote as about 25% He, is what they call abundances by mass of [...] Helium (Y), which means $Y = mass\ of\ Helium / mass\ of\ Hydrogen$, and this is indeed about $25\%$.


Could Hot Jupiter systems sustain Trojans?

Yes, hot Jupiters can have stable Trojans.

A great analysis of this very problem is given by Kislyakova et al. (2015). They suggest that super-hot outgassing Trojans may be an explanation for the ultraviolet anomalies seen in the WASP-12 and HD 189733 systems. As part of their analysis, they explore the photogravitational stability of Trojans of various size, and while they show that meter-sized bodies can be ejected on timescales of around a million years, Io-sized objects can be stable over the lifetime of the system. It may also be worth noting that although they found many stable tadpole orbits, they did not find any stable horse-shoe orbits (although they do not show that such an orbit cannot exist).

As for the actual formation and capture of such a Trojan, Beauge' et al. (2007) modeled the inward migration of a massive planet, with its semi-major axis decaying over a time scale of $10^5 - 10^7~\mathrm{yr}$. Their results suggest that a Trojan satellite with a tadpole orbit close to $L_4$ will be maintained during the migration.


What is the mass of hotspots in the Cosmic Microwave Background radiation?

I don't remember reading any paper title specifically about the hot spots you refer to, so I guess that they are not as "strange" as the cold spot.

Assuming that the temperature fluctuations are well described by a Gaussian distribution with mean 2.72548 and variance 0.00057 source, the probability of having the cold spot of the observed size and temperature is very low. According to a recent Planck paper this probability is of order of 1% or smaller. The probability of the hot spots is larger (1.5 to 5%), making them more "normal".

This probably explains while the cold spot got more attention that the hot ones.

  Is this a side-effect of our observation methods or does it represent some actual feature of the early history of the Universe?

This is tricky. A few scenarios:

The CMB map in the question shows fluctuations of order 10^-4 K. But extracting this signal from observations is very complicated by the fact that on top of the CMB radiation is "polluted" by foreground objects (mostly our own Galaxy, but also extragalactic point and extended sources) that create spurious fluctuations orders of magnitude larger than the CMB ones. This video is great to have an idea of this. If any of the above foreground components is not well understood or some is not accounted for, we could be left with some residuals that we wrongly interpret as CMB anomalies.
The physics we know is the correct one and the cold spot is simply there. But we physicists don't like that in the Universe there are special places
The cold spot is a signal of new/unknown physics or that our standard model is not correct. For instance could be that the assumption that the CMB is Gaussian could be just wrong and we have to re-think our theories about the early universe


Why does shell fusion produce more energy than core fusion?

Ultimately this is more of an overly long comment, as I think a more satisfying and complete answer would properly explain things in a more concrete fashion—more of a "it has to do this because..." answer than my "it can do this because..." one.

The short of the answer to the first question is that helium fusion needs ~25 times the temperature that hydrogen fusion does.  The proton-proton chain initates around $4\times 10^6$ Kelvin, whereas helium fusion doesn't begin until around $10^8$ Kelvin.  So when the main stage ends and the helium core contracts and the temperature rises, the "edge" of the core can have temperatures well in excess of the minimum hydrogen fusion temperature, and so a shell around it can have temperatures well beyond it.  Fusion rates are (approximately) polynomial in temperature, with the degree depending on the reaction in question, so small increases in temperature can produce substantially more fusion.  The gravitational force is strong enough to overwhelm the pressure from the induced fusion, and so will contract the surrounding shell to temperatures in excess of the minimum needed.  This is basically what happens in the cores of main sequence massive stars (relative to, say, the Sun).  Actually, our own Sun's energy is mostly from the proton-proton chain and has a core temperature of around $1.57\times 10^7$ Kelvin, nearly four times the minimum necessary.  And still, the core needs to be nearly 10 times hotter than that to initiate Helium fusion.

For the second question, the short of the answer is that the core has undergone thermal expansion after the Helium flash, and so occupies the temperature ranges most conducive to a strong hydrogen fusion rate.  The material outside the core is now at lower temperatures and pressure, so the fusion rate is reduced substantially.  So the energy output comes principally from the core, and the helium fusion at near minimum temperatures releases less energy than the hydrogen shell at (well) beyond minimum temperatures did.  Thus the star overall produces less energy and contracts.

The remaining questions are explained in similar fashion: one has to pay attention to the sensitivity of reaction rates to temperature, and what the temperatures in those shells actually are.  The sensitivities are different for each reaction chain, and the temperatures can go well beyond the minimum necessary.


What observational data convinced Stephen Hawking that Cygnus X-1 was indeed a black hole and caused him to break into Kip Thorne's office?

From The Unknown Universe: What We Don't Know About Time and Space in Ten Chapters  by Stuart Clark:

  By 1998, Hawking was ready to concede the bet. He thought that although the specific evidence for Cygnus X-1 had not changed, there was now so much evidence for other black holes dotted around the galaxy an the wider Universe that there was no more room for reasonable doubt. Besides, [...], he had bigger fish to fry and a new bet to concentrate on. So Hawking paid for Thorne's prize.

Although Kip Thorne himself apparently still had some doubts until 2011  [see here]:

  "For forty years, Cygnus X-1 has been the iconic example of a black hole. However, despite Hawking's concession, I have never been completely convinced that it really does contain a black hole - until now," said Thorne. "The data and modeling described in these three papers at last provide a completely definitive description of this binary system."

The three paper he is referring to are:

Reid et al., “The Trigonometric Parallax of Cygnus X-1”
Orosz et al., “The Mass of the Black Hole in Cygnus X-1”
Gou et al., “The Extreme Spin of the Black Hole in Cygnus X-1”


Given a star's mass, age, and composition, how do I calculate the rest of its properties?

In astronomy research, models of stars are computed using large software packages that solve a set of differential equations that describe the structure of a star as it evolves, mostly because of nuclear fusion transforming elements, under a number of assumptions.  (I once wrote a more detailed answer about this on Physics.SE.) So I'd say the first option is to find and operate one of these programs. One of the easiest to access and use is MESA but there are many others that exist, although they often aren't freely available.

Another option is to use (probably by interpolating in) large tables of models that have been produced using those codes.  MESA is used to produce the MESA Isochrones and Stellar Tracks for which the isochrones Python package provides an interface, but there's also the Dartmouth Stellar Evolution Database and the PARSEC grid, among others.  (Apologies to all the isochrone grids I've missed!)

You can also try your hand with the program SSE, which uses analytic fits to a grid of models from the late 1990s. While SSE implements them, the analytic fits themselves are described in Hurley, Pols & Tout (2000).


Nobody has ever needed such a word, and it doesn't exist.
"Spaghetification" is, of course, a joke word, but each time you make a new joke based off an old one, the less funny it becomes.
If you just want a (poor) joke:  Teslascind

In order to capture @pela's ephemeral comment in a more durable post:

Magnetaaarrgh!


The US Naval Observatory has a web page which lets you print a table of moonrise/moonset times for any location, together with twilight times. If you use this approach, you would print the data and then examine it for a suitable date. I don't know of a computing resource where you would put in your requirements it would report the appropriate date and time.


I emailed the authors of the paper, asking whether blue dwarf stars could

  "become hot enough to pass the thresholds for Type B or Type O"

and one of them replied:

  "We use the term 'blue' to mean 'bluer', so that when stars become
  blue, they get hotter than their usual main sequence temperatures. ...
  The point of the paper is that smaller stars get bluer ... But 'blue'
  does not correspond to a particular temperature, and does not mean 'as
  hot as an O star'."

So it looks like I read the H-R diagram correctly. For the stellar masses represented therein, none of the blue dwarf stars actually reach a high enough surface temperature for type B or O, and white type A stars are the closest any of them will come.

However, that doesn't answer the question for stars with stellar masses not represented in the diagram, for example $0.15M_☉$, $0.13M_☉$ or $0.135M_☉$. The authors of the paper didn't run their simulation for these, and there doesn't seem to be enough information in the diagram to make deductions regarding their suface temperature. So until more research is done in this area, the question of whether any blue dwarf stars can actually become blue remains unanswered.


How can I know the source size using the spectrum variability?

A source cannot coherently vary on timescales shorter than the source size divided by the speed of light.
That is because there is no way that different points on the source could "communicate" with each other and arrange for a coordinated increase or decrease in brightness.
Therefore the shortest timescale of variability gives an upper limit to the size of the emission region.


What is the numerical value of $c$, the SR does not say that. It is a global parameter of our Universe, we need to measure it and substitute it into the SR formulas.

There are also more trivial global parameters. Like the dimension of the spacetime. With (space) dimensions more or less than 3, the formulas of the classical mechanics would be the same.

All the essays talking about "multiverses" or "alternate Universes", are playing with the consequences of the current theories, but substituted with different global parameters than we have now. We could imagine, they are playing with alternative Universes.

However, here we have two major problems.

The logical problem. What does "Universe" mean? The word has latin root, "uni versum" means "to contain everything". The "Universe" is the thing what contains everything. How can multiple be existing then?

For example, the sci-fi topos on which a parallel 3D spacetime referring as "another Universe". No, it is not "another Universe". If there would be proof that such a thing exists, then "our Universe" and this "alternate Universe" would be the "Universe" on its original meaning. We could refer the alternative as an "other spacetime" or "parallel space" or so.

We have also a major problem, what is science. If we can access the parallel 3D space, i.e. if we can interact with it, then it is not "another Universe", it is just a newly found region of ours. But what is no interaction is possible between them and us? Then they are not existing. They might be existing like that our thoughts exist. In any case, it is not physics/astronomy any more, it is phylosophy in the best case.

Professional scientists generally get itchy if they need to answer not science questions. It is because you are assuming rhat they know it, while they know that it is not even science. For example, how hot is a 10 solar masses supernova, that is their field. Thus, your question will be likely closed as unclear, because it is.

What you can find:

You can find popular science texts about playing the current theories, but with different global constants. For example, "what if speed of light would be different" will give you likely useful google hits.
General relativity has some interesting topological extensions. For example, the Kerr-solution looks as if rotating black holes would bind different Minkowski-spacetimes together and so.
There might be interesting hits for googling for "string theory landscape".

In any case, make it more clear, what do you understand on "multiverse" or so, use science terminologies for that. You can find these terminologies by googling forums.

Probably the most popular google keywords will change some decade later.


Argument of perihelion or most planets/bodies changes very slowly over time due to higher order perturbations from other planets' motions (mostly Jupiter and Saturn for the solar system). General relativistic effects also cause the perihelion to advance over time, though this effect is smaller than the others for most purposes.

So given enough time, the arguments of the planets' perihelia would likely end up being fairly randomly distributed at any given time. Also, the planets' orbits are often dynamic on such timescales due to the effects of higher order perturbations showing up, which can cause eccentricity changes, which also affect the positions of perihelia.

So, my guess would be that it is okay to have the arguments of perihelia randomly distributed, since it is inconceivable (at least for me) that any sort of resonances would be visible at this level in order for the distributions to be non-random.


Do all stars of a given age and mass have relatively the same emission spectrum?

The spectrum of light emitted by a star depends mainly on its surface temperature, with smaller variations associated with composition, surface gravity and magnetic activity$^{1}$.

The surface temperature of a star is determined by its mass and evolutionary phase and therefore by its age.

Stars spend most of their lives on the core hydrogen burning main sequence. During this phase, a simple rule is that more massive stars have hotter surface temperatures and their spectra are more heavily weighted to shorter (bluer) wavelengths.

The appearance of the sky is caused both by the spectrum of our Sun and the physiology of the eye. Light is scattered in our atmosphere according to the inverse fourth power of wavelength. At the same time, there is comparatively less violet light in the spectrum of sunlight at the top of the atmosphere and the eye is less sensitive to that light (and some of it is absorbed, most of its ultraviolet wavelengths). It is the case that a hotter star than the Sun would have a spectrum richer in violet light and this would increase the amount of violet scattered light from the sky. Whether that would be sufficient for us to view the sky as purple, with our eye physiology, I am unsure; but probably not (see Why are there no green stars? ).

More massive stars also "evolve" faster, because they burn their available fuel much faster. An "evolved" star is one which has finished fusing hydrogen in its core and moved on to "shell" burning around the core or burning heavier fuels in its core. Shell burning stars tend to be bigger and cooler than main sequence stars of the same mass.

$^{1}$ Increased magnetic activity can drastically increase the amount of light from a star at UV and X-ray wavelengths, by orders of magnitude. This is primarily a feature of comparatively low-mass stars (like the Sun or lower) and is driven by rapid rotation. Rapidly rotating (single) stars are young. This extra short wavelength light is not energetically important to the star, in that the vast majority of its radiation is still at visible and infrared wavelengths.


I saw an orange light in the sky which changed into flashing lights, what is this?

Your description matches that of a fireball, which are typically large meteors.  As they enter the atmosphere they heat up and glow.  The colour will depend on their speed and composition.  As they get hotter, they often break up into several pieces, which follow the same trajectory.  Much the same effect arise when old satellites or space debris re-enters the atmosphere.


What would be the required conditions for a lunar eclipse to occur only once on a precise annual basis?

A lunar eclipse occurs when a full moon occurs at the same time as a lunar node (when the moon crosses the ecliptic - the plane of the Earth's orbit around the sun)

The time between full moons is 29.53... days (although it varies slightly due to the moon's orbit not being circular) This is the synodic month. The time between nodes is 27.21... days. This is the draconic month (because of the dragon that eats the sun!) It is shorter than the time between full moons because of the curved motion of the Earth around the sun, and because the gravity of the sun distorts and rotates the orbit of the moon.

Now on Earth, 223 synodic months is almost the same as 242 draconic months. And so an eclipse will recur every 223 months, or 6585 days.

Now you want an eclipse to recur every year. For that you would need the length of the synodic month, and the draconic month to be an exact fraction of a year. If you change the size of the orbit of the moon you will vary both the length of the synodic and draconic month. If you change the size of the Earths orbit you can change the difference between a synodic, and draconic month, but you also change the length of the year.

So you end up with a juggling game: You have two variables to change, the Earth-Moon distance and the Sun-Earth distance. And you get three values: Synodic, Draconic month and length of a year. You aim to get both of the months an exact factor of the year. It's probably possible to achieve this, but you may end up freezing or baking the Earth. You have also changed the calendar (so "September" may not exist)

Then you need to consider the perturbations of other planets and so with time the length of the month will vary, and your three-way co-incidence will break eventually.


Hulse-Taylor binary pulsar - what is the rate of mass/energy loss from the source?

For reference, the relevant bit from the paper is:

  The observable pulsar is a weak radio source with a flux density of about $1\,\mathrm{mJy}$ at $1400\,\mathrm{MHz}$. ... Our most recent data have been gathered with the Wideband Arecibo Pulsar Processors (“WAPPs”), which for
  PSR B1913+16 achieve $13\,\mathrm{\mu s}$ time-of-arrival measurements in each of four $100\,\mathrm{MHz}$ bands, using $5$-minute integrations.

Those are millijanskys, aka milli flux units, so that the flux density is about
$$1\,\mathrm{mJy} = 10^{-29}\,\frac{\mathrm{W}}{\mathrm{m}^2\cdot\mathrm{Hz}}\text{,}$$
and hence the detected irradiance is on the order of $10^{-27}\,\mathrm{W}/\mathrm{m}^2$. Since we're about to make rather uncertain assumptions anyway, I won't bother worrying about doing more than an order-of-magnitude calculation.

  Assuming that this flux is uniform across a conical beam with cross-sectional radius 5 arc degrees and assuming that the source is 21,000 light years from Earth ... - How much energy is emitted (per second) from the source in the beam?

A spherical cap has surface area of $A = 2\pi Rh$, and here $R = 21\,\mathrm{kly}$. Now, I'm unclear what cross-sectional radius means if measured as an angle, but I take it to mean that the opening half-angle of the cone is $\frac{\vartheta}{2} = 5^\circ$, in which case
$$A = 2\pi R^2\left(1-\cos\frac{\vartheta}{2}\right) \sim 10^{39}\,\mathrm{m}^2\text{.}$$
Thus, the power would be $P\sim 10^{12}\,\mathrm{W}$, but note that in addition to the assumptions you've just listed, we're only talking about a particular radio band.


Why were solar constant measurements before TSIS-1 all about 0.3% high?

From the abstract of Kopp & Lean (2011) "A new, lower value of total solar irradiance: Evidence and climate significance":

Scattered light is a primary cause of the higher irradiance values measured by the earlier generation of solar radiometers in which the precision aperture defining the measured solar beam is located behind a larger, view‐limiting aperture. In the TIM, the opposite order of these apertures precludes this spurious signal by limiting the light entering the instrument.

(emphasis mine)
For example, in the case of the ACRIM instruments used on the Solar Maximum Mission, the Upper Atmosphere Research Satellite, and ACRIMSat:

Notably, for the ACRIM instrument NIST determined that diffraction from the view‐limiting aperture contributes a 0.13% signal not accounted for in data from the three ACRIM instruments [Butler et al., 2008]. This correction lowers the reported ACRIM values, resolving part of ACRIM's difference with TIM. In ACRIM and all other instruments, the precision aperture used to define the measured solar beam is deep inside the instrument with a larger view‐limiting aperture at the front, which, depending on edge imperfections, in addition to diffraction can directly scatter light into the absorbing cavity. Additionally, this design allows into the instrument interior two to three times the amount of light intended to be measured; if not completely absorbed or scattered back out, this additional light produces erroneously high signals. In contrast, the TIM's optical design places the precision aperture at the front so only light intended to be measured enters (Figure 4a).

The paper goes into a bit more detail about the testing done to determine the reasons for the instrumental differences.


Jupiter is a gas giant, with a mass approximately 317.8 times that of Earth, and its atmosphere has a composition that's typical of gas in space: almost 75% hydrogen and almost 24% helium, (barely different to the primordial gas created by the Big Bang). However, its interior also contains rock and metal components.

Until quite recently it was thought that Jupiter's rocky & metallic core was fairly small and compact. Various models gave estimates of a core mass ranging from 7 to 18 Earth masses. But gravitational data from the Juno mission has changed the picture rather radically. It seems that Jupiter's core is diffuse rather than compact, extending fuzzily to almost half the planet's radius! At present, we aren't quite sure of how such a core was formed, but the leading hypothesis is that Jupiter's primordial core was shattered by an extreme impact event.

From Nature, DOI: 10.1038/s41586-019-1470-2 The formation of Jupiter’s diluted core by a giant impact by Shang-Fei Liu, Yasunori Hori, Andrea Isella:

  The Juno mission has provided an accurate determination of Jupiter’s
  gravitational field, which has been used to obtain information about
  the planet’s composition and internal structure. Several models of
  Jupiter’s structure that fit the probe’s data suggest that the planet
  has a diluted core, with a total heavy-element mass ranging from ten
  to a few tens of Earth masses (about 5 to 15 per cent of the Jovian
  mass), and that  heavy elements (elements other than hydrogen and
  helium) are distributed within a region extending to nearly half of
  Jupiter’s radius.

  Planet-formation models indicate that most heavy elements are accreted
  during the early stages of a planet's formation to create a
  relatively compact core and that almost no solids are accreted
  during subsequent runaway gas accretion. Jupiter’s diluted core,
  combined with its possible high heavy-element enrichment, thus
  challenges standard planet-formation theory.

  A possible explanation is erosion of the initially compact
  heavy-element core, but the efficiency of such erosion is uncertain
  and depends on both the immiscibility of heavy materials in metallic
  hydrogen and on convective mixing as the planet evolves. Another
  mechanism that can explain this structure is planetesimal enrichment
  and vaporization during the formation process, although relevant
  models typically cannot produce an extended diluted core.

  Here we show that a sufficiently energetic head-on collision (giant
  impact) between a large planetary embryo and the proto-Jupiter could
  have shattered its primordial compact core and mixed the heavy
  elements with the inner envelope. Models of such a scenario lead to an
  internal structure that is consistent with a diluted core, persisting
  over billions of years.

  We suggest that collisions were common in the young Solar system and
  that a similar event may have also occurred for Saturn, contributing
  to the structural differences between Jupiter and Saturn.

In contrast, the total current mass of the asteroid belt is roughly 4% that of our Moon, so just under 0.05% of the mass of the Earth. Undoubtedly, Jupiter has swallowed numerous asteroids and comets over its lifetime, but even if it ate all of the asteroids in the asteroid belt that would only amount to less than 1% of its total rock and metal content, compared to the primordial rock and metal that it has had since its formation, including whatever rock & metal it inherited from the core impactor hypothesized by Liu et al.


Accuracy of calculating the vernal equinox?

Calculating the exact time of the vernal equinox is essential for many astronomical calculations.

I dispute that claim. What is true is that calculating the exact time of the vernal equinox is essential for some astrological and religious calculations.

My question: Is the above quoted algorithm the most accurate way of calculating the vernal equinox for times far in the future or past?

Of course not. The value of 365.2425 days is an exact value; it is the average number of days per year per the Gregorian calendar. The Gregorian calendar repeats over a 400 span. In any 400 span, there will be 97 leap years (96 non-century leap years, plus one century leap year) with 366 days and 303 years with 365 days. That results in 146097/400 days in a year on average, or exactly 365.2425 days.
The Gregorian calendar was developed as a replacement for the Julian calendar because scholars attached to the Catholic Church were finding it increasingly more difficult to correctly calculate the date on which Easter should fall. The Julian calendar had a leap year every four years. That was a bit too much, and it resulted in an ever increasing number of days between the Jewish Passover and the Christian Easter. The switch to the Gregorian calendar, which is where that 365.2425 values comes from, was motivated by religion rather than astronomy.


Terminology for empty space at the edge of the observable universe?

There is no name for this.

As we look further in space, we also look further back in time. The "edge of the observable universe" is in the early universe. At an early time in the evolution of the universe, the whole of space was so hot and dense that it was opaque.  In whichever direction we look, we can't look back further than this. The is called the cosmic microwave background. There is no direction in which we can look in which we don't see the cosmic microwave background. There is no direction that contains no visible matter.

There are directions that contain no galaxies or other more nearby objects, but there is no name for these directions.


The Three Elements in the Milankovitch Cycles

The primary driver of ice ages over the history of the Earth is much more Earth science than astronomy.  The modern ice age cycle (last 2.6 million years or so) is only possible with relatively low levels of CO2 in the atmosphere and land masses near the North Pole where glaciers can form.  Other factors in the modern ice age period are thought to be the formation of the Isthmus of Panama, perhaps the relatively permanent antarctic ice sheet, and just maybe, the formation of the Himalayas as well.

The set of circumstances required on Earth that make milankovich driven Ice ages possible are pretty complicated and have to be set just about right.  When they are just right, then the Milankovich cycles, which are quite weak, can take over and be the drivers of ice ages.   Prior to 2.6 million years ago, the last time the Earth went through a period of rising and receding ice ages was 440 million years ago when most of the land was on the South Pole.  CO2 was much more abundant, but the single continent sitting over the south pole made the formation of ice sheets possible.   Over most of Earth's history, the Milankovich cycles haven't governed ice ages.

That said, onto the astronomy bits of this question:

  The question is how connected those three elements are, in the event
  someone wants to change the numbers in a worldbuilding process to make
  either a longer or shorter ice age:

There's a strong correlation between the Milankovich cycles and the length of recent ice ages, so the answer here is yes, if you were able to adjust the "numbers" then the length of ice ages would change accordingly.

The 3 Milankovich cycles combine into two primary patterns, the 40,000 year cycle and the 100,000 year cycle (more on that shortly).  These were observed first by geologists and later tied to Milankovich cycles.  What starts and stops ice ages is complicated and there's a few moving parts, so there's not 100% consensus on Milankovich cycles driving ice ages, but the correlation is strong and as far as I've read, this idea is largely agreed upon.

Ice age Cycles

From about 2.3 million years ago to about 800,000 years ago, the 40,000 year ice age cycle was dominant, and for the last 800,000 years, the 100,000 year cycle has been dominant.  The 40,000 year cycle is thought to be the stronger of the two, and one theory as to why the 100,000 year cycle became dominant 800,000 years ago is that the Earth grew slightly cooler, perhaps with the glaciation of Greenland.   See 100,000 year problem.  The 40,000 year cycle still plays a role even within the 100,000 year cycle currently the dominant one.  Article on that here.

Axial tilt.

Axial tilt is on a pretty consistent 41,040 year cycle and it's strongly tied to the arguably somewhat misnamed, 40,000 year cycle.

Axial tilt is the cause of seasons on Earth, so when the Axial tilt is high (over 24 degrees), the seasonal variation increases, meaning, warmer summers and colder winters on both hemispheres.  When it's low (below 23), it means more mild seasons.  While this doesn't change how much sunlight hits the earth, it does change climate on Earth for other reasons,  The overall result is that the more mild seasons lead to a cooler earth.

From Wikipedia

  This trend in forcing, by itself, tends to make winters warmer and
  summers colder (i.e. milder seasons), as well as cause an overall
  cooling trend.

The reason for this, briefly, is that it still snows in high latitudes in the Northern Hemisphere during mild winters and snow and Ice takes longer to melt during mild summers.  If this persists over enough years, Snow cover can build up, which causes Albedo to rise and reflect more sunlight back into space, and less summer melting of ice, over many years, can lead to an ice age.  Once an ice age gets going it's self perpetuating, sometimes referred to as feedback mechanisms.

Axial Tilt reached a maximum about 8,700 BCE and it will reach a minimum in about 11,800 CE.  The warming of the Earth from the Axial tilt maximum isn't sudden though, it begins several thousand years before the maximum and continues for several thousand years after.   This fits nicely with the ending of the last ice age around 10-11,000 BCE.  We're currently in a mid-point in the Axial tilt cycle and it's gradually approaching a cooling effect, though, at least for now, the effect of man made climate change is far bigger than the gradual Axial Tilt cooling.

Axial Precession

Precession is a bit more complicated.  The Earth is on a 26,000 year "wobble",  that moves the North Star and other stars around in a circle in the night sky, but what matters with this Milankovich cycle is what month the Earth is closest to the sun, or, at Perihelion.  The change in Perihelion over time works on roughly a 21,000 year cycle, because it combines Axial precession with Apsidal precession.

Currently the Earth is closest to the Sun in January, but that will gradually change and in about 10,500 years, the Earth will be closest to the Sun in July.  When the Sun is closer, the Earth gets slightly warmer, so the current position of this cycle leads to milder seasons in the Northern Hemisphere (which can lead to cooling) and more extreme seasons in the Southern Hemisphere.   Unlike Axial Tilt which affects both hemispheres in the same way, precession affects each hemisphere in the opposite way to the other.   This, in effect either adds to Axial Tilt's effect or subtracts from it.   As pointed out above, the simplest factor is that milder seasons in the Northern Hemisphere that are ice-age friendly and more extreme seasons are not.   So when perihelion is in January, that somewhat cools the Earth and when it's in July it somewhat warms it.  We're currently in a "cold" period of this cycle, we were in a warm one 10,500 years ago, which also times well with the end of the last ice age. This cycle is moving towards a gradual warming and more extreme Northern Hemisphere seasons currently working in opposition to the Axial tilt effect.  It's cycle is roughly twice as fast and so this also ties in nicely with the 40,000 year cycle too, as these 2 periods (21,000 years and 41,000 years) are close to in sync.  These two cycles are thought to be key factors in driving the greening and droughting of the Sahara desert.  Article here and here.

Eccentricity

The Earth's orbital period and semi-major axis of it's orbit remain roughly unchanged.   What changes with eccentricity is how far the focal point (the Sun is at one of the focal points of the ellipse), moves from the center of the elipse.   The effect of the Earth's orbital eccentricity changing is two-fold.  First, Axial precession only matters if the Earth's orbit is an ellipse.   If the Earth's orbit is circular, the precession Milankovich cycle has no effect.  Precession has maximum effect when the Earth's orbit is at it's most elliptical.

The 2nd effect is that a more elliptical orbit means that, because planets move more slowly in their orbit when they are further from the sun (Equal areas in equal time, per Kepler's law), a more elliptical orbit means that over the calendar year, the Earth gets less sunlight because it's average distance form the sun over time is slightly higher.  So, low eccentricity means slightly warmer, high eccentricity, slightly colder, even though the planet passes through an entire orbit every year, the total energy the Earth receives does drop slightly when the Earth's orbit is most eliptical.

In addition, greater eccentricity amplifies the effect of the Axial precession, which when it's at it's highest, tends towards ending ice ages, so this effect operates in both directions, which is part of the reason why the 100,000 year cycle is smaller.

In effect, eccentricity multiplies the effect of precession, but it has an additional effect that works in opposition to the precession ice age driver.  (Does that make sense? - I can try to clean up if not).

Precession and Axial Tilt can add together or cancel each other out.

and there's other effects.  How much sunlight is reflected off the high albedo south pole, how much sunlight warms the antarctic ocean, how strong the Atlantic current is.   The entire picture is hugely complicated, but from an astronomical point of view, eccentricity is the only one that can reduce or increase total solar energy hitting the Earth.   Axial tilt and precession have no effect on how much sunlight hits the earth, they only drive the variation between the seasons.

  Does the duration and extent of eccentricity affect those of obliquity
  and precession?

The extent of eccentricity directly increases the seasonal variation effect of precession.

  Or does the duration and extent of obliquity affect those of
  eccentricity and precession?

No, the obliquity doesn't affect either of those, but the effect of obliquity can add to, or cancel out the effect of precession.

  Or does the duration and extent of precession affect those of
  eccentricity and obliquity?

Precession doesn't effect eccentricity (which way the Earth is pointed obviously doesn't effect eccentricity), but precession can add to or subtract from Obliquity.

That's the gist of it.

You can run some numbers if you like, but that gets even longer.  The sunlight energy that reaches the earth and how it varies by axial tilt is longitude dependent, so any calculations on changes in energy by changes in axial tilt will vary based on longitude.  At many latitudes, the summer solar energy is more than double what it is for winter.  Even a one or two degree in the angle of axial tilt variation can make a measurable difference in the seasonal variation.

Precession energy variation isn't longitude dependent, but it varies every day with the earth's orbit.   Some bad math on it, with the current eccentricity of about 0.0167, what that means is that at perihelion, the Earth is about .9833 AU from the sun and at aphelion, about 1.0167 AU. Because solar energy diminishes with the square of the distance, the roughly 3.4% variation in distance from the sun works out to about 7% more solar energy hitting the Earth perihelion to anhelion.   When the Elliptical orbit peaks, that ratio exceeds 20% and when it's minimized, less than 2%, but those are ratios by season and location, the total energy the Earth receives from the sun doesn't change, only seasonal variability changes.

That's as far as I'll go with the numbers, as far as the timing, that's pretty straight forward, some of that covered above:

Axial Tilt, when at a maximum it tends to melt glaciers and leads to warming, this last happened 10,700 years ago and fits with the end of the last ice age.   Minimal tilt can lead to cooling and the earth will enter an Axial Tilt Minimum in about 9,800 years.   The entire cycle, high to low back to high lasts 41,040 years.

Precession is significantly amplified with high eccentricity and significantly reduced with low eccentricity.   Earth is currently in a low eccentricity so the precession effect for the last 10,000 years or so has been relatively small.  10,500 years from now precession will be at peak seasonal variation in the Northern Hemisphere, which will work against the Axial Tilt's cooling.   In about 21,000 years, Precession will again be working towards more mild seasons in the Northern Hemisphere, eccentricity will be high and the Axial Tilt will be past it's minimum, but still in a low point.   So, taken together, we might see an ice age begin to form somewhere around 18-20,000 years in the future, but we have little to worry about.  It's not difficult to generate enough atmospheric CO2 to prevent that ice age from happening.   We're already well over the necessary amount of CO2 to prevent a coming ice age.

Finally, Eccentricity was at a minimum about 9,000 years ago and will reach a maximum in about 27,000 years in the future.  Eccentricity is the least consistent of the cycles, it varies between about 90,000 years and 125,000 years and there's a larger, 400,000 year cycle on top of that.

If parts of that aren't clear, I can try to tidy up, or just ask.


photon gas pressure and Independence on refraction index

Photons always travel at the speed of light, wherever they are. This is a consequence of them being massless particles.
Although "light" travels slower than $c$ in a refractive medium, the individual photons making up a light beam do not.
e.g. https://physics.stackexchange.com/questions/19203/what-is-the-mass-of-a-photon-in-non-empty-spaces


This article says the moon may start moving closer to the Earth in the distant future; could this be true?

Jason Barnes is certainly a highly credible source.  He is a planetary scientist and one of the leads on the Dragonfly drone now located on Mars.
The idea that the Moon will someday reconnect with the Earth is not new to him, however.  Here is a link to a Space.com article from 2007 which explains the same mechanism.
Earth's Moon Destined to Disintegrate
It is safe to accept that the article you link to reflects current thinking on the fate of the Moon-Earth system.


Is it coincidence that Einstein predicted exactly twice the outcome of Newton for the gravitational deflection of light?

As far as I know Newtonian prediction is based on Soldner's work in 1801 and Einstein 1911 also predicted around $0.87$arcsec (he was also accused for plagiarizing Soldner's work the article:Historical Note on the Problem of Light Deflection in the Sun's Gravitational Field explains why the accusations were wrong).

The Newtonian approach accounted for the space curvature, as did special relativity which Einstein first used, but it missed the part that not only space is curved but space time is curved. So the factor of two was because of the spatial curvature, that's because by Minkowski metric we consider that light travels flat so that $\rm{d}s^2=0$.The correct answer would be to use the Schwarzschild metric and get the correct answer.

This paper gives more insight on the formulas and the correct approach. Gravitational Bending of Light


Image processing techniques to distinguish between stars and galaxies in an image?

If you have the CCD data and instrument profile, then a star may be treated as a "point source" and a galaxy as an "extended source". This means that, under ideal conditions a star will have it's light spread through the "point spread function" of the telescope, usually these objects have a Gaussian(ish) intensity profile with one pixel of the CCD claiming most of the light and adjacent pixels falling off in intensity, while a galaxy will have an extended, flattened profile with 2 or 3 or 20 pixels claiming most of the light and then falling off in adjacent pixels.

If you have the full CCD information, this is the method of choice. This breaks down when galaxies are so far away that they are resolved smaller than the "point source" stars (larger telescopes can resolve farther away galaxies as extended than smaller, back yard telescopes).

If you just have catalog data, such as colors, then you want to look for items falling off of the "stellar color locus." Stars, in color space tend to sit on a "ribbon" in color-color space (see this from Yanny+2000)

Objects with colors which do not lie on this "ribbon" are special objects. For example the box labeled "Q" is Quasars, which is a type of galaxy. Not shown in this image is a "cloud" of objects which are galaxies (in this image, the cloud will start around that quasar box and extend much redder in both color axes). If you take all of your objects from a telescope and plot them in any(ish) color-color space you will find a tight band, which are stars, and a cloud near this band (which are galaxies). This is because stars operate as a blackbody, while galaxies operate as a dual blackbody (with a lot of light emitted by the stars, following the same blackbody radiation profile, and a lot of gas absorbing this light and re-emitting it in cooler, infrared blackbody colors).

This method is not perfect, this is a statistical method for selecting say 90% galaxies.

Note: Rob is absolutely correct that you cannot do any of these with jpeg images. A lot of jpegs, especially promotional images have had their colors doctored, or even include false colors (for example to represent ultraviolet or infrared light; this is also why you can't do this with random jpegs, each camera will have it's own way of representing color, so my polaroid camera picture will give different colors than a modern random DLSR camera... you can only do this if all the images are collected from identical cameras). jpegs also do not include the "full CCD information" ie. the intensity of light falling onto each pixel of the CCD.

Note 2: Yes you can estimate the PSF for a telescope with an image, but only a CCD image which shows the photon count in each pixel. A CCD image is a 3d image, which shows how many photons fall into each bin, a jpeg does not have this information, so it is... impossible I think, unless the jpeg is produced to show the photon count and not the color.


Can you see the stars when it is trickling?

Yes you can. You just need a partly clear sky (to see the stars) and part cloud (to produce the rain).

For an example of suitable conditions, look for pictures of a moonbow.  (I've only seen one once, personally.)


Not in general, but sometimes there is a dominant direction.
When the Earth passes through a stream of debris from a comet or asteroid,
a
meteor shower
occurs, and those meteors appear to come from a point in the sky called the radiant.
Since the parent bodies have different orbits, different shower radiants appear in different parts of the sky.
For example, the Geminid radiant culminates earlier in the night than most, and the Perseid radiant is well north of the Ecliptic.
As the Earth can encounter meteors from any direction at any time, there are usually a few sporadic meteors unrelated to any active radiant.
Meteor observers have identified some
not quite random
directions for these.


Is it "weird" that all disc galaxies rotate once every billion years?

It is not weird.

The comment is about a certain class of galaxy, and not just a class but a stage of galaxy formation and development within that class.

We start with a fairly constant distribution of matter within the universe.

Stars for when this matter clumps together. This clumping is going to have a fairly even distribution.

Stars then clump together to form structures that we identify as galaxies.

The distribution of this clumping is also going to have a fairly constant distribution.

This carries on up the chain to clusters of galaxies, and clusters of cluster and so on.

Going back to stars, we identify main sequence stars. These are stars that start of with a mass and composition that is very common and then have common life cycles. They take so long to burn up certain percentages of their hydrogen, so long burning combinations of hydrogen and helium and then so long going up the periodic table forming lighter elements and in the process becoming the different types of stars we define as being on the main sequence.

For galaxies it is similar.

Spiral galaxies need to be of a certain size and angular momentum to generate their signature spiral structure. They did not start out as spiral galaxies. And they will not remain spiral galaxies. They are simply how galaxies of a certain size and angular moments appear at certain stages in their development.

This means that the outer edge angular velocities of these types of galaxies (for a specific definition of their outer edge) are going to be similar.

For some information on the development of spiral galaxies and other galaxy types:

https://astronomy.swin.edu.au/cosmos/S/Spiral+Galaxy+Formation


Where can I find a database on the masses of different galaxies?

As a starting point, I would suggest searching on VizieR for catalogues of galaxies. E.g. select "Galaxies" in the "Astronomy" menu (on the right-hand side of the initial form) and put "Masses" in the "Find catalogs" search box (the upper one, the lower one is for searching by position which is less useful here).
In the results section, the elliptical icons on the right-hand side allow you to see roughly what the sky coverage is for the catalogue. Once you select a catalogue, you can take a look at what fields are there.


What is the smallest diameter black hole that can be formed naturally?

The mass at which a star is able to condense into a black hole upon its death is called the Tolman–Oppenheimer–Volkoff Limit, which is roughly 2.17 solar masses. At this mass, the Schwarzschild radius of the black hole (the size of its event horizon) is about 6410 meters by the equation

$$r_s = \frac{2GM}{c^2}.$$

EDIT: I'd also like to add that the theoretical minimum mass for a black hole is the Planck mass, $2.2\times 10^{−8}$ kg, which would yield a radius of $3.267\times 10^{-35}$ meters, though these would not be formed by stellar collapse, though they could have formed as primordial black holes in the very early universe.


How exactly will DESI simultaneously capture individual spectra from 5,000 galaxies using optical fibers?

You can probably get most if not all of your questions answered by perusing the main DESI web site, which I encourage you to check out.

There is, for example, a nice video describing the assembly of the main focal plane elements (the fibers and the associated robot positioners) here.

But in simple terms: the circular focal plane is divided into ten wedges (or "petals"). Each wedge holds an array of 500 fibers and their associated robotic positioners. Each set of 500 fibers is collected at the back end and passed outside the telescope to a spectrograph, where the fibers are arrayed into a line to pass their light onto a slit. That is, there are ten separate spectrographs (that's your "bank of spectrographs"), each of which has a single slit with the light from 500 fibers passing into it. (Each spectrograph then has dichroics splitting the light from the slit into three different wavelength regimes and three different cameras, each with a different grating -- 360-555 nm ["blue"], 555-656 nm ["red"], and 656-908 nm ["infrared", though this is still handled by a CCD and it not really what modern astronomers usually call "infrared"]).

The fibers are pretty densely packed into the individual wedges, and so the robotic positioning is done by tweaking/wiggling each fiber a small amount around its default position within a circular hole (you can see glimpses of this in the video), rather than the wholesale movement of individual fibers across the whole focal plane that the 2dF instrument in your video link does.

One of the ten focal-plane wedges of DESI, with about 60 (of its eventual 500) fiber-plus-robot-positioner elements inserted.


Is the sun any brighter during a solar eclipse

The Sun is the same as ever. It's just that people tend to stare at it for long times during the eclipse. A quick glance doesn't do much damage, but prolonged staring could be bad.

Those who see the phase of totality have an additional risk. After the Sun goes completely dark, and it then finally shows up again, some people feel compelled to keep watching that tiny sliver of light without protection for a long time. Don't. When the actual surface of the Sun is visible again after totality is over, it's time to put the googles back on.

Do not use regular sunglasses. They typically don't block the kinds of radiation they should block to allow you to watch the event safely. There are several options here:

Very dark welding glasses. Ask a welder or go to a welding shop. They have these special glasses to protect themselves from the radiation from the welding arc, which is similar to the Sun's radiation. These glasses are numbered to show how dark they are. For viewing the Sun, use the darkest ones, labeled #14. A welding mask with a #14 glass is perfectly safe no matter how long you're looking at the Sun. #13 glass might be safe too for short durations, but it's not recommended. Anything lower than that is not safe.

Goggles made specifically for watching the Sun. There are many kinds of them. As long as they pass the ISO 12312-2 international safety standard they're fine.

I recommend the goggles made of Baader solar film. They show the Sun in its original color (not red, green, orange, etc). There are several kinds here, too; the Baader AstroSolar Silver/Gold Film passes the ISO standard, these are what I use. You can buy them online in various places and they're very cheap.

More info:

https://eclipse2017.nasa.gov/safety

https://eclipse.aas.org/resources/solar-filters


Brightest most colorful star in eastern morning sky not near any constellations; rises about 4 or 5 am?

From 38° north latitude, Sirius rises in the east-southeast just before dawn in late August.
Most of the naked-eye stars in its constellation Canis Major rise later.
Orion's belt points toward Sirius and appears above it when they are rising.
As the Skymaps.com evening sky map shows, Antares sets in the southwest several hours earlier.
Saturn is currently in Sagittarius, which is in the south on August evenings.

Refraction by the changing atmosphere makes stars twinkle and even appear to change color.
This effect is more pronounced when a star is bright or low in the sky.
Planets generally do not twinkle because they span wider angles than stars do.


We can certainly speculate.

There are dozens of moons in our own Solar System. I've done some preliminary calculations of their apparent size as seen from the planet vs. the apparent size of the Sun at that distance. The large moons (Jupiter's 4 Galilean satellites, Saturn's Titan, Neptune's Triton) are all substantially larger in the sky than the Sun is. I think there are some satellites that are fairly close to the apparent size of the Sun, but I haven't done all the calculations.

The apparent size of our Moon has changed over time, as the Moon has gradually moved farther away. We are coincidentally in a period of history in which it happens to be very nearly the same apparent size as the Sun.

The criterion for an exoplanet to have solar eclipses like the spectacular ones we have here on Earth is a moon that happens to have an angular size large enough to cover the photosphere, but not so large that it also hides the corona.  For a larger moon, you'd have eclipses in which the corona is visible, but not all the way around the moon. For a smaller moon, you'd only have annular eclipses.  (It could also get interesting if you consider eclipses as seen from other moons.)

So given the distribution of sizes and distances of moons in our Solar System, we can guess that situations where the apparent size of a moon and sun closely match is fairly rare, but since there are moons whose apparent size is smaller than the Sun and others whose apparent size is larger than the Sun, it probably happens sometimes.

The one piece of the puzzle that we're still missing, I think, is the typical sizes and distances of satellites of Earth-like planets. Moons the size of ours orbiting habitable planets might be common or very rare. If they're rare (say, if Mars-like moon systems are far more common), then Earth/Moon style eclipses might be very rare for habitable planets.


Would we have more than 8 minutes of light, if the sun "went out"?

If nuclear fusion were to suddenly stop in the centre of the Sun, then the only clear signature we would have of this is the lack of detectable neutrinos received at Earth, starting about 8 minutes after the reactions ceased. The Sun however would continue to shine for tens of millions of years at roughly its current luminosity.

The power source is not "stored" photons. The Sun itself would simply resume the slow gravitational contraction that was halted about 4.5 billion years ago when nuclear reaction rates at the centre were able to increase sufficiently to supply the radiative losses from the surface of the Sun.

The characteristic timescale for the contraction is about
$$\tau_{\rm KH} = \frac{GM^2}{RL},$$
which is 30 million years. i.e. The Sun has enough gravitational potential energy to supply its current luminosity for tens of millions of years.

While this is happening, the Sun would approximately maintain its current luminosity, but decrease in radius, meaning that its surface temperature would increase.

Once the Sun had contracted to a few times the size of Jupiter (so about 30% of its current radius), the contraction would begin to slow, because the electrons in the core become degenerate and the pressure increases with density by more than expected for a perfect gas. The slowing contraction decreases the rate of potential energy release and hence the solar luminosity. The contraction continues at a slow rate until the Sun becomes a hot "hydrogen white dwarf" a few times the size of the Earth, which then cools to a glowing cinder, with no further contraction, over billions of years (see What would the Sun be like if nuclear reactions could not proceed via quantum tunneling? for some more details).

Even if you were to not allow the Sun to contract, it would take some time to radiate it's thermal energy. This timescale is approximately
$$\tau_{\rm therm} \simeq \frac{3k_B T M}{m_H L},$$
which assumes the Sun is a perfect gas of protons plus electrons, with an average temperature $T$. If we take $T =10^7$ K and the current solar luminosity, then $\tau_{\rm therm}=$ 40 million years.

On the other hand, if your scenario is just that light from the Sun stops being emitted, then of course it goes dark on Earth about 8 minutes later.


How many stars are in the constellation Canis Minor?

You possibly are confused by these two entries in Wikipedia (click on the quotations to go to the original distinct entries:

Canis Minor contains only two stars brighter than the fourth magnitude, Procyon (Alpha Canis Minoris), with a magnitude of 0.34, and Gomeisa (Beta Canis Minoris), with a magnitude of 2.9.

and

This is the list of [56] notable stars in the constellation Canis Minor, sorted by decreasing brightness.

The first statement is about stars brighter than the 4th magnitude, of which there are two, and not about all the others. Those two stars are NOT a binary. Procyon is 11 lightyears away and Gomeisa is 170 lightyears away. Procyon itself is a binary, but for the purpose of general observation is considered to be one star.

The second statement is about "notable stars", which is rather arbitrary. The list is 56 stars long, but in fact is one were to map every star visible to telescopes, there would be thousands.

Another quibble: What perchance is the exact area in the sky that is assigned to Canis Minor? This is not precisely defined. See below.

~~~~~~~~~~~~~~~~~~~~~~ and ~~~~~~~~~~~~~~~~~~~~~~

Note the completely different boundaries.


Are there other planetary systems where gas giants are on the inside to rocky planet orbits?

The Kepler-20 system has planets with masses in the following order, going outwards from the star:

Kepler 20b:  $\approx 10 M_\oplus$
Kepler 20e:  $\approx M_\oplus$
Kepler 20c:  $\approx 16 M_\oplus$
Kepler 20f:  $\approx 1.5 M_\oplus$
Kepler 20g:  $\approx 20 M_\oplus$
Kepler 20d:  $< 20 M_\oplus$

If Wikipedia is to be believed, Kepler 20b may be a rocky world;  but at the very least, Kepler 20c is a hot Neptune and has a rocky planet (Kepler 20f) outside its orbit.


I think it's useful to realize the meaning of "shape" is not the same as in "what is the shape of this object I'm holding." Because we are a part of the universe, "shape" is about how things work (eg, how light moves through the universe), rather than "is the universe a sphere, cube, hypersphere or some other 'shape'."

This question is probably too broad to be answered here. I suggest reading the WikiPedia article on the 'Shape of the Universe'.