Is there a plausible causal mechanism to explain why the Sun would be heating up faster/ sooner than we thought? Question for a novel

The Solar Neutrino Problem

  The solar neutrino problem concerned a large discrepancy between the
  flux of solar neutrinos as predicted from the Sun's luminosity and
  measured directly. The discrepancy was first observed in the mid-1960s
  and finally resolved around 2002.

  The flux of neutrinos at Earth is several tens of billions per square
  centimetre per second, mostly from the Sun's core. They are
  nevertheless hard to detect, because they interact very weakly with
  matter, traversing the whole Earth as light does thin air. Of the
  three types (flavors) of neutrinos known in the Standard Model of
  particle physics, the Sun produces only electron neutrinos. When
  neutrino detectors became sensitive enough to measure the flow of
  electron neutrinos from the Sun, the number detected was much lower
  than predicted. In various experiments, the number deficit was between
  one half and two thirds.

The problem is practically solved today. It wasn't so until $\approx$ 2002. However, a little chance that we know something not enough well, still exists, but it is little.

The currently accepted solution of the problem is this: yes, we know the Sun enough well, but the neutrinos can change flavor on the way they reach us. Thus, for example, if an electron-neutrino becomes muon-neutrino, then the detectors capable to see only electron-neutrinos, won't detect it.

It is today a hot research topic in the particle physics, thus some surprising result in the future isn't yet closed out. The main problem is that the neutrino practically don't interact with anything (a light year of lead would stop half of them), so there are only very little possibilities to measure their properties.

The KATRIN neutrino experiment

  KATRIN is a German acronym (Karlsruhe Tritium Neutrino Experiment) for
  an undertaking to measure the mass of the electron antineutrino with
  sub-eV precision by examining the spectrum of electrons emitted from
  the beta decay of tritium. The core of the apparatus is a 200-ton
  spectrometer. In 2015, the commissioning measurements on this
  spectrometer were completed, successfully verifying its basic vacuum,
  transmission and background properties. The experiment began
  running tests in October 2016. Regular measurements started
  2018-06-11, with a projected duration of 5 years.

As far I know, too much surprising results aren't expected from this - most likely, the electron neutrino mass of some tenths of eV will be found, or possible the result will be that the experiment is not enough precise to find anything. (In this case, we will still get an "upper limit").

However, there is a little chance that some surprising result will happen.

For example, such a neutrino mass could be found, which can be explained only by some hyphotetical effect (like sterile neutrinos, which might also contribute to the solution of the dark matter problem).

The idea

Go back to the 80ties, where a possible solution to the solar neutrino problem was a different working and internal structure of the Sun, which looks the same for us, but generates lesser neutrinos. By analogy, a similarly different Sun should be expected, which goes into a red giant phase soon. (Or, at least its luminosity will increase enough in the near future to make the Earth inhabitable).

Note, we also know a lot of other stars today, there are very good models running on big computers, and these are enough sophisticated to close this possibility out with a good probability. Thus, the Sun should be somehow exceptional on these results.


Is sundial time entirely dependent on solar azimuth?

The sundial translates the position of the sun to the time of day, so it depends on the path the sun takes across the sky, this is called the ecliptic.

Because the earth's rotation is tilted with respect to its orbit around the sun, the ecliptic shifts across the sky during the year, which is also the cause of seasonal change on earth. Yet the highest altitude of the ecliptic will always be due south, which means noon is well defined every day of the year.

Now to answer the question; if the day length (from sun-rise to sun-down) is exactly 12 hours,  the sun will rise at an azimuth of 90 degrees and set at 270 degrees. However, this happens only twice a year, namely at the vernal equinox (first day of spring) and the autumnal equinox (first day of fall).

At the longest day, the summer solstice, both sun-rise and sun-down azimuths will be at their highest shift northward. On the other hand, during the shortest day, the winter solstice, the azimuth-shift will be maximally southward. This last bit applies to the northern hemisphere, for the southern hemisphere the seasons and therefore day lengths are reversed.

So in short, you have to account for what place on earth your sundial is at and what time of year it is.


How to know that the 21cm Hydrogen line is the actual emission and not any other redshifted line?

No, not really.  The first thing is that we know that  ${H}$ is far more abundant than other elements or simple molecules in the universe.  The next thing is that the 21 cm line comes from a relatively unusual hyperfine splitting, and there just aren't any other sources near that wavelength and in intensity levels that can easily be detected.

In most cases, astronomers have other methods of estimating objects' speeds, so any measurement of 21cm apparent redshift that was inconsistent with those estimates would be an indication that the wrong line was being observed.


How many light years away is Earth from the closest outer edge of the black hole at the center of the Milky Way?

As @Py-ser already said, there is the very clear information about that, although his link correctly is here.

As we can read there, the distance of this is around 25000 light years, with a precision of 1400 light years.

Normally, the size of most galaxies is around some ten thousands of light years. Compared to the black holes, their size (the diameter of their event horizon) is some kilometers (stellar black holes) or some astronomical units (some millions - hundred millions of kilometers).

Even the size of the event horizon of the greatest known black hole is around the size of the solar system, which is around some thousandth of light years.

You don't need to ask, "how far we are from the nearest edge of Sagittarius A*", you can simply ask "how far we are from Sagittarius A".


Determining the extinction by counting stars?

The general idea is that the more extinction there is, the less you'll be able to see stars. So there is a direct relation between the decrease in flux observed for any individual star and the number of stars you can see in that general direction. So the surface distribution of star counts is an excellent tracer of optical extinction, and $\Delta m = 2.5 \log\frac{N}{N_0}$ is a fairly good approximation in many cases.

This relation between $N$ and $\Delta m$ is not derived mathematically, but rather observed empirically (here or here, for instance), under the assumption that the density of stars is the same in the direction of reference and in the direction of interest. This means that the extinction is measured with another method (for instance looking at how much specific emission lines are absorbed), counting the stars, and then fitting a curve that will give the relation between star count and absorption.

But why don't we just use the other methods directly, might you ask! Well the other methods require data such as high-enough resolution spectroscopic data that aren't always available for the region of the sky you are studying. Then star counting gives you a close enough guess without being prohibitively expensive.


Why can we sometimes see the moon during the day?

The Moon makes a full orbit around the Earth once per month. From full moon to full moon, it is 29.53058886 days (synodic month).

Full moon happens when the Moon is at one side of the Earth (right side in the image), and the Sun is at the other side. This way, Moon is fully iluminated by Sun (except in the cases where it is exactly in the opposite side of the same line, where you have a Moon eclipse). In this phase, Moon is at its highest altitude at midnight.

Then, as the Moon orbits, it comes closer to the Sun in the sky. This means both that it shows us less iluminated percentage and that its rise and set get delayed. At Last Quarter, Moon is at its highest altitude at sunrise. This means that you will be able to see the half moon figure on the sky during the morning (and last half of the night).

Then it comes New Moon, where the Moon is nearest to the Sun in the sky, and almost invisible, since it shows us the dark side during the day. Its highest altitude is at noon, but you will not be able to see it. You can, if you are lucky, see a Sun Eclipse.

Finally it comes First Quarter. To put it short, highest altitude is at sunset and you are able to see Moon during all the afternoon (and first half of the night).


Is the turn-off point of the main sequence the same as the terminal-age main sequence?

TL;DR: Turn Off point (TO) means the location of the "knee" in the HRD of clusters of stars. TAMS is an imaginary line in the HRD that is defined by the location of stars of different mass at the end of hydrogen burning. It constitutes the upper boundary of the main sequence.

More details:

There maybe some confusion because the terms are not completely specific.

A Zero Age Main Sequence star (ZAMS) star is a star that, after formation, has reached hydrostatic equilibrium and just started hydrogen burning. But ZAMS can also mean an imaginary line in the HRD that is formed by the location of all ZAMS stars of different mass. This line constitutes the lower boundary of the main sequence.

A Terminal Age Main Sequence (TAMS) star is a star that has reached the end of hydrogen burning. TAMS can also mean the line in the HRD diagram that constitutes the upper boundary of the main sequence.

The main sequence can thus be considered a band bounded by the ZAMS and the TAMS in which Main Sequence stars may be located. In the following figure (Maeder A., Meynet G., 1989, Astronomy & Astrophysics, 210, p. 155) this band (and other areas of slow development phases) is shown as shaded area:

With time (and hydrogen consumption) a star moves from its ZAMS location (determined by its mass) up and right to its TAMS location. The most massive stars evolve more quickly, reach the TAMS earlier and then move away from the main sequence.

The Turn Off point is only relevant for clusters or groups of stars that formed at the same time. With increasing age of the cluster, its stars move away from the main sequence, starting with the most massive ones in the upper left area, leaving more and more of the upper area of the "band" unoccupied. The TO point can be thought of „sliding down" the TAMS with time. From the position of the TO the age of the cluster can be determined.

https://commons.wikimedia.org/wiki/File:Open_cluster_HR_diagram_ages.gif#/media/File:Open_cluster_HR_diagram_ages.gif


The Earth does spin like an unbalanced top. The Earth's rotation axis is not fixed. It instead moves in a complex manner due to a combination of external torques exerted by the Moon and Sun, a torque-free nutation due to the oblate shape of the Earth, and also due to changes on and in the Earth.
The torque-induced motions are called precession and nutation, distinguished by period. The largest and slowest of these motions is the axial precession. This causes the Earth's rotation axis to trace out a cone over the course of 26000 years.

(source: nasa.gov)
The torque-induced nutations are also cyclical motions induced by the Moon and the Sun. These are much smaller in magnitude and have a much shorter period. The largest of these has a magnitude of about 20 arc seconds and a period of 18.6 years. All other nutation terms have much smaller magnitude and have shorter period.
The torque-free nutation would have a period of about 305 days if the Earth was solid. The oceans, the atmosphere, and the outer core alter this. The Chandler wobble has a period of about 433 days and a magnitude of less than an arc second. Because the Chandler wobble isn't as predictable as are precession and nutation, it's lumped into a catch-all category called "polar motion." The redistribution of water over the course of a year (e.g., snow on Siberia in the winter but not in the summer) results in a yearly component of the polar motion.
There are lots and lots of other factors, all small. Polar motion is observed after the fact.


It would have to be a big meteorite to supply the quantaties we have here and therefore support the nuclear break down theory.ie- hydrogen to helium etc.

In respect of delivery by cosmic objects, the atmospheric pressure on the moon would result in a low boiling point and the evaporation velocity(due to low gravitational attraction) would exceed the escape velocity of the moon and meet with no atmospheric resistance.
This is the way I see it.
The body of water, although spread over the surface, would consider itself as an independent body and have its own "existence parameters" with regards to its environment.

The ability of Mars to retain water vapour is much reduced by its lower gravitational strength and atmospheric density. Can water exist at these parameters continuously, the evidence shows not.


How many meteors hit the moon every day or in how many days does a new meteor hit the moon?

We generally like you to check google before posting questions here.  I posed your question to google and amongst other links, I got these:

http://science.nasa.gov/science-news/science-at-nasa/2006/13jun_lunarsporadic/
http://www.slate.com/blogs/bad_astronomy/2014/02/24/lunar_impact_video_of_an_asteroid_hitting_the_moon.html

Per Bill cook in the top link:

  No one knows exactly how many meteoroids hit the Moon every day. By monitoring the flashes, we can learn how often and how hard the Moon gets hit."

And in the second one:

  The Moon is smaller and has less gravity than Earth, so it gets hit less often than we do.

Both articles mention MIDAS (the Moon Impacts Detection and Analysis System).  Since the first link is from 2006, perhaps soon we will have a good estimate for you.


Is there any role today that would justify building a large single dish radio telescope to replace Arecibo?

Arecibo wasn't just a radio telescope, it was a radar telescope, bouncing megawatt-level radio signals off various bodies in the Solar System.  A single-dish transmitter is far superior to a phased-array or other composite system, because the beam pattern is a simple Airy disk rather than a complicated pattern formed by tens or hundreds of such disks.


Why does this twilight sky flat field have a grid of dark pixels?

Yes, it's some sort of CCD structure originated from the manufacturing process. CCD chips with large area were produced by chunks of several hundred pixels. see http://heasarc.gsfc.nasa.gov/Images/astroe/about/xis_config.gif

And sometimes position offsets between these chunks can be detected.

from Wilken et al., 2010, MNRAS, 405, L16


Is there a verification of the solar system barycenter as it is theoretically determined?

Yes, measurements do exist. JPL takes very precise observations of many objects in the solar system and tries to obtain a location for the solar system barycenter.

The solar system barycenter is a hot topic especially in terms of PTA's, or pulsar timing arrays - we need precise a precise location for the solar system barycenter to do work with these pulsar timing arrays. I'll put some links at the bottom as well to help.

JPL does get its own calculations of the solar system barycenter, and AFAIK, they do this with use of what they call the Solar System Ephemeris - see more here and here, at their Solar System Dynamics page. They get precise locations of many objects in the solar system and then try to calculate a center of mass from there.

A cool walk-through of the effect of the eight planets and Pluto (and some other stuff) on the movement of the Sun.


As days get longer, why isn't the added daylight split evenly between sunrise and sunset?

It's a consequence of the equation of time, which represents the time difference between apparent solar time (time as measured by a sundial) and mean solar time (a fictitious device; essentially mean solar time is time as measured by a clock). Below are two plots from the referenced website.

Figure 1: Equation of time. Currently (early January), a sundial will be slightly behind a clock and is getting slower.

Figure 2: Time derivative of the equation of time. Apparent solar time changes most rapidly from early December to early January, with the maximum change occurring on December 25.

Days are currently getting longer in the northern hemisphere, but noon is advancing by 20 to 25 seconds per day. Sunset advances by half of the increase in the length of day plus that 20 to 25 second advance in noon. Sunrise advances by half the increase in length of day less that 20 to 25 second advance in noon.

The increase in the length of day (time from sunrise to sunset) depends on latitude. In Bogota Columbia (4°35′53″N latitude), length of day increases by only 3 to 10 seconds per day during January, growing throughout the month. That tiny change in length of day means sunrise continues to advance throughout the month of January in Bogota. On the other hand, in Reykjavík, Iceland (64°08′N latitude), length of day increases drastically from day to day, even at this time of year. Sunrise started becoming earlier in Reykjavík on Christmas day.


Using SkyChoord to read in multiple coordinates.

From the documentation

>>> c1 = SkyCoord(ra=10*u.degree, dec=9*u.degree, distance=10*u.pc, frame='icrs')
>>> c2 = SkyCoord(ra=11*u.degree, dec=10*u.degree, distance=11.5*u.pc, frame='icrs')
>>> c1.separation_3d(c2)
<Distance 1.5228602415117989 pc>

The rest of the code is just reading the excel files and printing the results. What you have now is incorrect, even without the "z" coordinate. You can't calculate the separation of two points in spherical coordinates by Pythagoras' theorem: eg (30*, 0*) and (30*, 359*) should be very close. You need to convert to cartesian coordinates first, which is what the astropy module does.


Magnetars are the most widely-accepted explanations for two observed classes of objects:

Soft gamma repeaters (SGRs)
Anomalous X-ray pulsars (AXPs)

Under the magnetar hypothesis, these classes of objects are explained as highly magnetised neutron stars, evolving from a soft gamma repeater (expected lifetime ~10000 years) to an anomalous X-ray pulsar (expected lifetime ~10000 years) as the rotation period lengthens and the magnetic field decays.
The AXPs are pulsars, and at least some SGRs have been identified with pulsars (e.g. Sgr 0526-26 = PSR B0525-26). So under the magnetar hypothesis, magnetars can indeed be pulsars.
It's worth noting that the magnetar hypothesis may not explain (all?) SGRs and AXPs: there does seem to be evidence that some of these objects do not have especially strong magnetic fields compared to pulsars, e.g. SGR 0418+5729 (Rea et al. 2010), and there have been suggestions that some of these objects may actually be white dwarfs (Lobato et al. 2016), perhaps somewhat similar to the white dwarf pulsar in AR Scorpii.


Has stellar evolution ever been modeled analytically?

Analytic models have been applied to various phases of the evolution, though it would be impossible to apply a single model to all phases because the physics changes so much.   Also, a star will often have very different physics going on in various different parts of the star, so analytic models sometimes have to treat different parts separately and then unify the results across boundaries (just as numerical simulations do).  For example, I've seen different polytrope indices used in the convection, radiative, and core regions of the Sun.

I realize that your interest is when there is not a steady-state assumption, but rather time is a dynamical variable.  But it is not always necessary to use time as a dynamical variable to do evolution.  You can simply do a steady-state analytical model (like a polytrope, perhaps supported by a numerical piece that solves for some parameter like core pressure), and allow the parameters in your solution to be time varying in some simple analytical way.   For example, you could study how mass loss affects a star by doing steady-state analytical models and just let the mass change with time according to some analytical mass-loss prescription (such as "Reimers' Law", something simple).  So steady-state analytical models can be elevated into evolutionary models if you simply have an analytical way to change the parameters with time.

Another simple example is the evolution of a fully convective protostar.  You simply fix the mass and initial radius, and you solve the interior by assuming it's all at the same entropy (a reasonable approximation for fully convective stars).  Then you fix the surface temperature to lie on the Hayashi track, which for a very simple model could mean just pegging the surface T to 3000 K.  That and the initial radius determines the luminosity, and the constant entropy assumption fixes the internal structure, so then you simply let it lose energy at the rate of the luminosity, and use the internal energy as the variable that changes with time, always updating the radius to be consistent with the new internal energy (a la the virial theorem), and that gives the new luminosity and so forth.  A simple fully analytic model until the star is no longer fully convective (and we then might call it a pre-main-sequence star).

I've also seen white dwarf cooling done analytically.  It's a similar idea-- take the surface temperature as an initial condition and just let it lose heat via its luminosity.  The radius doesn't really change, so all you need is to keep updating the surface temperature as a function of the internal energy, which can be handled via some analytic internal heat transport treatment.  If you are willing to make approximations that address the key physics, you can do almost anything analytically.


Right now it doesn't look like much. It has a magnitude of about 12. And appears as a single point of light. So it requires the upper end of amateur equipment to observe. If you want to measure the variation, which is only 0.2 magnitudes, you would need to take images. So you would need a proper photo-imaging system.

In other words it is a tricky amateur target. You could try using an online telescope. The star is within the range of the Bradford robotic telescope.  (Except this is offline and doesn't have an expected date to be back in service :(

In the Digital sky survey (using professional equipment), the star appears in the centre of this image. This has very high magnification, this image is about 4 arcminutes across, about 1/8 the apparent size of the moon.

It is hard to give an exact spec. There is a formula: $m=\log_{10}(D)\times 5 + 7$ which calculates the limiting magnitude $m$, from the diameter of the mirror in cm $D$. This suggests you need at least 13cm mirror. However it assumes clear and stable skies, so in practice you would need something clearly in excess of that.


Hubble Space Telescope (HST) observing modes

"Staring mode" is the traditional way of simply pointing the telescope and exposing the detector.

In "spatial scanning mode", you slowly move the telescope, so that the image is slightly smeared out in the spatial direction.

The figure below shows the principle: On the left is how a regular image is taken; in the middle, a regular spectrum is taken in staring mode, and in the right panel, the detector is moved during the exposure, resulting in the spatial scanning mode. The farther you scan spatially, the brighter and object you may observe before over-exposing, but the downside is that more objects will start to overlap, ruining the spectra.

Left panel: "Imaging"; each observed object shows up on the detector at its corresponding position on the sky.
Middle panel: "Staring mode"; when a grism (sort of like a prism) is inserted, the light from each object is spread out according to its wavelength, producing a spectrum.
Right panel: "Scanning mode"; if the detector is moved slightly during exposure, the spectra are spread out perpendicular to the wavelength direction, effective using a larger number of pixel to collect the photons in. However, if the detector is moved too much, the spectra begin to blend.

This picture, from HST's WFC3 handbook shows the difference in a real observation: It's quite small, but particularly for the "$0^\mathrm{th}$ object" (on the left) you can see that in the staring mode it's over-exposed, creating diagonal spikes, which are reduced in spatial scanning mode:

In the picture, the objects are located in the vertical direction, while their spectra are dispersed in the horisontal direction. You can see that in the spatial scanning mode, the objects are slightly broader vertically.

The advantage of the scanning mode is that you can expose for a longer time, without the detector getting saturated (which can be a problem for bright stars). When you expose for longer, you collect more photons and hence obtain a higher signal-to-noise ratio (S/N), meaning that your observation becomes more "accurate". The figure below (from these notes) shows the advantage of a high S/N:

Two spectra of the same object, with the right having been exposed 9 times longer than the left, resulting in a $\sqrt{9}=3$ times higher S/N. Determining for instance the central wavelength of this spectral line becomes much more accurate with higher S/N.

Note that both modes refer to so-caled slitless spectroscopy. A way to avoid the spectra to overlap is to insert a "slit" which allows only the light from a narrow (of the order of an arcsecond) part of the sky to be observed. In that way you will only obtain spectra of objects lying exactly along the slit, but in return you will have a "cleaner" spectrum.

Note also that you can obtain the same effect by dividing your observation into multiple staring mode exposures and then add them together. Scanning mode is a more practical way of not having to do this.


Why a blue spot in some hubble images of NGC 4302?

That's a region of recent star formation in the disk of NGC 4302. Regions of recent star formation include short-lived, high-mass O and B stars, which are blue (because they're hot) and luminous enough to outshine the (redder) lower-mass stars that are also present. If you look carefully at the image, you can see hints of blue light from other parts of the disk (e.g., in the upper right and upper left sides of the disk). You can also see lots of recent star formation in the disk of the neighboring galaxy, NGC 4298.

If you look at the full-resolution (84 MB) version of the image available here, you can see that the blue region resolves into many blue pinpricks in the midst of a fuzzier blue haze, a clear indication that it's made up of lots of bright blue stars (or small clusters of bright, blue stars) and a larger number of somewhat fainter blue stars. You can see the same thing going on in the blue regions of NGC 4298.

There are probably other, similar regions in the disk of NGC 4302; the reason this particular region shows up so well is probably because it's located in the outer part of the disk on the side closest to us, so there's relatively little dust blocking its light.

(Although there is undoubtedly ionized gas in the vicinity of those stars, the gas is not producing enough light to show up in the image -- you would in fact see a reddish/pinkish region if it was mostly light from ionized gas.)


Why levels of radio contours maps are given in mJy/beam and what does it mean?

Jansky is defined as  $1 Jy= 10^{-23}erg/s/cm^2/Hz$. So all the energy coming from a given solid angle per time, per frequency bin and per detector area.

This is convenient for sources of small angular extent (smaller than observing beam), e.g. for point sources, because the flux remains constant for varying beam sizes. For extended sources, the surface brightness is often described with units of Jy per solid angle. Radio contour maps, e.g. of interstellar clouds, usually show objects that are larger than the beam, so that the observed fluxes are a function of the beam size. To clean the beam influence from the date Jy/beam (beam area in steradian) is used.

So it is a surface brightness. For a flux of 1 Jy measured with a beam of 1 sr solid angle we find:   $1 Jy/beam= 10^{-23} erg/s/cm^2/Hz/sr$.

Note, that 1 sr is already a huge portion of the sky. Beams are much smaller, on the order of arcsec to arcmin diameters.


How do you refer to comparative temperature?

Possible, but rare.  The reason is that many things are not linear with respect to temperature.
Volume of gas is in direct proportion to temperature (at given pressure) but we rarely need to consider this.
But, for example, the density of water is markedly non-linear with temperature.
Moreover our physiometric response to temperature is also non linear. We dont experience 300K as being 4% higher than 288K.
As such, planetary temperatures are usually described in Kelvin, Celcius or Fahrenheit (or even Rankin if you look hard enough) rather than being referred to Earth temperaturees.


A 1 solar mass, Earth sized black dwarf would have a surface gravity of about 360 000 g which probably rules out manned exploration by anything we would normally think of as human. For similar reasons, mining would be quite challenging.

Another obstacle is that the Universe is not old enough to have produced any black dwarves yet. The oldest white dwarves still have a surface temperature of thousands of Kelvins.

Indeed, if humanity is still around when they have formed, visiting and mining them will probably be easy.


Hubble law, cosmological redshift and distance

I think that the wikipedia page on Hubble's law is reasonably clear. The distance in Hubble's law is the proper distance. This is the separation between two objects measured by observers at the same cosmic time. That is, if you imagine (instantaneously) stretching a load of metre rulers end-to-end from us to a distance galaxy, it is how many metre rules you would need. The velocity in Hubble's law is the rate of change of proper distance with cosmic time.

On large enough scales we find that that the ratio of velocity to proper distance is the Hubble parameter, which itself changes with cosmic time.

$$ v(t) = H(t) D(t)$$

In practice we cannot measure the velocity or proper distance in Hubble's law - we can generally only estimate these quantities for a galaxy as we observe it some time in the past, when it emitted the light we detect. This is why Hubble's law in terms of measured redshifts and estimated distances is only applicable over relatively small (cosmologically speaking) distances and for recession velocities much less than the speed of light.

For more distant galaxies the distance cannot be calculated from a redshift without a cosmological model for how the Hubble parameter changes with cosmic time. This in turn depends on the adopted cosmological parameters. See Evolution of the Hubble parameter

Proper distance is also discussed here.


What good evidence exists for the 9th planet as spoken of by Caltech?

What they have at present is best described as a theory based on data that is not precise enough to make a definitive statement.  They are telling people they think something is out there and roughly what they think it might be, but they really don't have accurate enough data to make any statements beyond that.

The fact that the possible range of distances they suggest is so large tells you all you need to know about the accuracy of the data being insufficient to draw reliable conclusions.

My biggest problem with this claim is that we have a historical lesson that suggests caution : Pluto.  Pluto was found when looking for an entirely different object ( coincidentally about the same mass as the new planet X, if memory serves me ).  It transpired that the orbital anomalies that led to predicting a Planet X 1.0 were later evaporated by more accurate measurements and theory.

Are we now seeing the same sort of error ?  Could be, might not be.  All we can hope is that the quest for an explanation generates either the result claimed or, if not that, better data, more data and perhaps more accurate simulations and theory.

I am reminded that, in the past, quite eminent and respectable scientists have claimed any number of things, which would later prove incorrect.  Cold fusion leaps to mind.  The problem with humans looking at data is that, sometimes, they see what they want.  I think this planet X 2.0 claim needs a colder and more objective, perhaps even cynical, examination, away from the media.


Is it possible to break apart a neutron star?

It would appear theoretically possible (to some degree) through extreme applications of recycling to trigger mass shedding in pulsars.

Pulsars are rapidly spinning neutron stars, the fastest class of which are millisecond pulsars. The current belief is that they build up rotational speed through accretion, a process known as recycling. One study, Recycling Pulsars to Millisecond Periods in General Relativity (Cook, et al), explores the limitations of this process.

The following chart shows their results:

At the point where the dotted lines meet the two plots, you can see a reduction in mass at those energy levels. This is due to the angular velocity of the body creating instability which results in mass shedding - essentially mass at the equator of our neutron star being flung off the star due to the body's angular velocity.

Unfortunately, this is not exactly an easy process.

  The timescale to accrete the required rest mass, ~0.1 M☉, at the Eddington limit, ~10-8 M☉yr-1, is ~107 yr. This timescale is largely insensitive to the adopted nuclear equation of state. If other astrophysical considerations require a considerably shorter time scale, then the simple recycling scenario described here will have to be modified beyond the variations explored in this paper.

(Note however that the research here is actually attempting to avoid such instabilities, and they accomplish this by adding even more mass, such that the body can support even greater rotational velocity without encounter instability. Additionally, they're trying to create millisecond pulsars, but we don't need to do this as they exist naturally, so we could save ourselves a lot of time by (very carefully) approaching an existing millisecond pulsar)

I don't think this would exactly be breaking apart (despite Wikipedia's use of that exact verbiage to describe it), but it allows for the return of mass that was at one point in a neutron star.  Of course, chances are our theoretical neutron star miners are very likely to be the ones who put that mass on the neutron star to begin with. On the other hand, this (hopefully) accomplishes the task without reducing the object to a quark star or black hole.

  Cook, G. B.; Shapiro, S. L.; Teukolsky, S. A. (1994). "Recycling Pulsars to Millisecond Periods in General Relativity". Astrophysical Journal Letters 423: 117–120.


How to calculate distance from object to point on celestial sphere

The shortest angular distance between two points on the celestial sphere is measured along a great circle that passes through both of them.

The equation your program is using is
$$ \cos \theta = \sin \delta_1 \sin \delta_2 + \cos \delta_1 \cos \delta_2 \cos (\alpha_1 - \alpha_2), $$
where $(\alpha_1, \delta_1)$ and $(\alpha_2, \delta_2)$ are the right ascension and declination of the two points on the sky (expressed in degrees, then converted to radians).

In terms of output from your program its harder to help, especially as you have not given the full output. The first three columns should be self explanatory - columns 2 and 3 are just the coordinates expressed in degrees. I am guessing that the third column from last, that you haven't shown, gives the separation between your object and the catalogue objects and that the penultimate column is the angle that the great circle between the points makes on the sky. That looks right because the fourth object in the list has almost the same RA as your input object but  is 67 arcseconds due south (i.e. at 180 degrees).


Do any known exoplanetary/solar bodies have "annular" eclipses similar to Earth's?

This will depend the position of the observer and (obviously) the relative sizes of the star and the eclipsing body.

For an intelligent observer standing on the surface of a planet the most obvious and likely candidate for an eclipsing body would be a moon of that planet. The nearer the planet is to the sun the larger that moon has to be, and the further the planet is away from the star the smaller the moon can be.

Finding planets around stars is hard enough, finding moons that will be orbiting quite closely around those planets across interstellar distances is even harder (I'm not going to say impossible, but it's pretty close) with current technology, so at the moment the answer is "None, that we know of".

Also don't forget that, according to current theories, the moon was formed when a large Mars sized body collided with the nascent Earth, the chances of another Earth/Moon type system is probably remote. This means that most natural satellites are likely to be Phobos sized bodies. Therefore to get an eclipse the planet would have to be further out from the star (so the star looks smaller) and that would tend to put it on the edge of the "Goldilocks" zone, making the likelihood of there being an intelligent observer somewhat rare.


The term "superficial" means "on the surface," so "superficial gravity" is the same as surface gravity. As @pela pointed out in the comments, the author of the article is Portuguese and in that language the word for surface is 'superficie.'


Distance between each dish in an array telescope configuration

Physically there is nothing dictating the distances between dishes.

These telescope arrays are interferometers. By combining the signal of the two dishes you can achieve a spacial resolution of a giant virtual dish that is about as large as the distance (called the baseline) between the two real telescopes.

A nice example of the power of this technique is the VLBI, which is essentially such an array only the individual dishes are actually just observatories all over the world.

For more detail on how this all works exactly take a look at the wiki pages on aperture synthesis and astronomical interferometry.


How significant is a planet's density to the formation of life?

You could probably get away with replacing molten iron, 7.87 g/cc, in the core with aluminum, 2.70 g/cc, and still generate a substantial magnetic field: Molten Metal Magnet

  It’s easy to create a magnetic field by using a battery to force an electric current through a loop of wire. But Earth’s core, a rotating mix of iron and nickel with internal flows driven by the passage of heat, has no battery and no wires. Instead, it creates magnetism by means of self-sustaining feedback. Liquid metal moving through a magnetic field generates a current, similar to that induced in the moving coil of an electric generator. That current in turn generates the magnetic field. This “self-generation” mechanism can dramatically amplify the small, random fields that always exist in magnetic materials.

Sodium was used in the linked article, however any molten metal or conductor, should do, and sodium, at 0.97 g/cc is just not dense enough to sink to a planet's core.
You'd have to do some hand waving over "an iron poor/aluminum rich Bok globule", but I think you could get your planet, with a sufficient magnetic field to fend off solar winds.


Is there any theoretical or empirical research about planetary systems with a black hole in their center?

Since planets are known to exist around neutron stars (e.g. see Wolcznan & Frail (1992); and see the list of "pulsar planets" - technically, these were the first exoplanets ever discovered), then it is difficult to see any fundamental reason why there should not be examples orbiting black holes.

In fact, since it is probably feasible to form black holes via direct collapse, without an associated supernova then maybe the hazards for planets are not so severe.

Against this, must be set the fact that black hole progenitors are likely to be more massive than neutron star progenitors and the role of winds and radiation on the formation of planets is still not well established.

Planets orbiting neutron stars are/were found from a timing analysis of pulsar signals. The same phenomenenon is not present for black holes and direct imaging or observing a transit is not remotely feasible at present.


A moon in eccentric orbit dipping below Roche limit

Comet Shoemaker-Levy 9 (SL9 for short) is a great example of a moon in a highly eccentric orbit that passes through the Roche limit at periapsis.
SL9 was discovered in 1993, but is thought to have been orbiting Jupiter for 20-30 years prior to discovery. It passed through Roche limit of the Jupiter/Comet pair and is thought to have broken apart in July of 1992. The pieces then collided with Jupiter in July of 1994.
SL9 had an extremely eccentric orbit ($e \approx 0.9986$), with apojove of almost a 1/3 AU!  This "loose" orbit allowed massive orbital perturbations by the Sun at apojove, which eventually led to its demise. Here is a nice figure of its last passes:

Note:

In this case, the tidal forces were dominant over the gravitational forces, so the SL9 fragments never came back together once they were broken apart.  But SL9 passed deep into the Roche boundary of Jupiter prior to its collision. This may only be a partial answer to the above question. If SL9 had grazed the Roche boundary just enough to be barely broken apart, I don't know if it would have come back together prior to hitting Jupiter.

After SL9 was split apart by tidal forces, as is shown in the above image, the pieces got further and further apart. This is exactly what we expect to happen since the pieces in higher orbit have a slower orbital speed and the pieces in lower orbit have a faster orbital speed. If SL9 had been in a stable eccentric orbit, the fragments would have continued to break up until they were small enough to withstand the tidal forces. Over many orbits, they would spread out and intermingle into an eccentric ring.

This may not be the only time an object is first broken up and then later collides with a larger body.  Check out this set of craters on Ganymede!


Is mass+energy conserved when a new universe forms inside a black hole?

Under the assumption that there is some sort of "Big Bang" scenario, then we are assuming an expanding universe.  General relativity does not require the conservation of mass-energy on a universal scale in a changing spacetime (arguably, GR doesn't even have a concept of energy on a universal scale), so there is no a priori reason why this black-hole-universe cannot be comparable to our own (in whatever senses we pick).

A simple way to see why energy conservation must be violated, even in a vaccuum, is to first observe that the vacuum energy density is fixed.  So if spacetime is expanding (or contracting), then we are changing the total volume without changing this vacuum energy density.  Keeping the density the same but increasing the volume means more total energy; decreasing the volume with the same density means less total energy.

We can also easily observe this violation.  You may be familiar with the concept of redshift: light coming to you from a source that is moving away from you (or emitted from a gravitating source) is shifted towards the red side of the spectrum.  This stretches out the wavelength, so the light has less energy.  The energy doesn't go anywhere, it's just gone.${}^*$

We might also note that, with Noether's theorem in hand, we know that time translation invariance implies conservation of energy.  But a non-static spacetime is inherently not time translation invariant, so conservation of energy is not required.

${}^*$ Well, some may try to regain conservation of energy by asserting that there is an energy of the gravitational field to consider.  This isn't adopted by everyone, but it can be done if you're careful with your definitions.  It just doesn't work as generally and easily as you might naively hope for.


How to convert horizontal coordinates using NOVAS?

This is the reply I got from the US Naval Observatory itself:

  No, we do not have that transformation in NOVAS.  Generally, altitude and azimuth are not determined to very high accuracy, so using them to obtain RA and Dec, which are much more precisely defined and measured, does not make a lot of sense.


What is meant by "vastness of space, which now filled a volume of a hundred million light years"?

I think this is at best a weird typo, but more likely a confusion by the authors (who are not cosmologists or astronomers, but a biologist and a geologist).
The book is 10 years old, but our view of the timeline of the evolution of the Universe was pretty much the same then. Note that the calculation of the size of the Universe as a function of time is a bit more complicated than you assert, because it expands while photons are traveling.
The three number that the authors give — $200\,000\,\mathrm{yr}$, $2\,700\,^\circ\mathrm{C}$, and 100 million lightyears (Mlyr) — do not correspond to the same epochs, as I will discuss here:
Recombination began at t ~ 200,000 yr
The process the authors discuss is known as the recombination of hydrogen, followed by the decoupling of light from the gas. At an age of $200\,000\,\mathrm{yr}$, the Universe had cooled to $4\,500\,\mathrm{K}$, and atoms began to recombine. At this point, the region that is the observable Universe today had a radius of almost 30 Mlyr, i.e. a volume of some $10^5\,\mathrm{Mlyr}^3$. However, the observable Universe at that time was much smaller, because light hadn't traveled so far — the radius was less than half a Mlyr.
Photons decoupled at T ~ 2,700 ºC
The photons didn't decouple yet, though. Exactly when this happened is a somewhat extended period of time, but can be taken to be the time when the mean free path of a photon is of the order of the size of the observable Universe. This happened around when the Universe was $380\,000\,\mathrm{yr}$, at which time it had cooled to $3000\,\mathrm{K}$, or $2\,700\,^\circ\mathrm{C}$. At this time the radius of today's observable Universe was still only around 40 Mlyr, while the observable Universe at that time was still less than 1 Mlyr.
The diameter of the Universe reached 100 Myr much later
When the Universe was roughly half a million years old, the radius of today's observable Universe had expanded to 50 Mlyr, so its diameter was 100 Mlyr. But firstly, this was quite a lot later than the recombination/decoupling, and secondly it doesn't make much sense to refer to the size of today's observable Universe, since that had no physical significance at that time. The radius of the then's observable Universe didn't reach 100 Mlyr until the Universe was almost 20 million years old
Summary in a figure
The figure below shows how the progression of recombination, from ~100% ionized gas when the Universe was around $200\,000\,\mathrm{yr}$, to ~100% neutral gas when it was $\sim 400\,000\,\mathrm{yr}$. I calculated this by solving the Saha equation assuming a pure hydrogen gas, i.e. neglecting helium, but this is a minor contribution so I think it should be okay.
Along the line you see corresponding temperatures in red, and ratios between the photon mean free path and Hubble distance (~size of the Universe) in green. When this ratio is of order unity, photons decouple. The secondary $x$ axis show the corresponding redshift.


Are there currently any planned or proposed missions to measure the gravitational fields of other planets in our solar system?

There are no such missions in an advanced state of planning, however we do have a good idea of the gravity field around Mars, gleaned from observations of anomalies in the orbits of the various orbital probes.

These data were gathered into a map of the gravity field of Mars

According to that NASA article:

  The map was derived using Doppler and range tracking data collected by NASA's Deep Space Network from three NASA spacecraft in orbit around Mars: Mars Global Surveyor (MGS), Mars Odyssey (ODY), and the Mars Reconnaissance Orbiter (MRO).

The research is published as Antonio Genova et al. 2016, Seasonal and static gravity field of Mars from MGS, Mars Odyssey and MRO radio science, Icarus, vol. 272, pp. 228-245; doi: 10.1016/j.icarus.2016.02.050

In addition, the Cassini Spacecraft has made detailed gravitational measurements of Saturn and and along with imaging, internal structure details of its moon Enceladus. Also the Juno Spacecraft has made detailed measurements of Jupiter's internal structure via maps of it's gravity field as well.


As one might expect,  wikipedia is our friend:

the resulting supernova explosion expels much or all of the stellar
material with velocities as much as 10% the speed of light (or
approximately 30,000 km/s). These speeds are highly supersonic, so a
strong shock wave forms ahead of the ejecta.


What does it mean to say 'space exists?'

This is a very complex question, and perhaps more appropriate for the Physics or Philosophy stacks. I will attempt to give you an initial direction, but really I think this is too broad for this stack. I'm merely writing here because comments are too short.

In a very practical way, space is simply that which allows objects and events to have relative position, direction, and extent. There is still disagreement over whether space is a thing in itself, or merely a relationship between things, or part of a conceptual framework. See wiki

In relativity, the dominant concept is not space, but spacetime - closely related to a fundamental constant of the universe (speed of light) and to gravity. Space itself, or time itself, are less important, but the 4-dimensional metric of spacetime is far more fundamental, in a sense.

  Does it exist in the same way substances exist?

We don't know. See the wiki link for the philosophical debate.

  what do we mean by 'space exists?'

It means this universe is built in such a way as to allow relationships of position or direction. This is a bit of a circular definition, but it's the best we have.

  What does it mean for space to be created?

Actually, that happens all the time, even now. The so-called dark energy actually makes more space, continuously, even now. That simply means that, whereas a while ago there was X amount of distance between galaxies A and B, now there's X + Y amount of distance. The low-level mechanism that allows this creation is not well understood.

It could be imagined that something similar happened during the Big Bang, except it started from zero. Again, the low-level mechanisms around the origin are not well understood. To understand that we first must be capable of understanding something far more simple - the physics of the center of a black hole. To do that, we would need something like quantum gravity, which is a part of Physics that has not been invented / built yet.

If this seems overly speculative, it's because you're asking a very profound and difficult question - so difficult that it exceeds the limits of current science and even philosophy.


How to configure Celestia to work with a spherical mirror projection on a dome

According to Paul Bourke's page on screen capture

  While only the commercial version of Celestia supports fisheye, it also does not support warping of fisheye (although some versions have been created that do). The solution outlined here has been tested successfully with a fisheye supported version of Celestia.

It seems that Celestia in its free version is not providing any support for dome projection and the commercial version requires tweaking before you can use its support for fisheye projection and convert it to Spherical Mirror Projection.


By "visible to the naked eye", I take it you mean "visible from Earth with a small telescope".

Saturn's rings are largely water ice, and so they reflect more sunlight back to us.

Jupiter's rings, have lower proportions of ice, and lots of smaller dust particles that tend to scatter light forward rather than back to us.

The ring systems of Uranus and Neptune are made of really dark material, so also don't reflect much light in our direction.


Names of specific galaxies in Hubble's XDF

The XDF data release
has images in FITS format, which includes a world coordinate system to map image coordinates to celestial coordinates.
Then you can query SIMBAD
to see what galaxies are near those coordinates.

For example, I loaded a WFC 60mas/pixel image into a FITS viewer,
which indicates that the face-on spiral at center left of the PR image
is near J2000 3h32m40.8s -27d46m16s.
(To align the PR image with the equatorial coordinate grid, rotate it about 50 degrees clockwise.)
SIMBAD found this galaxy at that location, B-band magnitude 22.

To do this in Python code, you could try using
astropy.wcs
to get celestial coordinates from the FITS image and
astroquery.simbad
to look up objects of interest.


There should be nothing special about crossing the "event horizon" - the line beyond which light cannot escape and so, in theory at least, one might "travel into a black hole" and not be aware of any physical changes at all.

However, I suspect what you mean is what would happen if one travelled to the centre of a black hole. Here we may speculate but our current theories of physics breakdown at this "singularity" and so we cannot know - nor is it easy to think of how we might design an experiment, given our currently available technologies, to test any theory we have.


What would the night sky look like if the Milky Way were the only galaxy in the universe?

I feel sure this is a repeat, but couldn't immediately find it. The only things in the night sky we can see (with the naked eye) that are not part of our own Galaxy are (on a good night) the Andromeda galaxy and the Large and small Magellanic clouds. Every individual star brighter than $V=6$ and visible to the naked eye is in the Milky Way.

So it would hardly look any different.


What is the long term fate of the gas giants?

The timescale on which Jupiter cools is reasonably well understood and predicted by the current generation of evolutionary models.

Jupiter's luminosity is provided mostly by gravitational contraction. For a planet that only contains gas governed by the perfect gas law, the appropriate timescale for this contraction (or indeed for the luminosity to fall significantly) is given by the Kelvin Helmholtz timescale.
$$ \tau = \eta \frac{GM^2}{RL},$$
where $M$ and $R$ are Jupiter's mass and radius and $L$ is its current power output (or luminosity), and the parameter $\eta \sim 1$. This timescale is a few $10^{11}$ years.

However, giant planets like Jupiter are not governed by perfect gas laws. The gas in the centre of Jupiter is dense enough that electrons become degenerate. Degenerate electrons fill the available energy levels up to the Fermi energy. Their consequent non-zero momenta of the electrons exerts a degeneracy pressure that is independent of temperature. As a result, the rate of contraction slows and the release of gravitational potential energy slows; the planet is able to cool and remain in hydrostatic equilibrium without the same degree of contraction.

One can express this change using the $\eta$ parameter. For Jupiter $\eta \simeq 0.03$ (Guillot & Gautier 2014) - i.e. the timescale for the luminosity to fade is 30 times quicker than the naive Kelvin-Helmholtz time and Jupiter's luminosity will scale as the reciprocal of its age and will fall by a factor of a few in $10^{10}$ years. In a trillion years, the luminosity of Jupiter will be lower than it is now by roughly a factor of 250.


How many asteroids are named after musicians? Is there a searchable list for this?

I don't think you can do better than search the wikipedia pages, where there is a list https://en.wikipedia.org/wiki/List_of_minor_planets_named_after_people. Or you can search yourself through https://en.wikipedia.org/wiki/Meanings_of_minor_planet_names, if you don't trust wikipedian's curation

But you may need to be quite subtle about how you search, since searching for "music" won't find those that are described as "composers", nor those who are "sopranos", or "violinists" and so forth.  There are also edge cases. William Herschel (who may have coined the name "asteroid") was also a classical composer of note. Or "644 Cosima", named after Wagner's second wife.  How about 1683 Castafiore, named for a fictional "musician"?


Lightning may have been detected on Mars, although it currently appears to be rare, and attempts to replicate the 2006 results have failed so far.
New research found that the low pressure on Mars might be the reason why lightning is uncommon.  The atmospheric pressure on Mars appears to be at a minimum for making lightning, as opposed to just coronal discharge. With less atmospheric pressure than it has now, more static charge would build up on each grain, making a sudden lightning bolt more likely.  More pressure, and there would be more grains flying around, building up charge more quickly and increasing the chance of lightning.  Thus the chance for a lightning bolt to happen, rather than just coronal discharge, is much lower than it is on Earth, and is in fact at a minimum.  This could explain why there has been only one detection so far.  Source


Is there a luminosity class for brown dwarfs?

The SIMBAD page for the binary brown dwarf Epsilon Indi B lists the components as T1V and T6V, indicating they use the normal dwarf luminosity class V.
There are also T subdwarfs, e.g. Burningham et al. (2014) give the spectral type of ULAS J131610.28+075553.0 as sdT6.5. This follows the usual convention I've seen where subdwarfs are written with a prefixed "sd" rather than using the Roman numeral luminosity class VI.
Schneider et al. (2020) also indicate that WISEA J041451.67-585456.7 and WISEA J181006.18-101000.5 are extreme subdwarfs, of spectral classes esdT0±1. Again this is indicated by a prefix ("esd") rather than a Roman numeral luminosity class. They also mention 2MASS 05325346+8246465 as being of spectral type esdL7.
Zhang et al. (2018) list a number of L subdwarfs (sdL), extreme subdwarfs (esdL) and ultra-subdwarfs (usdL).


What equipment do I need to measure the spectrum of a star?

Depending on the type of camera you use, you may be able to photograph stars without a telescope. I know that there are apps for cell phones that allow you to take long exposures, and there are some point-and-shoot cameras that have a "bulb" setting or allow multi-second exposures, and certainly an SLR-type will allow it. You'll need to stablize your camera thought.
Either way you can use either a transmission diffraction grating (glass or low-cost flexible film-type) or a wedge prism to disperse light into different colors.
If you use a free-standing camera, you can afix the dispersing element in front of the camera's lens. If you are photographing through a telescope you'll need to put it at the camera end. The disperser will usually spread light out by several degrees or several tens of degrees, so if you put it in front of the telescope lens the spectrum will be spread out way too far, unless you are using a very low-dispersion grating or prism specifically designed to be put in front of a telescope!
If the disperser partially covers the camera, then you'll get both an image of the star and of the spectrum. That's helpful to identify the position of lines, since you can measure the distance from the undispersed star to each line. If you use a grating that is not blazed or imperfectly blazed, then you'll get both +1 and -1 orders and you can measure the distance between the two appearences of a line without needing the central start, but it will be there anyway because most gratings will pass at least some of the 0th order.
Since the star light is spread out over a much larger area, the spectrum will be much dimmer than the undispersed image, so as you mention, you'll have to overexpose.
There's an example of a commercial product in the question Has anyone seen an actual spectrum of a satellite made by an amateur photographer?

I don't mean to advocate a commercial product, this is a handy example, and Tom Field is a contributing editor to Sky and Telescope magazine.

above: from here.

above: from here
See the FieldTestedSystems' YouTube video How to capture star spectra in your backyard


Why do Jovian moons fade when transiting Jupiter's shadow?

It's pretty simple, really. The shadow of Jupiter, just like the shadow of the Earth, is not razor-sharp. There is an intermediate region, called penumbra, where illumination is partial. This is due mostly to the fact that the Sun is not a mere dot, but has a measurable size. The fact that the planet itself does not have a sharp edge also contributes a small amount.

http://en.wikipedia.org/wiki/Umbra

Penumbra can be clearly seen during Moon eclipses on Earth. The next one is on April 15 - a few days from today.

http://eclipse.gsfc.nasa.gov/LEplot/LEplot2001/LE2014Apr15T.pdf

http://www.skyandtelescope.com/astronomy-news/observing-news/aprils-total-eclipse-of-the-moon/


You're envisioning the Big Bang as a cosmological "explosion" in space where the universe is the resulting material expanding in outward all directions.

The problem is, the universe doesn't work like that.

The universe isn't a region of space that is expanding outward into another thing where you can (even hypothetically) fly out to the border and say, "Yup, that's about all there is. Let's use these borders to find the center of this expanding sphere."

The Universe is literally everything there is: space, time, and everything it contains and ever will contain. And the word contains is even a bit of a misnomer in that it suggests a container with boundaries. But the universe is simultaneously both unbounded and finite at the same time. "Finite" refers to the fixed amount of stuff this universe contains (matter, energy, etc)… and unbounded because this thing we know as "the universe" has no borders in a sense that we point to or even experience. So how would you even define a "center"? There isn't one.

There's a famous way to help visualize an expanding universe that is both finite and unbounded without a center or borders; it's called "The Balloon Analogy." Imagine our friends in Flatland living in two-dimensional space… where everything they know (their entire universe) exists on the surface of a balloon. If you start to inflate that balloon (the expanding universe),  all the little astronomers on the surface will observe that all the surrounding galaxies are moving away from them — and the farther away those galaxies are, the faster they seem to be moving away.

That's pretty much what most cosmologists believe is happening to us.

Going back to that balloon analogy, picture yourself existing on the surface of that balloon-universe and ask these questions again — In my expanding universe (the surface of the balloon), where is it's center? Everything is expanding outward in all directions, so if we rewind back in time, certainly everything should converge somewhere, right? Can we just find the borders of this outward expansion and calculate the exact center? So basdically… "Do we know the exact spot where big bang took place?"

Be careful taking the balloon analogy too far, because it starts to break down in many ways. But the answer to where the expansion of the universe emanates from really is that it emanates from everywhere; everything we know is contained within the origin of our own existence, and there is no center and there are no borders by any definition of existence that we can experience.


How co-planar and co-rotatory are the Milky Way and its constituents?

As far as we know exoplanetary systems have orbital planes that are randomly distributed with respect to the Galactic plane. Indeed our own ecliptic plane is quite inclined with respect to the Galactic plane - as one can readily tell from the fact that the planets are not always seen against a background of the Milky Way.
Further details and some references can be found in answers to the related questions Detection of exo-planets and Do the axes of rotation of most stars in the Milky Way align reasonably closely with the axis of galactic rotation?


If galaxies are moving away from each other then why are the Milky Way and Andromeda galaxy coming towards each other?

The farther away, the faster the galaxies move away from us. But that's only the overall expansion of the universe. Locally velocities can differ and are to be added to the overall expansion. The Andromeda Galaxy is close enough to Milky Way to be able overcome the overall expansion of space. The Andromeda Galaxy and the Milky Way attract each other by gravity.

Hubble's law applied to Andromeda Galaxy/Milky Way returns an expansion of space of less than 70 km/s, since Hubble's constant is about 70 km/s/Mpc, and the distance is about 2.5 million light-years, less than 1 Mpc (= 3.26 light-years, see Parsec). That speed is slower than the about -300 km/s helio-radial velocity (space expansion already subtracted) of the Andromeda galaxy, hence feasible to overcome.


Different education systems differ, however

At school you would take maths and physics courses, at least covering calculus.

As an undergraduate, taking (or majoring in) physics. Also probably doing some more maths and perhaps some astrophysics courses.

As a postgraduate doing Masters study in astrophysics leading to PhD research in astrophysics.  By now you could say that you are an astrophysicist.

Then working at a university or similar institute.

This makes it all sound easy, but I think I should add a warning. Getting a permanent (research) position at a university or similar institute in astronomy is highly competitive, and to get there takes a combination of hard work, high competence, high motivation, and luck. Many highly competent people end up moving out of astronomy and use their skills elsewhere, for the simple reason that society does not spend enough money on astronomy to employ all highly competent people who want to spend their life on astronomy.


Should BD in this sector means Brown dwarfs or Black dwarfs?

Looking at the diagram as a whole, the bottom line seems to be the type of object that a star in that category will evolve into.  So a large star that is variable due to mass loss will explode in a type II SN and evolve to either a Black Hole, or a Neutron star (which may become variable as a pulsar but ultimately evolves to a non variable NS.
Looking down the right. We see "mass exchange variables (ie novae) and dwarf novae such as U Gem or Z And will ultimately evolve into one of three types of stellar remnant: Black dwarfs, neutron stars or black holes. Black dwarfs are the final stage of evolution of white dwarfs.
Therefore I surmise that BD means Black Dwarf.


The colour of saturn as it appears to the naked eye

Planets do scintillate, just much less often - it takes much greater turbulence to make them twinkle. I've seen Venus twinkle quite a few times, especially when it was close to horizon.

Light pollution makes no difference when observing the planets in the Solar System. They are far too bright to be affected by it.

Saturn should be an off-white when observed with the naked eye. That being said however, if the planet is close to horizon and atmosphere is turbulent, it can cause some weird color effects. But then the color would appear to change rapidly.

In any case, as someone else said in comments, no planet looks like a "ball" to the naked eye. They are all points of light just like the stars.

Check this guide, it should tell you the best method to locate Saturn these days (use the image at the top of the article):

http://www.skyandtelescope.com/observing/sky-at-a-glance/this-weeks-sky-at-a-glance-september-4-12/

If the object you're looking at is in the right place with regard to Antares and the other things in Scorpio, then it's probably Saturn, no matter what color it seems to be. Color is very subjective and can be modified by the atmosphere in some cases. Position is not subjective.

Don't worry too much about color. For comparison, Jupiter is a more pronounced shade of butter-yellow than Saturn, so that's less controversial, you don't see people argue about the color of Jupiter. But a lot of people see Saturn as plain white; I see it as off-white, the color of old PC cases.

If you can borrow some good binoculars, you should see the ring. Lean the instrument (or your elbows) against something solid (like a table or wall), try and keep the binoculars very steady, and watch the object. Be patient and hold steady. You should see the ring as a tiny streak across the planet, kind of like the letter phi: Φ. Just regular binoculars should be enough to make this observation, and it's pretty awesome when you see it for the first time.

In a bigger instrument the real shape of the ring becomes evident.


Is the Large Magellanic Cloud contained in the Milky Way?

The short answer is that the Magellanic clouds are not part of the Milky way; they are satellite galaxies of the Milky way.

The image below shows the Andromeda galaxy. Note the small extra galaxies, marked Messier 32 and Messier 110. They are not part of the Andromeda galaxy, but are satellites of it. They would appear like the Magellanic clouds of the Andromeda galaxy.


Seyfert galaxies differ from other active galaxies (most notably quasars) in that their galactic nuclei are lower in luminosity compared to the rest of the galaxy. Quasars have nuclei that easily outshine the rest of the galaxy. Seyfert galaxies, on the other hand, host active nuclei that do not outshine the rest of the galaxy by the same amount.

Interestingly enough, in his original analysis, Seyfert focused on emission lines, noting that in this class of galaxies, there are strong high-ionization emission lines present in certain parts of the spectrum. This alternate definition is also used today. LINERS (Low Ionization Nuclear Emission line RegionS) are very similar to Seyfert galaxies if this definition is used; they are differentiated because LINERS also contain low-ionization emission lines.

References:

Seyfert (1943)
Popping (2008)
A Knowledgebase for Extragalactic Astronomy and Cosmology: Seyfert Galaxies


Is the flat earth cosmology scientifically justifiable today?

I realize this queston might be closed, and perhaps this should've been a comment, but it got too long:
I was in a radio show last spring with a flat-earther. I really tried to understand him, rather than just ridicule him. We went to the beach with his 87x magnifying camera, to watch the coastline 19 km away. If my model of the geometry of Earth were right, we would be able to see the buildings on the other side of the belt, but not the shore. If his model were correct, I thought we would be able to see the shore, but it turns out they have an ad hoc explanation that has to do with the vanishing point on a flat Earth lying below the ground, thus making sufficiently distant objects disappear.
So, apparently this is their explanation.
When after five minutes I still didn't understand this, he told me it was no wonder that I didn't understand; it took him two  years to understand.
Well, big surprise, we couldn't see the shore. We could in fact see a bit more of the buildings than we should be able to if there were no atmosphere. I assigned this to refraction (which can actually move the horizon several tens of kilometers away, or even ~100 km over water in the springtime when the air is getting warm but the water is still cold), but since he didn't believe in refraction, that didn't convince him.
We then talked a bit about what mechanism might produce a flat Earth. The conversation sort of ended when I realized he didn't believe in gravity either…
Is a flat Earth scientifically justifiable today?
The question title has now been edited to a more easily answerable one. The answer is — unsurprisingly to most people on this site, I suppose — a big, resounding "NO"! The flat Earth theory is not a theory, in the scientific sense of the word. It's not even a hypothesis. You could call it a model, and in many cases, it's a fine model, namely on scales much smaller than the horizon distance. You may assume a flat Earth if you want to calculate the area of the parking lot. This is analogous to Newtonian dynamics being a fine model for small velocities and gravitational fields. It works fine if you want to calculate the force of an apple falling on Newton's head. But everybody knows it become less exact, the larger and faster the apple.
I suspect that the use of the word "theory" in everyday language influences how people think about science. "It's just a theory", they say, without realizing the enormous amount of work, experiments, verifications, and falsifications that go into building a scientific theory.
Flat-Earthers in general don't realize, I think, that in science you can't just assume that something works in another way, without this assumption having severe consequences for many other theories.
Why not?
The list of reasons that a flat Earth is incompatible with a range of well-established theories is long. Here's a subset:

Gravity

Gravity explains why a large mass becomes round. FE'ers have no explanation of why it could be flat.

Electromagnetism

The Sun and Moon are circulating 5000 km over Earth, held up by electromagnetic forces. This is completely impossible within the frames of the accepted theory of electromagnetism, but they don't propose a new theory of EM.

Astronomical distances

Standard trigonometry reveals that in their model, the Moon would look different from different places of Earth. It does, but much, much less than if it were 5000 km away (because it is in fact 400,000 km away)

Meteorology

The guy I talked to had no explanation for why cyclones rotate clockwise and counter-clockwise in the Southern and Northen hemispheres, respectively. The Flat Earth Society explains this by "The Wind Currents are put into gradual motion by the attraction of the Northern and Southern Celestial Systems, which are grinding against each other as gears at the equator line". I… I don't know what to say about this…

Constellations

The Southern Cross can be seen from Australia and South America. I'm in Oslo at the moment, which according to their world map is right in the middle between Australia and South America, yet I can't see the Southern Cross.

Satellites

FE'ers generally don't believe in Moon landings and space stations, but many satellites can be seen even with a relatively small telescope.

The disappearance of ships and other objects below the horizon.

Simple trigonometry shows that on a flat Earth, you should be able to see as far as the airmass allows you. On a round Earth, this is complicated by refraction, enabling us to see farther than if there were no atmosphere. But still, you can easily see how the Sun or Moon sets or rises partly below the horizon.

Lots of other inconsistencies

Stellar parallaxes.
The different weight of the same object at equator and the poles.
Eclipses (in particular the times at which they occur).
The movement of Jupiter's moons (which can be seen with a regular binocular).
Tides.

The problem is that there is no way to discuss these things with FE'ers. If you give an argument that they can't disprove, they will either claim that you're just wrong, or that "you think so because that's how you were schooled", or that you're a part of the conspiracy.
In particular the last point is important. Since the FE model, were it right, would imply that most of all physics would be wrong, that means that either

all physicists in the world are stupid, which makes it pretty amazing that we've made planes fly, computers work, bridges hold up traffic, compasses show us the way, as well as predicted stuff like Venus transits and the weather tomorrow. Or

all physicists are a part of a conspiracy, which would be equally amazing how none of the millions of physicists through history has confessed. Where's my bribe?!

Why am I not just ignoring them?
You may say that by writing this, I am just feeding the trolls, and giving people the impression that flat-Earthers are a problem for science. But in my opinion, the attitude that they hold toward science is much larger than just a few crackpots claiming what is obviously false. It's a symptom of something sad in our society, namely that "science is just one opinion, and my opinion is just a valid".
I acknowledge that scientists can tend to be cocky and should try to be more open to understanding why people don't believe us. But what makes a few people believe in a flat Earth is the same thing that
makes people deny that human activities affect the climate,
or makes them believe that vaccines are evil,
and makes some politicians get away with using a term like "alternative facts".


How will nearby galaxies some day expand beyond our horizon? (Neil deGrasse Tyson)

Assuming that Neil deGrasse Tyson is referring to the cosmic event horizon, he's right. But that doesn't really mean that galaxies "fall out of sight". He's right that they will disappear, but not because they leave the horizon.

Nearby galaxies don't disappear

First of all, there's a small thing to note that I'm sure he just left out to simplify matter a bit:

The Universe expands and drags galaxies along, but for galaxies that are sufficiently close, their mutual gravitational attraction keeps them "locked". Hence, we will always be able to see the galaxies in our Local Group. In the case of Andromeda, we will even end up merging, and I suppose that after a sufficiently long time, we'll merge with the other galaxies in our group, simply because we will keep orbiting around each other, so at some point we'll come so close so as to merge.

Galaxies don't leave the observable Universe…

Second, and more importantly, galaxies do not leave our observable Universe. The observable Universe consists of the region of the Universe from which light has had the time to reach us since Big Bang, and the "boundary" between the observable and the un-observable Universe is called the particle horizon. As time goes, the light from an ever-increasing number of galaxies will have had the time to reach us. This number will never decrease. Once inside our observable Universe, a galaxy will stay inside.

…but fewer and fewer galaxies will be able to send a light signal to us…

However, the distance at which galaxies may emit a light signal today, that we may receive some day in the future, only asymptotically increases to a finite value (of some 17 billion lightyears; see e.g. Davis & Lineweaver 2004), while the galaxies themselve continue to increase their distance. I suppose this is what Neil deGrasse Tyson refers to: Even though the galaxies we see don't vanish from sight, we will never see what's going on in them today.

…and in practice, even the ones we see now will disappear…

Moreover, even the galaxies that we do see will become increasingly redshifted until eventually all light from them will be in the radio regime. Furthermore, photons will arrive at a smaller and smaller rate, until for all practical purposes, they will be invisible to us.

…especially if $w>-1$

The above considerations hold true if the Universe expands, and accelerates, as we think it does. However, there is a possibility that the acceleration itself will increase in magnitude. If the equation of state $w$ of the dark energy thought to be responsible for the acceleration is smaller than $-1$, the distance to the point where the Universe expands faster than the speed of light may decrease indefinitely, such that galaxies will indeed leave the horizon. Eventually, even gravitationally bound galaxies will be separated, stars will be torn out of the galaxies, planets will be pulled from the suns and finally disrupted, culminating in a Big Rip.


First observation that the movement of a planet or asteroid in its orbit was affected by another planet?

My best guess: The late periapsis of 1P Halley in 1759.

In 1705, with the mathematical assistance of Issac Newton, Edmond Halley published Synopsis of the Astronomy of Comets which made the prediction that the comet observed in  1682 had previously been observed in 1531 and 1607 was the same object returning about every 76 years or so.  He included a rough estimation of the gravitational effects of Jupiter and Saturn, and predicted it would return in 1758.

From Wikipedia: Halley's Comet

  Halley's prediction of the comet's return proved to be correct,
  although it was not seen until 25 December 1758, by Johann Georg
  Palitzsch, a German farmer and amateur astronomer. It did not pass
  through its perihelion until 13 March 1759, the attraction of Jupiter
  and Saturn having caused a retardation of 618 days. This effect was
  computed prior to its return (with a one-month error to 13 April) by a
  team of three French mathematicians, Alexis Clairaut, Joseph Lalande,
  and Nicole-Reine Lepaute. The confirmation of the comet's return was
  the first time anything other than planets had been shown to orbit the
  Sun. It was also one of the earliest successful tests of Newtonian
  physics, and a clear demonstration of its explanatory power.

This predates the discovery of Uranus(1781) and Neptune (1846).


How gently could a comet/asteroid/meteorite "hit" Earth?

Yes, spacecraft do it all the time by using air resistance (and sometimes rockets) to slow down.
Meteorites enter the atmosphere at high speed, typically 10-70 km/sec, but the smaller ones are slowed by air resistance, so they typically hit the surface at just a few hundred kilometers per hour. Reference: http://csep10.phys.utk.edu/astr161/lect/meteors/impacts.html (that link is now dead).
As gerrit points out in comments, a sufficiently small micrometeroid, like a dust particle, probably could hit the surface gently.
Larger bodies are not affected nearly as much by the atmosphere. For any such body, the velocity at impact is going to be at least several kilometers per second. A body moving obliquely in the same direction as the Earth's rotation would have a slightly lower speed at impact, but the impact still could not be described as "gentle"; the Earth's rotational speed is still a small fraction of orbital or escape velocity.
Here's one way to think of it. Freefall trajectories are reversible. If you watch a movie of an incoming body in reverse, it still makes physical sense (ignoring air resistance). Any meteorite hitting the surface has to have been in deep space at some point before the impact. If there were a trajectory that allowed such a body to have a "gentle" impact speed, then it would be possible to start with the same body near the surface at the same "gentle" speed, but in the opposite direction, and have it reach deep space. Unless the meteorite has its own propulsion system, that's just not going to happen.
You can get to space with a lower starting speed by moving along with the Earth's rotation - which is why most rockets are launched to the east, to take advantage of that. Reversing such a trajectory can result in a slightly slower impact, but only slightly.


Would our galaxy appear as a spiral when seen from the Andromeda galaxy?

The "Galactic coordinates" of the Andromeda galaxy are l=121 degrees, b=-22 degrees.

That means the Andromeda galaxy is seen by us at an angle of 22 degrees to the plane of the Milky Way galaxy. Thus if you were at the Andromeda galaxy looking at the Milky Way, it would be neither face-on or edge on, but a bit closer to the latter than the former. You would still be able to see that the Milky Way had a spiral structure, because the plane of the Milky Way is much thinner than its diameter.

NB. This simple argument works because the Andromeda galaxy is more than ten times further away than the diameter of the Milky Way galaxy.


What is the current size of the SN1006 supernova remnant?

You were so close! The answer was actually given lower down on the Wikipedia page: roughly 20 parsecs. Since one parsec is about 3.26 light-years, we can calculate that that comes out to about 64 light-years, as this seems to corroborate. The outer layers of the remnant are expanding outward at an outrageous rate - 11 million miles per hour, according to NASA. I invite you to do the calculations to figure out how large it will be at a certain point in time.


A hybrid eclipse is one in which it is a total eclipse in some places and an annular eclipse is seen in other places.

As you may know, a total eclipse is one in which the moon completely covers the disc of the Sun; this allows the solar corona to be seen.  Usually the central disc of the Sun is so bright that the corona cannot be seen.  An annular eclipse is one in which the Moon is not quite "large" enough to completely block out the Sun - instead, a ring of the Sun's central disc can be seen around the Moon. This ring is too bright for the corona to be seen.  Photos of both eclipse types appear below.

Annular Eclipse (credit: Fred Espenak at www.mreclipse.com):

Total Eclipse (credit: Fred Espenak at www.mreclipse.com):

The type of eclipse is determined by the geometry of the Sun, Earth, and Moon.  Since the Sun and Moon are not constantly at the same distance from the Earth, their apparent sizes will differ. When the Moon is closer to the Earth it appears larger, and when the Sun is farther away it will appear smaller.  For this particular eclipse, the geometry is such that the western part of the eclipse's center line will see an annular eclipse, but the rest will have a total eclipse.


Eclipse Visible Light Not Dark as Expected

As seen in this comment, normal daylight is around 100,000 lux, but 10,000 lux is still considered daylight. So, unless you're getting close to 99%, it will still be fairly light outside.


Question about total absolute magnitudes of galaxies - negative or not?

The morphological properties of galaxies between 21 mag < I < 25 mag
  in the Hubble Deep Field are investigated using a quantitative
  classification system based on mea- surements of the central
  concentration and asymmetry of galaxian light.

Those are apparent magnitudes, not absolute.

The convention is to use $M_X$ for absolute magnitude and just $X$ for apparent mag (or m$_X$), where X is the bandpass symbol (U, B, V, R, I, J, L, H, K, etc).

And, the $V_T$ and $M_{V_T}$ (note the correct subscripting, which the authors failed to do) means the V band radial profile is extrapolated to infinite radius to give a total for the whole galaxy.


Pretty much every hydrogen atom that's in a glass of water has a proton that dates from 1 / 1000000 seconds after the big bang.  That's older than the cosmic microwave background, which dates from almost 400,000 years later.


Is TESS replaceable by gound-based-small-telescope arrays?

Depends on the wavelength ranges to be studied as well.  Quoting from the link you provided:

  The sole instrument on TESS is a package of four wide-field-of-view
  CCD cameras. Each camera features a low-noise, low-power 16.8
  megapixel CCD detector created by the MIT Lincoln Laboratory. Each has
  a 24° × 24° field of view, a 100 mm (4 in) effective pupil diameter, a
  lens assembly with seven optical elements, and a bandpass range of 600
  to 1000 nm

Atmospheric absorption has some serious peaks near 750 and 920 nm, which is one reason to place these cameras in orbit above the atmosphere.


Why is space-based VLBI scattering sub-structure "Hopefully, a new promising tool to reconstruct the true image of observed background target(s)"?

It is well known that the study of pulsars is hampered by the scattering effect - the distortion of radiation during the passage of the interstellar medium. Even very compact pulsars look like lanterns in fog. It is clear that this effect should be observed when studying not only pulsars, but also other radiation sources. And here Radioastron plays its role. The pulsar, like a lighthouse, illuminates the Galaxy, and the interstellar medium, like fog, blurs its image. "Radioastron", in turn, "filters" this radiation. It turned out that against the background of blurry images of objects in the Universe, there are ultracompact specks - a scattering substructure. Accordingly, the effect of the fine structure of scattering discovered thanks to the space interferometer will help to understand the nature of the turbulence of the interstellar medium, to determine the distance to the clouds, causing scattering of radio waves. This is a significant contribution to astrophysics and is interesting in itself. Today we already have a better understanding of the physics of turbulent flows in the interstellar medium. And most importantly, if we do not correctly interpret the results of studying the Universe, we will be able to correctly interpret the results of observations.
At the center of our Galaxy is a massive black hole - about 10 million
times heavier than the Sun. It is simply necessary to study it, but
scattering of radiation interferes with it. Note that the study of
black holes in modern astrophysics is one of the fundamental,
fundamental problems. Scientists solving them now know about the
effect of scattering substructure discovered by us and take it into
account in their works. Moreover, having obtained a true picture of
the spots of the scattering substructure, it is possible to restore
the true image of the object hidden from us behind the scattering
screen. This opens up tremendous opportunities for astrophysicists.
There are already results: a significant number of publications have
appeared in leading scientific journals describing observational data
on the scattering substructure and mechanisms for reconstructing true
images of space objects.

Lighthouses in the sky. It is difficult to study our Galaxy without “illumination”.
https://poisknews.ru/magazine/20721/


Equating critical energy density to matter density

By the mass-energy equivalence:

$E = mc^2$

If $E = 5500$ $\mathrm{MeV}$, then:

$m = \frac{E}{c^2} = 9.8 \times 10^{-27}$ $\mathrm{kg}$.


Hot and "warm" Jupiters expelling terrestrial planets?

It's not proof that they've ejected other inner planets, because there are plenty of other explanations for why we haven't observed companions. Steffen et al. (2012) analyzed Kepler data - likely some of the same examples you've looked at - and came up with several explanations besides the no-companions-because-of-planet-planet scattering hypothesis:

Inner planets never formed. It's possible that mechanisms in systems with hot Jupiters prevent inner planets from forming; the authors are unclear as to what those mechanisms might be.
The planets are too small to see during transits. This is the first explanation based on detection bias. Obviously, Kepler has its limits, and it's entirely possible that the systems have small bodies it simply can't detect.
The planets are too low-mass. It is possible that there may be planets with masses so low that transit-timing variations (TTVs) are too small for Kepler to see them.
The planets have high mutual inclinations. In other words, there might be planets with orbits highly inclined with respect to the hot Jupiters' orbits; we only detect the ones at inclinations favorable to detection from our angle.

The options the authors suggest rest mainly on experimental biases as opposed to theoretical possibilities.

Something I was confused about when I read your question was the assumption that hot Jupiters migrate mainly due to planet-planet scattering. Levison et al. argue that warm Jupiters (i.e. giant planets with semi-major axes of about 1 AU) are more likely to have migrated via planet-planet scattering, because it provides a stopping mechanism via damping, assuming the planetesimal number density scales appropriately. This happens when the energy needed to move planetesimals from their orbits is greater than the energy lost from the change in the planet's orbit. Given that planetesimals cannot survive long in orbits less than about twice the stellar radius, warm Jupiters reach semi-major axes no lower than 0.03 to 0.1 AU (see Murray et al. (1998)).

Hot Jupiters, on the other hand, may be driven largely by Type II gas disk migration, where giant planets create a gap in a protoplanetary disk that subsequently brings in material; this then brings the planet closer to the star, eventually leading to a hot Jupiter. Here's a visualization, from Planet Hunters:


Do Stars in Galaxies also move in elliptical orbits?

Planets orbit the sun in approximately elliptical orbits. The orbits of the planets are perturbed by each other, particularly by Jupiter. So the shape of orbits are very nearly, but not exactly elliptical.

A simple elliptical orbit is found when there is a single dominating mass, for example in the solar system the Sun is much more massive than the rest of the solar system put together.

Stars in galaxies do move. However, they don't move in simple elliptic orbits for the simple reason that the mass of a galaxy is not concetrated at a single point. There is a supermassive black hole at the centre of the galaxy, but although it is massive, its mass is dwarfed by the mass of the rest of the galaxy (it has a mass of about 4 million suns, the galaxy has a mass of 600000 million suns.) The stars move in orbits around the centre of mass of the galaxy, to which the black hole contributes only a very small amount. The shape of the orbit is a "wavy circle". It is not elliptical, and so doesn't have foci.


What spectral type of star has an absolute magnitude of exactly 0?

There isn't a one-to-one relationship between spectral type and absolute magnitude.
Instead, there is a mean relationship with a fair bit of scatter around it. The reason is that the luminosity of a star of a given effective temperature depends on its composition/metallicity and how far along in its main sequence lifetime it is.
Basically, late B-type main sequence stars (say B7/B8V) have an absolute magnitude of about zero. Alternatively there are low mass stars ascending the hydrogen shell burning giant branch (types of about K2-K5 III) that would have an absolute magnitude of zero.


What are the nearest galaxies I can observe?

The nearest one is the one you are on: Milky Way. It can be seen from any place, as it is all around us.

If you want to actually look at a whole galaxy in a simple view, then the nearest galaxies easy to be observed are the Small and Large Magellan Clouds, and the Galaxy of Andromeda.

There are galaxies nearer that those, but harder to be observed. A quite complete list is at https://en.wikipedia.org/wiki/List_of_nearest_galaxies


How can we learn the inclination of the orbiting plane of the exoplanets using radial speed method?

I assume you are talking about the radial velocity method.

Analysis of a radial velocity curve yields the minimum  mass of a planet $M \sin i$, where $M$ is the true planetary mass and $i$ is its orbital inclination (90 degrees would mean the orbital plane is in our line of sight).

In general, with no other information that's all you can say. In principle $M$ could have any value $\geq M\sin i$.

Of course increasingly small values of $\sin i$ are increasingly unlikely and the average $\sin i$ of a randomly oriented population is $\pi/4$.

If you see a transit then you know that $i$ is close to 90 degrees and can in fact estimate $i$ from the transit duration.

If you measure the star's rotation period and can estimate it's projected equatorial velocity from spectral line broadening, then you can estimate it's inclination to the line of sight. One could then assume that the planet orbits in the equatorial plane of the star and use the same inclination for its orbit.


Change In Direction of Asteroid Approaching Sun

No.

A body in orbit will maintain its angular momentum, it will maintain its rotation rate as it is deflected by the sun. If it is not rotating then the deflection won't change the direction it is facing.

(There may be some minor effects that could cause a little rotation but it won't "steer" to face forward.)


Why do black holes have jets and accretion disks?

When it comes to accretion disks, nothing is coming out of the black hole. That's just orbiting matter, though it is swirled around a bit by frame dragging. Even at high gravity, the ability to orbit around a massive body still exists. The gravitational force is already being "used up" to cause the orbiting (it accounts for the centripetal force), so there is no need for the gas to fall in.

As for jets, as far as I can tell there is no single explanation (I am not sure of this). One candidate explanation is the Blandford-Znajek process1

The following image is from Black Holes and Time Warps: Einstein's Outrageous Legacy, by Kip S. Thorne:

Basically, most black holes rotate, and sometimes the intense rotation can cause forces that overcome gravity, even by a few orders of magnitude.

When a black hole spins, magnetic field lines anchored to it2 spin along with it. Plasma (from the accretion disk) is then flung out along these lines, similar to what happens when you put a marble in a conical cup and rotate it. This is depicted in the first image.

In the second image, current passes through the field lines (I do not understand this one as well as the first, however this post has a reasonable explanation), accelerates plasma with a mechanism similar to an electromagnetic railgun. This is another way of creating jets.

Note that the energy here comes from the rotational energy of the BH, not the mass-energy of the "contents" of the BH (which is lost to the universe unless we consider Hawking radiation)

(I shall have a closer look at the paper when I have time and update the answer accordingly. Comments appreciated)

1. Blandford, R. D., & Znajek, R. L. (1977). Electromagnetic extraction of energy from Kerr black holes. Monthly Notices of the Royal Astronomical Society, 179, 433-456.

2. While the no-hair theorem forbids a naked black hole from posessing magnetic field lines, one with an accretion disk may have them as the field lines cannot "escape" through the disk.