How massive does a main sequence star need to be to go type 1 supernova?

This is ground that is probably duplicated in a variety of questions here and on Physics SE, so I'll keep it brief. You have also mixed in several different questions.

The Chandrasekhar mass has very little to do with determining what initial mass of object will end up as what particular type of stellar remnant (or black hole).

Whether a star will end up exploding as a supernova depends primarily on its initial mass, but also whether it has a binary companions. There are (basically) two routes to supernovahood.

If the star is more massive than about $8M_{\odot}$ it will progress through several nuclear burning stages. The core of the star does not become degenerate and continues to get more dense and hot through each burning stage. It ends up as iron. Once the core mass of iron exceeds about $1.2M_{\odot}$ (which is the Chandrasekhar mass for an iron composition), then it collapses and we get a type II (core-collapse) supernova.

In this route a $3 M_{\odot}$ star gets nowhere near being able to go supernova. It will burn hydrogen and helium, produce a degenerate core of carbon and oxygen. This degenerate core can cool whilst maintaining the same pressure. The outer layers are shed through thermal pulsations and a dense stellar wind in the asymptotic giant branch phase, leaving behind a white dwarf. The relationship between the initial mass of the progenitor and the final mass of the white dwarf is not a straightforward fraction. It probably is about 50% for a star like the Sun, but the fraction is more like 15% for a $7M_{\odot}$ initial mass. The maximum mass of a white dwarf formed in this way is probably about $1.1-1.2M_{\odot}$ and some way below the Chandrasekhar limit for a C/O white dwarf ($\simeq 1.39M_{\odot}$).

The preceding paragraph is more-or-less what should happen for all stars between about $0.6 M_{\odot}$ (except they haven't had time to do so yet) and $8M_{\odot}$, except that there is a small "grey area" at the upper mass end ($7-9M_{\odot}$) where you might produce slightly more massive O/Ne white dwarfs.

Once a white dwarf has formed and if it is in a binary system, then the white dwarf could merge or accrete more mass. At some point close to the Chandrasekhar limit, it ignites. This causes a type Ia (detonation or deflagration) supernova explosion (or at least this is the leading model for how this works). This is really the only route whereby a star with initial mass $<8M_{\odot}$ could end up going supernova.


I have mulled over this a couple of times (it's a really interesting question!), and hopefully come up with a somewhat enlightening answer. I haven't been able to find a good, modern reference for these details (perhaps I just suck at literature searches...) so there's a little mucking around in the history books

The total timescale of evolution onto the main sequence for a protostar in the T Tauri mass range ( < 3 solar masses) is on the order (of magnitude) of several tens of millions of years. The ignition of fusion is not precisely a "runaway" reaction: however it occurs relatively quickly and once it starts, gravitational contraction quickly ceases.

The evolution of a 1 solar mass protostar follows these basic steps. Things are a little different for different masses - too complicated to explain here but the references should provide ample further reading!

A Jeans-unstable cloud of gas and dust begins to contract, exchanging gravitational potential energy for kinetic energy, and thus heat. The luminosity of the protostellar cloud increases as it collapses. It takes around 100,000 years for the initial period of rapid collapse to finish, at this point the cloud is very luminous (perhaps 20 solar luminosities and 8000K).
Over the next 1 million years, the protostellar cloud slowly contracts and cools to around 4500K. The protostar then travels down the Hayashi track, contracting further but changing little in temperature - its luminosity continues to fall. This is the stage where T Tauri stars are at. Most T Tauri stars are younger than 3 million years old.
The star then follows the Henyey track, where the luminosity begins to slowly increase again as a radiative zone develops in the star's core and it continues to slowly contract. This can take some tens of millions of years.
Finally, the conditions in the core are extreme enough for fusion to begin. The timescale from all the energy being provided by gravitational contraction to all the energy being provided by fusion, is on the order of 1 million years. The star's luminosity (counter-intuitively) decreases again when this happens, as the energy from fusion doesn't quite offset that from gravitational contraction, which ceases when fusion begins.

  Figure: the The Lg/L curve describes the amount of energy gained from gravitational contraction over the total luminosity of the star. The logarithmic time axis is in seconds (reproduced from Iben (1965), Figure 3).

  References:

I. Iben (1965), Stellar Evolution. I. The Approach to the Main Sequence
R. Larson (1972), The evolution of spherical protostars with masses 0.25 M_solar to 10 M_solar
L. Henyey et al (1955), The Early Phases of Stellar Evolution

  Interesting reading I came across for somewhat higher mass protostellar formation:

F. Palla and S. Stahler (1991), The evolution of intermediate-mass protostars. I - Basic results


What is the likely closest encounter for a typical star during the Milky Way Andromeda Merger?

Suppose the sun moves through a column of Andromeda stars $L$ parsecs long with density $\rho$ and random positions. The probability of encountering at least one star within $r$ of the sun along this column would be $$F(r)=1-e^{-\pi r^2 L \rho}$$ (basically, what is the probability of no "success" when doing a Poisson sample of the column volume times density).

Setting $F(r_{1/2})=1/2$ to find the distance where we should expect a 50% chance of a star more nearby we get $r_{1/2}=\sqrt{\ln(2)/\pi L \rho}$. If we plug in $\rho=0.14 $ per cubic parsec and $L=1000$ parsec (assuming a flat disk-disk collision) I get $r_{1/2}=0.02$ parsec. That is 4125.296 AU, reassuringly far.

To get the mean distance we can use the not very well known but useful formula $E[r]=\int_0^\infty (1-F(r)) dr =\int_0^\infty e^{-\pi r^2 L \rho} dr = 1/2\sqrt{L \rho}\approx 0.042$ parsec.

Depending on your views of disk thickness and angle on merger $L$ and $\rho$ may vary a fair bit. A sideways collision might have $L=67$ kpc reducing the distances by a factor of 8.1. Direct collisions still remain very unlikely, but messed up Oort clouds seem very likely.


When a neutron star accretes matter, will its mass increase?

The neutron stars have about 1.1 to 3 solar masses. If the neutron star accretes mass, its mass will increase and once it crosses the Tolman–Oppenheimer–Volkoff limit, the star will collapse to form a black hole.

On way of this happening is in the case where one of the binary stars becomes a neutron star as in X-ray pulsars. The neutron star receives gas supply from its companion, which increases its mass,for example CenX3.

Source: nasa.gov

Though this method could lead tothe formation of black hole, no observational evidence exists as of today.


What does Stephen Hawking mean by 'an infinite universe'?

Due to the finite speed of light, and the finite age of the Universe, only a portion of it is observable. When people talk about "the size of the Universe", "the number of stars in the Universe", etc., they usually refer to the observable Universe, i.e. the sphere in which we are centered, and which has a radius given by the distance light has been able to travel in the 13.8 billion years since the Big Bang. Note that since the Universe is expanding, this radius is more than 13.8 billion light-years. In fact it's 46.3 billion light-years.

Observations indicate that, on large scales (i.e. above roughly half a billion light-years), the Universe is homogeneous (the same everywhere) and isotropic (the same in all directions). Assuming that this is indeed true is known as the cosmological principle. If the rest of the Universe follows this principle, then there are three possible overall "versions" of universes that we can live in. We call these versions "flat", "closed", and "open". Whereas a globally closed universe would have a finite extent, globally flat or open universes must be infinitely large.

The observable Universe is, within measuring uncertainties but too a very high precision, flat (e.g. Planck Collaboration et al. 2016). Hence, we might think that the whole Universe is, in fact, infinite. But sort of like standing in a large forest with limited visibility doesn't tell you whether the forest is just larger than you can see, or if it's infinitely large, we can't with our current theories and observations know whether the Universe is finite or infinite.


Planets positions (azimuth, altitude) API

Astropy is one option:

from astropy.time import Time
from astropy.coordinates import solar_system_ephemeris, EarthLocation
from astropy.coordinates import get_body, get_moon
from astropy.coordinates import SkyCoord, EarthLocation, AltAz
from astropy import units as u
import time;

t = Time("2019-08-11 11:00", scale="utc")
loc = EarthLocation(lat=38.2464000*u.deg, lon=274.236400*u.deg, height=0*u.m)

with solar_system_ephemeris.set('jpl'):
  moon = get_body('moon', t, loc)

altazframe = AltAz(obstime=t, location=loc, pressure=0)
moonaz=moon.transform_to(altazframe)

print(moonaz.alt.degree,moonaz.az.degree)

If you want a library you can ship with a product, you'll want something much smaller.  I am actually working on a library converted to many different languages to do just that.
 Only the JavaScript version has a working Alt Az example, but it should be easy to convert to other languages (and will be eventually).


What is the LSST now? Where does LSST end and Vera C. Rubin Observatory begin?

The LSST Project is in charge of the construction project; building the telescope, camera and observatory and data pipelines and act as the "prime contractor". This includes designing and setting up the data processing and data distribution but the Project's job is essentially "done" once things start operating and the observatory transitions into regular operations. Once the Project delivers the observatory and it's signed off as complete, then the day-to-day operations transitions over to the NSF’s National Optical-Infrared Astronomy Research Laboratory. They will manage LSST along with other ground-based assets such as the (former) NOAO telescopes and the two Gemini telescopes. They will be the ones in charge of making the survey actually happen and keep functioning.

The Project was setup by the LSST Corporation LSSTC website which represents the institution and international partners, works with the Science Collaborations and is generally in charge/supports getting the science out of the observatory.

So as per the press release, the now named Vera C. Rubin Observatory consists of the mountain top facility in Chile which contains the 8.4-m telescope, now named Simonyi Survey Telescope after an early donor who got the primary work started, the commissioning camera (ComCam) and the main 3.2 Gpix DOE LSST Camera, along with Auxiliary Telescope and its dome and the headquarters in Tucson, AZ. This will be carrying out the 10yr sky survey, now backronymed to be Legacy Survey of Space and Time (LSST) to keep the same acronym.


The site to which you are referring is Sarmisegetusa in old Dacia, which was a well known royal citadel of the Illyrians in Roman times.

Sarmisegetusa was a fortress, not an observatory. The reconstructed posts there were used to hold up ceilings and walls.

Sarmisegetusa backs up against face of the mountain, so half of the horizon cannot even be seen from the site. That fact alone excludes the possibility that anyone was doing any astronomy there.


The paper describing this finding is van Dokkum et al. (2018). In a galaxy, the ratio of the stellar mass $M_\star$ to dark matter mass $M_\mathrm{DM}$ is normally very small, increasing with mass until Milky Way-sized galaxies where it reaches $\sim1/30$, then decreasing again.
But the dwarf galaxy NGC1052–DF2, seems to contain little or no dark matter. Galaxies of that mass ($M_\star\sim2\times10^8\,M_\odot$) typically has several hundred times more DM than stars.

How the galaxy was formed is not known, but the authors speculate on a few different mechanisms that all have to do with the fact that gas, in contrast to DM, may cool and condense and thus form clouds of very high $M_\mathrm{gas}/M_\mathrm{DM}$ ratios:

NGC1052–DF2 is located neat an large elliptical galaxy (NGC 1052) which could have gone through a merging event, tidally stripping a chunk of gas from one of the mergers. This is consistent with NGC1052–DF2 having a large velocity wrt. the elliptical.
NGC1052–DF2 could have formed from low-metallicity gas that was swept up in quasar winds (as described in Natarajan et al. 1998).
Lastly, NGC1052–DF2 could have formed from the fragmentation of gas accreting onto the elliptical, possibly aided by shocks.

EDIT (thanks to @WayfaringStranger): A fourth possibility is that the authors have misinterpreted the data. Shortly after the paper was put out, several other papers criticized the statistical methods used by van Dokkum et al. to infer their result (Martin et al. 2018;
Famaey et al. 2018;
Laporte et al. 2018).
van Dokkum wrote in a very long reply on his blog how at least the first of these papers actually confirm, rather than refute, his results. I am not enough of a statistician to comment on who's right and who's wrong, but note that there is currently an ongoing debate on the Facebook group astrostatistics.

You also ask whether the lack of DM is related to its "lack of stars". I wouldn't say that NGC1052–DF2 "lacks stars", anymore than the Milky Way "has too many stars" — it's just a small galaxy. But in general, the smaller a galaxy is, the larger the scatter in the $M_\star/M_\mathrm{DM}$ ratio is. Small galaxies, or small clumps of gas, have shallow gravitational potentials, so a small galaxy can more easily get stripped of gas, and a small chunk of gas can more easily escape a galaxy, or accretion stream, without attracting dark matter. In contrast, if would be very hard to conceive a very large galaxy having a considerably different $M_\star/M_\mathrm{DM}$ ratio, and indeed the scatter for massive galaxies is less than a factor of two (e.g. More et al. 2010).


How is IR spectroscopy used to determine the composition of asteroids?

It uses the same fundamental conept of mapping between emission-line wavelengths to certain transitions. Similar as we know that 21cm line is the transition of spin-flip of a neutral hydrogen.

Infrared (IR) regions is typically where the molecular lines are seen. Wikipedia has good and brief discussion.

Asteriods are cold so we expect molecules to form. Therefore, we expect to see lines in IR region the most. To be more specific, surface temperature of asteriod is ~346 K, which is equivalent to ~83714 A at max emission (assuming blackbody radiation and following Wien's law); this is IR.

Also note that, what we see is the surface of the asteriod, not the inside.


Does the sun have a feature like the red spot on Jupiter?

The Sun has lots of features "like the red spot", but they are dissimilar too.

Similarities: The Sun's photosphere - the bit we can see - is entirely gaseous; the photosphere rotates differentially with solar latitude; the gas is turbulent. There are features that can be seen quite easily - these are the dark magnetic sunspots, typically of size a few thousand km; and the pattern of bright points surrounded by dark lanes, known as granulation, typical sizes of order 100 km.

These features are associated with the convective upwelling of hotter material from below. In sunspots that process is inhibited by magnetic fields so that the surface temperature is lower and that area looks dark in comparison to the rest of the photosphere. Granulation is the visible appearance of the tops of the upwelling convective cells.

However, these phenomena are short-lived compared with the GRS on Jupiter. Sunspots have lifetimes of maybe a month or two and then the magnetic fields are reordered by the Sun's differential rotation and sheared apart. Granulation is ever present but the detailed pattern shifts on timescales of hours as different convective cells rise and fall.


The main flaw with your definition of a "generalised planet" would be the boundary between stars and planets. And, in particular, the status of brown dwarfs, that are kind of "failed stars", that could not start to burn their hydrodgen.

With this regard, the definition of a planet as it is now is probably the best one (or the less worst one), because it is then possible to draw a line between planets and stars (and in particular brown dwarfs), because a planet is then an object formed by accretion in the debris material of a forming/newly formed star, whereas a star is, in general, an independent object formed by collapse and accretion (there are now observations of forming brown dwarfs; see for example the review by Luhman (2102) or the recent paper by André et al. (2012)). So you have two types of celestrial objects, well defined by two types of formation mechanisms (core accretion for the planets vs. gravo-turbulent collapse for the stars (brown dwarfs included). Then you can also clearly distinguish between "real" free-floating planets (that are then planets expelled from their orbit and floating around in the galaxy) and brown dwarfs (that form independently, where they lay).

Bottom line: if your object, in any environment (including any type of accretion disk) is form by core accretion: it is a planet. If your object is form by gravitational collapse (with a later, unavoidable phase of accretion onto the central object): it is a star.


Could an object, assuming possible, escape black hole by travelling above constant speed?

Assume it is possible to travel faster than c

We normally cannot use physics to answer questions about scenarios that break the laws of physics. But for this scenario, we can say that if the ship can travel backwards through time, then it can escape from the event horizon. Just about every FTL scheme can be used for backwards time travel, and as far as we know, backwards time travel is physically impossible.

Rather than thinking about this problem in terms of escape velocity, its better to think in terms of worldlines. The velocity of a body depends on the observer measuring it, and which coordinates they're using, and dealing with that stuff near a black hole gets tricky. The usual Schwarzschild coordinates break down at the EH, and different observers measure quite different things, depending on their location and motion.

Inside the event horizon of a Schwarzschild black hole, all worldlines travel towards the singularity, without exception. As you move towards the future, you move towards the singularity. So the reason you can't escape from inside the EH is that there are no paths that go outside the EH. Unless you can magically travel backwards in time, so you can follow an in-falling worldline in reverse.


Why are we so quick to proclaim the geological inhospitability of other planets based on extremely minimal information?

It is not simple to address all these points since they are simple expressions for complex processes.

1.) Mars's core is frozen

Translating frozen as solid. It is still unclear if Mars' core is solid or liquid, see @userLTK's answer: it is curently seen as being viscous. A liquid core could help maintaining a magnetic field. Mars has a very weak magnetic field that does not shield it like the earth's magnetic field does. This is adverse to the development of complex organic molecules and the basics of simple life. Maybe InSight brings us more insight into this one.

2.) Mars has no recent volcanic activity.

That appears to be incorrect. Mars has no plate tectonics that offer cycles (e.g.carbon). One can speculate that tectonis are helpful for a biologic evolution and complex life, offering renewal of needed elements, thermostats, being helpful in case of planetwide overfreezing, ... but this is debated and speculative.

There is possible polar volcanism and recent lava flows in the calderas of the Tharsis Montes (Olympus Mons and neighbours).

3.) There are no large deposits of carbonates or other carbonaceous minerals/materials on Mars.

There are carbonates, but not organic. That means that in the past organisms have not built up sequences of sediments like on earth. And it is true that remote sensing will not suffice for a qualified final judgement. But there is nothing more to do atm.

4.) The total quantity of water on Mars is less than 1% that on Earth.

Unclear, but probably not totally nonsensical. Though there is water, or rather brines. Water isn't exactly rare in the solar system. Mars probably had a water ocean early, but may have lost it qickly to space. Otoh it can be debated if amounts of water have been sequestered in the Martian mantle. This water could sum up to several meters worth of water coverage.

5.) A perchlorate layer covers the entire Martian surface.

Exaggerated, but perchlorates were found in samples of Marsian regolith and under UV radiation result in a bacteriocidal environment. No potatoes for Marc ...

6.) The soil of the Moon, Mars, and Venus would need to be massively modified to support plant life.

Well, that is indeed a belittlement. It is far beyond our capbilities to mobilize the necessary masses and energies. One could imagine greenhouses; and test runs have been/are being made in Antarctica. But who wants greenhouse stuff every day ;-). There is this study concluding that even if we could mobilize all the CO2 in all available reservoirs including the upper crust of Mars, that would only rise the atmospheric pressure by a few percent. Not enough to significally warm the atmosphere or walk around without a pressure suit (oxygene supply allways needed anyway).

7.) Venus was volcanically resurfaced in its entirety.

I have no idea, but so are large parts of Earth, constantly actually. But on the Venusian surface there are ~450°C and 95bar atmospheric pressure. The atmosphere is almost pure CO2. Excluding life until further notice is a valid guess.

8.) There are never any breaks in Venus's cloud layer, no matter how small or infrequent.

Ok.

We could address these points one by one and search for proper publications of data from spacecraft, remote sensing and rovers and apply the principle of uniformity (that's what NASA does, but don't use it as a religion ...) and discuss further. But this has all been done multiple times. All in all, for Venus the judgement "is dead" is pretty natural, given the conditions. Mars may have seen microbial life in its beginning, let's say its first few hundred million years (speculative !), but today this is unlikely, though not impossible. More data needed, as you say.


Sedna, VP113 and the likelihood of the PX/Tyche/Thelistos hypotheses

... raise questions about how much we know about the true (IAU definition) number of planets in our solar system.

Eight.

Question: Does the discovery of 2012 VP$_{113}$ and 90377 . increase the odds of some kind of planetary object on the edge of the known solar system (the Oort cloud)?

2012 VP$_{113}$ is a minor planet, that does not imply that it is a "planet".
90377 Sedna is a large minor minor planet, also not a "planet".
The Oort cloud has so many tiny objects that they upset each other's orbit, occasionally sending comets into our solar system. Part of being a planet is having an orbit and clearing your orbit; these objects do neither.

How could we find out if it is very cold and dark?

Every object in space affects the movement of every other object.
We can detect tiny black holes at a distance, they are cold and dark; detecting a new planet in our solar system isn't beyond our ability, there simply isn't one there.
It's not impossible for a large object to begin orbit of the sun and establish that it will orbit a reasonably fixed path (some wobble is OK, drastic changes in direction or too close to something large enough isn't going to maintain it's orbit (and clearing ability)).
Pluto takes 248.00 years (90,560 days) to complete an orbit. Discovered in 1930 it lost its status as a planet in 2006. If something appears out of nowhere it will take time for it to be approved, so no surprises in the next few years.

I mean, how many 90377 Sedna or 2012 VP$_{113}$ objects would we need in order to guess its position and location?

Objects very distant to each other affect each other to a much smaller extent that objects which are closer to each other. As time passes, observations and new calculations are made, results are confirmed, and it passes IAU committee approval something might be discovered and become a new planet, instead scientists are looking outside our solar system for exoplanets.
Beta Pictoris (β Pic) is the second brightest star in the constellation Pictor. It is located 63.4 light years from the Solar System. Scientists believe there are a few planets in orbit around the star.
"The planet companion around β Pictoris" (Oct 2010), by Anne-Marie Lagrange, Mickaël Bonnefoy, Gael Chauvin, Daniel Apai, Et al.:

Abstract
The β Pic disk of dust and gas has been regarded as the prototype of young planetary systems since the 1980s and has revealed over the years an impressive amount of indirect signs pointing toward the presence of at least one giant planet. We present here the recently detected first giant planet around this star. We show how this planet could explain some very peculiar features of the star environment (disk, spectroscopic variability), and how it constrains the scenarios of planetary system formation (timescales, mechanisms).

Scientists can see far and do look for planets, it's unlikely that there's a 11th planet that's been unobserved. They have nicknamed β Pic's planet "b". Here's its photo:

Reading about this topic, I don't know how to quantify the odds of finding:

PX (Planet X): An Earth sized body perturbing the orbits of 90377 Sedna, 2012 VP$_{113}$ and other similar objects.

There is support for the existence of the object, but under the IAU definition imposed by your question it hasn't yet met the requirements to become a planet. The announcement does not mean there is a new planet in our solar system. The existence of this distant world is only theoretical at this point and no direct observation of the object nicknamed have been made. The mathematical prediction of a planet could explain the unique orbits of some smaller objects in the Kuiper Belt, a distant region of icy debris that extends far beyond the orbit of Neptune. Astronomers are now searching for the predicted planet.

Thelistos: A super-Earth (about 5-10 Earth masses times a O(1) factor)

Misnomer. Deleted from Wikipedia, redirects to planet X.

Tyche: (Now disfavoured by WISE data, I think it can not be excluded if it is extremely cold and "dark") Gas giant (Neptune-like, Saturn-like, etc.)

Disproven. Does not exist.

Nemesis: A "dark star"/brown dwarf object.

128 Nemesis is an asteroid, the other Nemesis is a hypothetical red dwarf or brown dwarf, originally postulated in 1984 to be orbiting the Sun at a distance of about 95,000 AU (1.5 light-years). Thought to be somewhat beyond the Oort cloud, it's postulated to explain a perceived cycle of mass extinctions in the geological record, which seem to occur more often at intervals of 26 million years.

Which objects are defined as planets is precisely defined, there's only some overlap for non-planets:

Here is the text of the IAU’s Resolution B5: Definition of a Planet in the Solar System (.PDF):

The IAU therefore resolves that planets and other bodies, except satellites, in our Solar System be defined into three distinct categories in the following way:
(1) A planet$^1$ is a celestial body that
$\quad$ (a) is in orbit around the Sun,
$\quad$ (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and
$\quad$ (c) has cleared the neighbourhood around its orbit.
(2) A "dwarf planet" is a celestial body that
$\quad$ (a) is in orbit around the Sun,
$\quad$ (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape$^2$,
$\quad$ (c) has not cleared the neighbourhood around its orbit, and
$\quad$ (d) is not a satellite.
(3) All other objects$^3$, except satellites, orbiting the Sun shall be referred to  collectively as "Small Solar System Bodies".

1 The eight planets are: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.
2 An IAU process will be established to assign borderline objects to the dwarf planet or to another category.
3 These currently include most of the Solar System asteroids, most Trans-Neptunian Objects (TNOs), comets, and other small bodies.


V838 Monocerotis "light-echo" images morphed into nice video, but why so few original images?

To get time on the Hubble Space Telescope is a difficult, peer-reviewed process. The time is usually about ten times oversubscribed. The scientific justification to get more images must be more than "it would make a nice movie".

The submission of proposals for HST time is a confidential process; so I don't know whether the principal investigators for these images asked for more at different epochs and were turned down, or whether they thought this many images were sufficient for the science they wanted to accomplish.

There is no technical reason why they couldn't have obtained more images. In fact more images were obtained (see this link to the Hubble archive) at later epochs between 2005 and 2012. A problem I guess with incorporating these images into the movie sequence were that the light echo gets fainter, more diffuse and starts to exceed the size of the detector, which would necessitate more than one pointing. They were also taken with a different camera, which might raise aesthetic compatibility problems. I show below a fairly crude colour composite I extracted from the archive for an observation in 2007.


How would a celestial map for Callisto depict the paths of Jupiter, the Sun, etc.?

I'm not sure this answers your question, but I used Stellarium (free) to generate this image from Callisto's north pole (so its celestial north pole, in Draco, is overhead) with orbit trails turned on:

Unfortunately, the image is not only messy, but may be inaccurate, since Stellarium doesn't do a great job of plotting orbits long-term: Stellarium 0.10.4: planet orbits change over time?

So, I wrote https://github.com/barrycarter/bcapps/blob/master/ASTRO/STELLARIUM/callisto.ssc to create a video of the view from Callisto's north pole, but the results are fairly uninteresting: https://youtu.be/O2GHJM54uhQ and come with several caveats:

I assumed that Stellarium is accurate, not just in where it displays the planet, but also in how it determines Callisto's rotational orientation, and any other details required to depict Callisto's celestial northern hemisphere.
The video is in "starchart mode", which means the stars don't move. In reality, the stars would make a complete rotation about every 16.69 days. More specifically, in the video, Jupiter moves through the constellations. In reality, Jupiter would remain fixed (Callisto is tidally locked), and the constellations would move.
The one year (+ about 2 months) period I chose is not "representative" and does not repeat. There may be quite a few more interesting things happening after the period the video represents. In particular, note that the Sun takes about 12 years (Jupiter's orbital period) to travel Callisto's ecliptic, and only a fraction of that travel is show in the video.


I have experience using this telescope.  It looks like you can focus correctly if you get a good view of the moon.  You probably don't want more magnification (the Andromeda galaxy is comparable in size to the moon).  It is easier to get and keep targets in the field of view with a low power eyepiece, and I suspect that is your problem.

Start with planets.  Use your low-power eyepiece, 20 mm.  Jupiter is the easiest to see as a disk, but it is unfortunately close to the sun right now so it is low in the west in the evenings.  With your 20mm eyepiece, it should be quite obvious as a disk with satellites and you may be able to see bands.

Mars is quite prominent right now in the evening sky but it is smaller than Jupiter.  Still, with your 20mm eyepiece, you should be able to at least tell it is a disk (and a bright orange one) if you have it in the view of the eyepiece.  Once you have it centered in view of your 20 mm eyepiece, you can try switching to your high-power (6mm) and see if that reveals any more detail.  Markings on Mars or quite subtle; often it looks like a featureless orange ball.

If your night sky isn't that dark because you are close to a city with its outdoor lights, it can be a challenge to get a good view of even spectacular "deep sky" objects like the Andromeda galaxy.  Again, use your low power eyepiece and no Barlow lens.  The core of the galaxy is much brighter than the extended glow around it, so it can appear star-like.  Try looking at with "averted vision" (don't look directly at it, to use the more sensitive light-detectors towards the edge of your field of vision) to pick out the faint glow that surrounds the core.  If you go to a dark sky location (one where you can really see the Milky Way) the XT8 can give a pretty impressive view of the galaxy where the elliptical outer glow will fill the FOV of your low-power eyepiece.

If it is hard for you to travel to a dark-sky location, you can try buying a deep-sky filter.  This filter tries to block the specific wavelengths thrown into the sky by outdoor lighting.  It makes everything you see through the scope dimmer and kind of green, but it can improve contrast on galaxies and nebula by making the background sky darker.


Can Pluto and Neptune collide anytime in future?

It's hard to find a good 2 dimensional representation, but Pluto and Neptune's orbits don't actually cross.

In fact, the orbits (not the planets but the orbits) never get within 100 million miles (I remember reading that, but can't find a link right now).  This is because Pluto's orbit is on a different plane.   It's easy to represent in 3D, hard to draw in 2D, but when Pluto is effectively the same distance from the sun as Neptune it's "below" Neptune, looking at the solar system from a sideways point of view.   When it's on the same plane as Neptune's orbit, which it only crosses twice in one of it's years, it's further away from the sun.

Source_1 and Source_2 and Source_3

An astronomer diagrammed the 2 objects orbits for the next 4 billion years and they don't intersect during that time.  Source

But there is a quirk in the calculations.   Pluto's resonance with Neptune is probably long term unstable and because of this, it's orbit could be subject to variations that leave open a Jim Carrey's chance of hitting Neptune.   Source

It's very unlikely, because they're not on the same plane and they're not orbiting at the same period and they're currently in orbital resonance which they would need to fall out of to even have a chance, so it's a lottery ticket's chance of happening but it could theoretically happen, in a billion or couple billion years.

It's more likely that Pluto would fly past Neptune and have it's orbit changed, and even that's still a long shot.  The most likely scenario is that they never get close, at least over the lifespan of the sun, but if they do get close, Pluto could fly further out into the solar system or closer in due to gravity assist.   It might even hit Earth.   But, I repeat, this is crazy-long-shot territory, but I think it's worth mentioning that it's about as likely to hit one of the inner planets as it is to hit Neptune.  Jupiter being the largest, might have the best chance of being hit by Pluto.

The question is also answered here, but because everyone else was answering this question no, I wanted to point out that it's just barely possible but extremely unlikely.


How do I download PSRCHIVE and Tempo2 for pulsar timing on Mac Mojave?

The documentation is somewhat confusingly written. It refers to a $PSRSOFT_DIR as a shortcut to where you unpacked the tarball, which everything is done relative to but doesn't require this shell variable to be set. So there is 1 thing to do and then you can do 1 of 2 things.

The mandatory thing (as it says in the docs) is to copy the psrsoft/config/profile.example to psrsoft/config/profile and edit if necessary (I didn't need any changes but I'm running on pretty vanilla CentOS/RHEL 7; MacOS X may well be different). Then your two options are:

You can then manually "substitute in" for the unset $PSRSOFT_DIR variable e.g.  run /path/to/Downloads/psrsoft/bin/psrsoft psrchive when the docs say to run $PSRSOFT_DIR/bin/psrsoft psrchive
You can set PSRSOFT_DIR in your user's shell startup files such as ~/.bashrc or ~/.bash_profile (~ is a shortcut to your home directory which works on Unix/Linux and I assume MacOS X) by adding export PSRSOFT_DIR=/path/to/Downloads/psrsoft/. You should then be able to run the commands as shown in the documentation.


Was that actually a shooting star during the supermoon eclipse on September 27th 2015?

There are about 5 sporadic meteors visible per hour most nights, and since thousands of people were taking photographs of the moon that night, it is not impossible that someone captured a meteor in the same shot as the moon.

A couple of things it was not

It was not an unused satellite. When they re-enter you see a fireball as it breaks up, not a single streak, as here.
It was not "Nasa marking half-time". The object would have been visible from quite wide area (but not world wide, not even countrywide) But the association with the eclipsed moon would only have been visible from a particular location. Nasa isn't going to be interested in entertaining the  good folks of Yakima, at the expense of everyone else.

What it could be:

It might be a meteor. Normally you would see a brighter head as the meteor changes brightness as it falls, but if this was a 1/2 second exposure, that could have been cut off.
It could be a satellite, which appear to be a steadily moving star, and would look like a streak in a timed exposure. However, looking at Heavens above doesn't show any satellites near the moon at that time.
It could be a deliberate forgery.

I reserve judgement. One would need exact locations and timings.


Why bother looking for Earth-like planets?

The possibility of exploring exoplanets is so remote it is not a factor. We are interested in Earth-like planets as there is only one type of planet that we know can support life, and that is the Earth-like ones.

We are interested in Earth-like planets as they may provide a habitat for alien life. The question of "does extra-terrestial life exist" is of intrinsic interest.


What would be the sizes of the bodies created from Jupiter's trojans?

The mass of the Trojans (both camps as far as I know) is estimated at around 0.0001 Earth masses (reference) (Note that this number is debated). The density of them vary but the highest found is around 2.5 g/cm^3 (reference) Assuming that the composition is mainly rocky/icy with very little gas, the act of combining all of them should make a rocky/icy object with that mass.

The mass of Ceres is estimated to be 0.00015 Earth masses with a density of some 2.1 g/cm^3 (reference).

If we assume that the object made from the Trojans has the same density then they should roughly make an object the same size or slightly smaller than Ceres (about 1 % the mass of the Moon). Make that into two equal bodies and you have half a Ceres per group (so each smaller than Ceres) (assuming that there are the same mass of bodies in each group originally).

Given that there is much uncertainty associated with this, I would bet that the mass and size would be smaller than this.
Whether they would qualify as dwarf planets, I'm not sure. But they would have to be captured into the orbit rather than be formed there as I'm pretty sure the gravitational influence of Jupiter would prevent any coalescence and gravitational stability of the Trojans (though I could be wrong on this).


How can I estimate the initial luminosity of a SNIa given initial mass of Ni-56?

Nickel 56  decays to Cobalt 56 via electron capture decay, with a half-life of 6.1 days and a decay constant of $\lambda = 1.31\times 10^{-6}$ s$^{-1}$.
About 1.75 MeV of energy is lost as gamma rays and a further 0.41 MeV in the form of an electron neutrino (Nadyozhin 1994)
Let's assume that we are talking about the period of time after the initial detonation, where the fusion energy of carbon and oxygen is released and is sufficient to unbind the white dwarf.
Let's assume that apart from the very first few seconds of the supernova, that the envelope is transparent to neutrinos, so that energy is lost.
Let's further assume that the gamma rays are able to thermalise rapidy in the envelope, that the energy is able to diffuse to the "photosphere" of the expanding fireball in $< 6 $ days and that the work done in expanding any ejecta is also negligible. This latter may not be justified in a type Ia supernova.
The decay equation $N= N_0 \exp(-\lambda t)$, means the rate of gamma ray energy deposition will be
$$ \frac{dE}{dt} = 1.75\ \lambda N_0 \exp(-\lambda t) \ {\rm MeV/s}, $$
where $N_0$ is the number of nickel nuclei you begin with.
Let's assume about $0.5M_{\odot}$ of Nickel is produced (see Childlress et al. 2015, incidentally, this paper illustrates how complex this question really is). This means $N_{0} \simeq 1.1\times 10^{55}$.
Thus I make $dE/dt$ (assumed to result in the emergent luminosity), when $t=0$, to be
$2.5\times10^{49}$ MeV/s, or $10^{10} L_{\odot}$.
This value is about a factor of two higher than the average type Ia supernova peak bolometric luminosity measured by Scalzo et al. (2014), which were well modelled with nickel masses of around $0.5 M_{\odot}$. So I would suggest that one or more of the assumptions above (probably the one about no work being done on the ejecta) is a bit flaky. However, I also notice that the peak luminosity occurs about 2 weeks after the initial rise, so I would suggest that the "instant" reprocessing assumption is also incorrect and that the released energy is smoothed out somewhat so that a lot of the nickel has already decayed by the time you get to peak luminosity.


How to convert from Black body intensity to MJy/sr?

Part 1
On the one hand, ${\rm 1\, ergs\cdot cm^{-2}\cdot s^{-1} \cdot sr^{-1}\cdot Hz^{-1}} = 10^{-3} {\rm J}/({\rm m^2} \cdot {\rm sr})$ has basic dimensions ${\rm mass} \cdot {\rm time}^{-2} \cdot {\rm angle}^{-2}$ and is a radio brightness.
On the other hand, there is ${\rm 1 MJy}\cdot{\rm sr}^{-1} = 10^{-20} {\rm J}/({\rm m^2} \cdot {\rm sr})$ which has indeed the same basic units. A possible difficulties could be the conversion from Jansky to SI units: $1\, {\rm Jy} = 10^{-26} {\rm W} \cdot {\rm m}^{-2} \cdot {\rm Hz}^{-1}$ and (less likely) the fact that ${\rm M}=10^6$. This said, there is a factor of $10^{-17}$ between the two values.
Part 2
We start with ${\rm 1\, ergs\cdot cm^{-2}\cdot s^{-1} \cdot sr^{-1}\cdot cm^{-1}} = 0.1 {\rm W}/({\rm sr \cdot m^2})/{\rm m} $ which is easily identified by Wolframalpha as unit for a volume scattering emission coefficient. This is not the same as the expression in part 1. However, since you state that it is about Black body intensity, you can follow the argumentation of uhoh in the comments to convert from a wavenumber (given in ${\rm cm}^{-1}$) to a frequency (in ${\rm Hz}$).

However if you'd like to try it yourself, start with $f= c \lambda$, take the derivative to get
$$\frac{{\rm d}f}{{\rm d}\lambda} = -c \frac{1}{\lambda^2} $$
and rearrange to get
$${{\rm d}\lambda} = -c \frac{1}{\lambda^2} {\rm d}\lambda$$
derivative to get
$${\rm d}f = -c \frac{1}{\lambda^2} {\rm d}\lambda$$
and use $c \approx 2.9979\cdot10^{10} {\rm cm}\cdot{\rm s^{−1}}$. Use that to convert your number in ${\rm cm}^{−1}$ to ${\rm Hz}^{−1}$ [...]


What differentiates a "group of rogue stars" from a galaxy?

It is just a poor choice of words. The comment refers to a discovery paper by Ferguson et al. (1998), where they used a very deep image in the Virgo cluster to establish that there were an excess of distant stars compared with a control field outside of the cluster.

This excess of about 630 stars were all in one tiny HST field of view, so form a "group" in some sense, but there is no suggestion that these stars are not found throughout the Virgo cluster. Indeed subsequent work has found evidence for intracluster stars in other areas of the cluster (e.g. Durrell et al. 2002).


Did big bang happen only one time or it might happen again somewhere million time away from our observable universe?

We don't know it, because the question isn't feasible thus far to experiments or observation.

But it's possible to develop theories far beyond our observable universe, even far beyond the multiverse theories described here in Wikipedia. There exist theories about a tranfinite hierachy of meta-levels of theories in mathematical physics, each level comprising all possible theories on the level below (beyond any notion of infinity) and all their interconnections (including hierarchies of interconnections between interconnections). To explain this in reasonable detail would need hundreds of mind-boggling pages, at least. So I won't even try to explain more details. At the end it's not even clear, whether there is a difference between mathematics (including a transfinite number of meta-levels) and physics (including a transfinite number meta-levels).

The anthropic principle tries to answer the follow-up question "Why do we live in exactly this universe with exactly these laws of nature?". But this kind of answer isn't satisfying from a scientific point of view, when looking for cause and effect.

If you're looking for a final answer comprising everything: There is no, because the notion "everything" leads to paradoxa, when used in an absolute sense. (See Gödel's incompleteness theorems, if you need more details.)


Open access table of visible stars with magnitude, coordinates, and possibly color?

The Hipparcos catalogue by van Leeuwen (2007) contains all the information you require, plus estimates of distance from parallax. It is open and free to use for scientific purposes.

http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=I%2F311

The direct page that describes the catalogue contents and ftp site is http://cdsarc.u-strasbg.fr/viz-bin/Cat?I/311

The tables themselves are at ftp://cdsarc.u-strasbg.fr/pub/cats/I/311


Astrochemistry - what does freeze-out mean?

Freeze-out is indeed a chemical term. It happens in the midplane of accretion disks where density is high enough to block UV ionization/chemical dissociation and limit heating from the central star. No one seems to have gotten around to writing up a layman friendly article on the subject yet, but these refs give the gist:

Protostars and planets V

Accretion Disks 1: During Star Formation

Organic Matter in Space (IAU S251) Evolution of Organic Matter

From ref 2:


Simple question about the phases of the Moon

The length of one lunar month is (on average) 29.53 days. You don't need to use sidereal days, since dates are based on a day of the sun, not of the stars. The calculation is just division

So you just need to count the number of days between March 20 and June 22 etc.

There are 94 days between those dates. And 94/29.53 = 3.18 lunar months.  So the moon will be crescent, on June 22nd (about 2 days before first quarter).  The other dates can be calculated similarly.

As a rough rule of thumb (that ignores things like the 30-31 pattern) the date of the new moon is earlier by about one day each month. By this reckoning, we would expect new moon on about June 17, Sept 14 and Dec 11, with first quarter one week later, etc.


This website has a mathematical in depth analysis of the Apollo 11 translunar trajectory. It looks to be a reasonably reliable resource but I've only had a quick skim through so you should check on the sources cited.
There should be enough information there to make a computer program to calculate the orbits.


30.4 billion lightyears.

The current distance — i.e. the distance that one would measure if we froze the Universe and started laying out measuring rods — is called the proper distance, or physical distance, in astronomy. By definition, it corresponds today to another often-used term in astronomy, namely the comoving distance. While the former increases with time, the latter is defined in a coordinate system that expands with the Universe, and so is constant at all times.

That is, the comoving distance to EGSY8p7 was the same when the Universe was half the size of what it is today, but the proper distance was half of this.

For galaxies so distant as EGSY8p7, we don't measure distances directly. Instead we measure the redshift of some spectral absorption or emission lines, and then use a model of the expansion of the Universe to convert this redshift to a distance.

From the FLRW metric, the resulting distance today of an object at redshift $z$ is given by
$$
d_C = \frac{c}{H_0} \int_0^z dz' \frac{1}{\sqrt{\Omega_r(1+z)^4 + \Omega_m(1+z)^3 + \Omega_k(1+z)^2 + \Omega_\Lambda}},
$$
where $c$, $H_0$, and $\{\Omega_r,\Omega_m,\Omega_k,\Omega_\Lambda\}$ are the speed of light, Hubble constant, and density parameters of the various components of the Universe, respectively.

For $z=8.68$ and with the latest cosmological parameters from Planck Collaboration et al. (2016), this integral evaluates to $d_C = 30.4\,\mathrm{Glyr}$.

For $z\rightarrow\infty$, you get $d_C = 46.3\,\mathrm{Glyr}$, which is "the edge of the observable Universe", also known as the particle horizon.

Note though that EGSY8p7 no longer holds the redshift record. The galaxy GN-z11 (Oesch et al. 2016) has a redshift of $z=11.09$, corresponding to a distance of $d_C = 32.2\,\mathrm{Glyr}$.


Why doesn't this paradox disprove (some) multiverse quantum gravitational theories?

The answer to your question for brane cosmology is simply that gravity follows the inverse-square law. We don't feel the gravitational pull of, say, Mars because it's so far away. Any other universes are so unimaginably (all right, that's hyperbole) far away in comparison that any gravitational effects by the matter in them would be very, very, very, tiny.

A similar argument might be to say that an infinite series always goes to infinity because you keep adding on terms. But this is often not the case, as with the series
$$\sum_{n=0}^{\infty}2^{-n}=2$$
It is infinite, but it converges.


What is the Lyman Alpha forest Used For?

According to UCLA's web-tutorial Lyman Alpha Forest (Wright, 2004), there are many 'clouds' of gas between us and a distant quasar (as an example) that absorb

  ultraviolet light at the wavelength of the Lyman alpha line of hydrogen at a wavelength of 122 nm.

However, as the clouds of gas have less of a redshift than that of the distant quasar, then their absorption lines are less redshifted than the distant object - a cartoon example is shown below (from the UCLA website):

Now, the significance is of the forest is that it represents clouds that are smaller than the smallest galaxies, thus

  We can only see these very low mass clouds by the absorption they produce in the strongest line of the most abundant element: Lyman alpha. Thus by studying the Lyman alpha forest we can learn about the density fluctuations in the Universe on the smallest observable scales.

A similar explanation of the significance of the forest, is given by Quasars, the Lyman Alpha Forest, and the Reionization of the Universe (Mortlock et al. 2011) is

  quasars like ULAS J1120+0641 are bright and at high redshift, lower redshift intervening material can absorb some of their light, leaving fingerprints on the final spectrum that we observe on Earth. Because hydrogen is the most abundant element in the universe, it should come as no surprise that it leaves the most prominent spectral signature, in the form of a forest of absorption lines.

Specifically, of major significance is that Mortlock et al. (2011) state that

  The Lyman alpha forest can be used to trace this re-ionization of the universe.


Human color vision is based on three types of "cones" in the eye that respond differently to different wavelengths of light. Thus, not counting overall brightness, the human color space has two degrees of freedom. In contrast, the spectra of stars are very close to a black body, which depends only on effective temperature. As one varies the temperature, the color of a star should make a one-dimensional curve in this color space. Thus, unless some perverse shenanigans are going on, it is intuitive that we necessarily miss most of colors, i.e. there will be no stars of those colors.

Our Sun actually has a peak at about $500\,\mathrm{nm}$, which is a green. However, that's just the peak: since the Sun also radiates lots of light with shorter wavelength (bluer) and also longer wavelengths (redder), the resulting mixture doesn't look green to human eyes.

An image from wikipedia on the color of a blackbody of a given temperature:

Note that the colors at near edges of this color space aren't accurate, because the sRGB standard used in computers only covers a fairly small triangle portion of it. Still, that's a complication that's not very important here.


Angles of sunrise and sunset viewed from a surface anyway oriented

In other words, at what hour angle $h$ is the Sun's azimuth $\mathtt{Az}_s$ at a right angle to the wall's normal vector (84$^\circ$ or 264$^\circ$)?

Using these formulas, which I've checked, from
Wikipedia: Solar azimuth angle,
$$\sin \phi_s = \frac{-\sin h \cos \delta}{\sin \theta_s} \\
\cos \phi_s = \frac{\sin \delta \cos \Phi - \cos h \cos \delta \sin \Phi}{\sin \theta_s}$$
where $\phi_s$ is the Sun's north-clockwise azimuth,
$\theta_s$ is the Sun's zenith angle (90$^\circ$ - $\mathtt{Alt}_s$),
$\delta$ is the Sun's declination,
and $\Phi$ is your geographic latitude.
Then $\tan \phi_s = \sin \phi_s / \cos \phi_s$, and
$$\phi_s = \mathtt{atan2}(-\sin h \cos \delta, \ \sin \delta \cos \Phi - \cos h \cos \delta \sin \Phi)$$
This formula yields results consistent with the
NOAA Solar Calculator in my tests.
We need to solve for $h$, but how isn't yet obvious to me; maybe someone else can help?

Notes:

The relation between $\phi_s$ and $\mathtt{Az}_s$ depends on whether $\mathtt{Az}_s$ is south-clockwise, south-counterclockwise, or the more conventional north-clockwise.
$h$ here is the same as $\omega$ in the ITACA article.
As you observed, formula 3.7 is undefined for a wall facing due north or south.
I find their azimuth notation confusing (is AAZ an alias for AZS or something else?) and the $\alpha$ on the left side of equation 3.9 is a mistake.
I believe ITACA formula 3.11 is correct. If we let $\cos \theta_i$ = 0, it reduces to something like the above where the surface is vertical, but it has the same difficulty of solving for $\omega$.


Is a trefoil orbit around a trinary star valid?

Because you're asking for a spacecraft, there is some wiggle room because spacecrafts can make adjustments.   An orbit around the Moon isn't stable both because of proximity to a much more massive body (the Earth) and due to the Moon's unusual lumpiness, but spacecraft can and have orbited the Moon when the orbit of least change is selected around the Moon and the spacecraft is able to make adjustments.
In your scenario (which I'll get to in a second), and doing some bad math which I won't retype here, the trefoil orbit of the smaller body (green), if it's a spacecraft does work.  I'm not sure why anyone would need a spacecraft to have such an orbit, but in your 3 star system, a trefoil orbit like that with occasional adjustments does work.
The problem is, your 3 star system would never happen.
It appears to be 2 central stars (Yellow and Blue) in a circular orbit around each other with Pink, more distant, in a circular orbit around the Yellow-Blue barycenter.   That much is fine, though both orbits being near circular is unlikely, but for a 3 star system to be stable, it needs to resemble 2 separate Kepler orbits, because an actual 3 body orbit where the 3 bodies are all massive and close, is always unstable.   You did the central 2 stars orbit each other and the 3rd, star orbits the inner two, but your Pink star is too close.
Your Pink star is 289 distance from the barycenter of Yellow-Blue and Yellow and Blue are 84 distance apart for a ratio of 3.4 to 1.  That's too close to be realistic.  There should be some eccentricity as well.
As your system is set up, Pink would exert tidal forces on Blue-Yellow and the system would destabilize.  Granted, you could avoid tidal forces depending on your units and the distance in the system, if you make the distances that much greater than circular orbits become less likely.
A final point, while you've set up a system where Green passes neatly between the Yellow-Green barycenter and Pink over several orbits, over the long term that would inevitably destabilize.   Green is also in a retrograde orbit which is less common.   You've set up an interesting system, but you didn't run it enough times to see the long term outcome, so it's problematic for several reasons.  Even if you balanced it just right so that it runs for a number of orbits, your system is unlikely to happen the way you designed it.
That said, certain trefoil orbits might be possible at least for a reasonable amount of time.  What's required is a 3/4 resonance and two massive bodies.  If you want to view the trefoil from a fixed point or barycenter.   If you view from one of the orbiting bodies, then I can give you an example.   Titan and Hyperion kind of do it, though both orbit Saturn in simple Kepler orbits when viewed relative to Titan, Hyperion has a trefoil orbit.
Your example of a retrograde orbit that passes between the two central stars (Yellow-Blue) and the outer star (Pink) probably a lot more rare and less long term stable (I would think), but running long term simulations is the stuff of computers, not my rough calculations.
However, with so many asteroids and comets moving about, maybe something like what you've set up might be rare but possible, if you could find a 3 star system that somewhat resembles your system, and that might be the biggest problem.
I did some looking and most 3 star systems are defined as "binary" with "companion" that is, 2 stars that orbit each other and a 3rd more distant star that much more slowly orbits the 2 inner stars.   I only checked a few though.
You might try to recreate your system with the 3rd star - Pink, at least twice or three times as far away, to get a more realistic set of circumstances.  It doesn't look like you can enter resonance orbits in your input, but try to look for orbital periods that work out to 3 to 4.  Orbits often look like petals of a flower when viewed from the right vantage point, so an orbit kind of like your setup might happen in the right circumstance.


How do we know that supermassive black holes can gain mass by means other than merging with other supermassive black holes?

The idea behind the paper (Shannon et al. 2013) that article is based on is to measure the gravitational wave background (GWB) produced by mergers of supermassive black holes, and determine which models of SMBH merger histories can replicate the SMBH population and the corresponding gravitational wave background. In this paper, measuring the GWB is done using pulsar timing - in particular, using the Parkes Pulsar Timing Array and some supplementary data from Arecibo. A pulsar timing array (PTA) detects (or attempts to detect - we have nothing definite yet) gravitational waves by measuring when individual pulses from pulsars arrive at radio telescopes. Gravitational waves should change the times of arrival (TOAs), so if you have enough TOAs from a selection of millisecond pulsars, you can constrain the GWB spectrum's amplitude $A$ and its associated energy density $\Omega_{\text{GW}}$.
The authors applied the aforementioned methodology and then considered four different models of SMBH population synthesis to try and replicate the observational results. The one which involved mass growth entirely through black hole-black hole mergers at low redshifts was ruled out at the 91% confidence level by the pulsar timing array measurements, while the others were more favored. These other models generally included SMBHs growing by accreting gas. No single one is a clear favorite, but the authors were able to rule out substantial regions of parameter space, and these three models were certainly favored more than the pure black hole-black hole merger model.
I want to emphasize something here that wasn't emphasized in the article: That merger model is focused on SMBH growth at low redshifts, and in particular on the SMBH population evolution at $z<1$. Why? It's because this is where the dominant component of the GWB we detect today is expected to come from (see e.g. McWilliams et al. 2013), so it's much easier to say something about low-redshift populations based on PTA data. This is also why the group is interested in how the other models fare at low redshifts for doing things like replicating the quasar luminosity function at $z<1$.
I feel like saying that the pure merger model has been entirely "ruled out" is maybe a bit strong; fortunately, pulsar timing arrays have made major advances since 2013, and we have stricter limits on $A$ and a better understanding of SMBH populations. The 2013 paper used only 20 pulsars, but PTAs have easily more than doubled that number in the interim, and that's only going to increase in the years to come. At the same time, the other models are certainly strongly preferred. I can look into whether this particular analysis has been replicated with newer data.


If I know apparent planetary positions how do I calculate the date?

Mars's ~72 day retrograde loop occurs every ~2.1 years and intersects a given constellation once or twice every 15 or 17 years.
The more information you have about the positions of other planets, e.g. Jupiter or Saturn, the more you can narrow the set of possible dates.


Neutron stars and distribution of heavy elements

I may do some more detailed calculation, but I think there is a misconception that has provoked your question.

The content of (e.g) gold, with respect to other elements in the solar system can be readily measured in meteorites. The Earth is expected to contain a similar abundance, but is very depleted in hydrogen and helium and somewhat depleted of lighter elements like carbon and sodium. The surface abundance of gold in the Earth is then a bit lower, because it sinks during the Earth's formation.

We expect the relative abundances of chemical elements to be quite smoothly distributed in space and time. Material that is produced in supernovae and neutron star collisions is mixed quite quickly in the interstellar medium. Thus the material that makes up the solar system is contaminated by the excreta of as many as a billion stars that lived and died before it's birth. Even if a neutron star merger occurred right next to the molecular cloud that formed the Sun, that cloud may have contained a million solar masses of gas, that would have diluted the signature of the kilonova event. We expect this to be true for all stars born in our Galaxy, except those that were born right near the beginning, where individual "pollution" events might become apparent.

The rate of these events in the local universe is only known observationally to an order of magnitude. In the past, it is also rather poorly known, but can be indirectly deduced from the rate of short Gamma ray bursts (of which we see only a small, uncertain fraction), if we assume that all sGRBs are merging neutron stars and that all merging neutron stars produce sGRBs. The rate in our Galaxy is extrapolated from the properties of the meagre number of identified double neutron stars and their orbital decay rates and is about 1 every 50,000 years (so about 200,000 over the lifetime of the Galaxy).

These rates require that about 0.0001 to 0.001 solar masses of very heavy elements is produced in each of these explosions to reproduce the solar system abundances. In the recent event, the amount of heavy elements in the ejecta appear to be in that range.


Why is the Lunar Node in a daily motion?

The nodes are the two points on the orbit of the moon at which the plane of the orbit crosses the elliptic. The position of the nodes change in a predictable way due to the perturbation by the sun (and the other planets). Since the orbit is constantly changing, the position of the longitude. The node is not the position where the crossing last occurred. Rather it is the intersection of two imaginary lines in the sky, the ecliptic and the orbit of the moon.

The position of the nodes are measured as an angle, clockwise from the first point of Aries, thus it is a longitude, or right ascension. On the first of September 2016 the longitude of the ascending node of the moon is 162.484 degrees, and decreasing slowly.

The linked pdf indicates a value of 12♍41, apparently this means 12 degrees 41 minutes within Virgo. The notation is not used in astronomy. If you are interested in the scientific study of the sky you should be aware that astro.com is an astrology website. The presentation of ephemeris may not represent scientific practice. I consider modern astrology to be pseudoscience and fraudulent.


"What happened before the Big Bang" is like asking what Alexander the Great's phone number was. It's a nonsensical question.

Space and time began with the Big Bang. "When" and "where" began with the Big Bang.


Exactly how does Canis Minor look like a dog?

Quoting from wikipedia:

  Canis Minor was one of the original 48 constellations formulated by Ptolemy in his second-century Almagest, in which it was defined as a specific pattern (asterism) of stars; Ptolemy identified only two stars and hence no depiction was possible. The Ancient Greeks called the constellation προκυων/Procyon, "coming before the dog", transliterated into Latin as Antecanis, Praecanis, or variations thereof, by Cicero and others. Roman writers also appended the descriptors parvus, minor or minusculus ("small" or "lesser", for its faintness), septentrionalis ("northerly", for its position in relation to Canis Major), primus (rising "first") or sinister (rising to the "left") to its name Canis.

It looks like the original (Greek) identification of the constellation by Ptolemy didn't attribute anything to it, let alone a dog. But over time, the constellation became known based on its proximity to Canis Major. Originally known as Procyon meaning "coming before the dog", i.e., it rises before Canis Major. This relation to Canis Major seems to have led it to being considered as a representation of a dog as well. The Minor attribute appears to be due to the fact that it is fainter overall than Canis Major.

Really though, you can't pick apart constellation patterns too much. Much of them don't look that much like their attributions and only evolved over thousands of years of stories and imagination. It's not like one guy sat down one day and said, what does this pattern of stars remind me of, and that was that.


Thick asteroid style fields, averaging around 100 meters apart

That's a very high density. It's not any "asteroid" field that would occur naturally and would be stable for a long time. I can only think of a few environments that would be close to that:

the ring around a big planet, like Saturn
the debris field shortly after a major planetary collision, like the one that created the Moon. It would be a very dangerous place to be in, because not all fragments would move at the same speed; there would be quite an ongoing amount of collisions.
maybe, and this is a very cautious maybe, the pile of material coalescing into a protoplanet

All of the above would be short-lived, on a cosmic scale. It would be a coincidence that you're there to see it, and you'd probably have to explain the coincidence somehow.

"Asteroid fields", the way most people imagine them nowadays (very high density), are largely fiction, originating in the iconic space chase sequences in the Star Wars movies, and the like.

  Nebula regions that are actually thick enough to obscure light, like
  clouds

On what scale? Quite a few nebulae obscure light, but we're talking on the scale of distance between two neighboring stars. There are some nebulae that glow from within but we don't quite see the star - that's an example.

If you're talking about blocking light on the scale of mere kilometers, that's not possible "in outer space". Not for nebulae, not for dust clouds or anything else. That would be a density approaching the atmosphere of a planet. Consider the Earth - you can see just fine kilometers away through its atmosphere, unless fog gets in the way.

  Naturally occurring fields of explosive gas or a physical material
  that does the same

Even if you could find something like that, which is pretty much impossible, it would be highly unstable, and would eventually decay into the lower energy state - i.e. it would tend to explode. Such things might exist for the duration of a cosmic blink of an eye. It would be quite a coincidence that you could find something like that out there. A coincidence that would require some explanation, and very likely would not be a "mere coincidence". I think that's called a plot point. ;)

Such things just don't occur naturally.

  Radiation levels high enough to eat through ship plating

It would melt off, rather than being eaten through. Radiation tends to be absorbed; it doesn't tend to chip material away. And when it's absorbed, it yields its energy as heat.

Also, there is no material that could shield nuclear radiation so well that it would melt off on one side, while blocking it to non-lethal levels on the other side. At least not within any reasonable thickness.

Anyway, such conditions might be found near extreme places such as the polar jets of massive black holes - but only while the accretion disk is very active.

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

  Naturally occurring anomalies of any sort, such as black holes, rogue
  planets and stars

Black holes are pretty ordinary, not anomalous in any way. There are huge black holes in the center of galaxies, and regular-size blackholes sprinkled throughout.

Not sure what you mean by "rogue planets and stars". Planets not belonging to any star system are actually thought to be pretty common. Stars not belonging to any galaxy are also not extraordinary, but of course the distances between them would be gigantic, since any such star, by definition, would be alone in intergalactic space.

  An example would be a protoplanetary disc. Could this allow for
  material in close proximity so you have rocks in orbit that are close
  together? What about clouds of material?

Yes and yes. But at that point it would evolve rapidly, coalescing into a planet. Not rapidly on the human scale, but rapidly on cosmic scale. To you, as a human being, it would seem quite stable.

  Would a forming star would have a thick cloud of material around it?

The transition between a disperse, rarefied cloud of gas, and an actively burning star with a clearly defined "surface" is very rapid. However, for a very brief time (maybe thousands of years? not sure), you might find something with a dense center, surrounded by a thin cloud; but even then, density near the central area would increase rapidly. Perhaps you need to ask an actual expert in stellar evolution; there are models that show exactly how each phase looks like and how long it would last.

If you're looking for large expanses of gas or dust at densities comparable to Earth atmosphere, such a thing is simply not stable on a cosmic scale. It either dissipates if there's not enough gravity to hold it together, or it's part of an active process of collapse as a protostar or protoplanet.


Why do Jupiter impact events look dark brown?

The initial impacts are brighter.  The team that observed the shoemaker levy impacts described them as "fireballs" and the initial pictures showed spots glowing bright after impact, though I'm not sure how much those images used the infra-red range, so, grain of salt, because I think you're asking about the visible spectrum.
Jupiter's bands are essentially Hadley cells where the darker bands are the warmer rising atmosphere and the lighter band is the cooling, more icy falling atmosphere.   The whiter bands across Jupiter's latitude lines, what you see is sunlight reflected off ammonia ice.   (the blue color of Uranus and Neptune is methane ice).  When gas giant planets get hotter, they tend to lose their pretty colors and become darker reddish or brown colors.  They hydrogen and helium that dominate the atmosphere are mostly transparent.  The color we see comes from ice-clouds and other molecules in the atmosphere.
Impacts on Jupiter, with the planet's high escape velocity,  creates an enormous amount of heat for any impact big enough for us to see from Earth and perhaps obviously, heat removes ice.
A variety of molecules play a role in Jupiter's reddish/brown colors, I'm not sure which is dominant, but phosphine gas/phosphorus compounds, Sulphur and hydrocarbons all reflect or scatter darker colors.  But the primary answer to your question is that the brown spots you see after impact are due to a lack of atmospheric ice in combination with sufficient mixing so that there's an abundance of colored molecules.  It's not too different from Jupiter's large storms that create it's dark or red spots.
A more recent image of an impact taken by an amateur astronomer.   The initial impact isn't dark.  It's lighter due to the heat of impact reaching above visible temperatures with presumably some atmospheric covering.

If you use an infrared camera, you probably see the spots remain brighter for some time, even as they become darker in the visible spectrum.


Is an expanding universe equivalent to a universe in which everything is shrinking?

Surely, from our perspective an expanding universe would look exactly the same as a universe in which everything is shrinking away from everything else?

This is false. If everything was shrinking away from everything else, that would imply that the recessional rate of distance we observe due to this shrinkage would be independent of distances. Afterall, all galaxies are shrinking at the same rate so the rate they "recede" is only dependent upon their shrinkage rate.

However, we observer that the more distant an object is, the faster it recedes from us. This is the premise of Hubble's law and is only explained if we assume the universe is expanding.

Furthermore, there are many objects in our visible universe which are receding from us faster than the speed of light. This is only possible because these objects are not moving through space, but rather space itself is expanding. In your scenario, these objects are shrinking in space (I presume) and there's no possible way they could shrink fast enough to appear to be receding faster than the speed of light.

  "Oh, but the red shift!" I hear people exclaim. Well how about this:
   The speed of light is simply slowing down.

There have been people who have tried to suggest that the universal constants (e.g., the speed of light, the mass of an electron, etc.) are not actually constant and instead time-varying (albeit slowly). No such theory has ever been successful.

Again though, your idea suffers from a few problems, even if you assume it to be true. There are multiple kinds of redshift. Redshift from receding objects occurs because space itself is expanding and causing the wavelengths to expand as a result - otherwise known as cosmological redshift. In your scenario, the redshift would be caused by the (faster-than-light) recession itself (since the galaxies are physically moving away from us), also known as doppler redshift. You then complicate the problem by making the value of the speed of light change over time. This would cause light, at the moment of emission, to be redshifted both by the doppler effect and by the slowing of $c$. As the light travelled, the time-varying of $c$ would have no effect on the wavelength. In this scenario we would have long ago realized that moving objects get a double redshift, namely the doppler effect and the time-varying $c$ effect. We just don't see that.

  If the speed of light is a measuring stick against which all things are measured, and if the speed of light is slowing down, then it means everything shrinks

Those two ideas don't relate at all. There's nothing suggesting the speed of light slowing down implies everything shrinks.

  high frequency waves generated in the past are observed with a lower frequency today

As explained above, your proposal would cause the redshift to occur at the time of transmission, not en route. So there wouldn't be "high frequency waves generated in the past" They would have been emitted as a lower frequency. Which itself is troubling because how then do you explain the CMB changing frequency over time?

  What is wrong with my alternative?

Aside from the above mentioned points, a huge number of things:

All the physical constants of nature are tied together. You can't just change one and hope that the others don't notice. If the speed of light is constantly decreasing that has drastic implications throughout all of physics. For example, if the speed of light changes, suddenly the electromagnetic force strength changes, atoms aren't stable, and the universe explodes! What is your proposal for stopping that occurrence?
Just how exactly are things shrinking? Are the atoms getting closing together? Are the atoms themselves shrinking? At some point you're going to hit a limit and your object becomes a black hole. Are you really predicting that eventually the universe will be nothing but black holes? My guess is that if you did such a calculation, you'd find the time it took to reach that point is about a second, but the Universe has been around for a few billion years.
What caused this initial shrinkage? Motion requires energy input. Where did this energy come from? How did it apply itself so uniquely as to cause every individual thing to shrink into itself and only itself?
How did the universe get to be so distributed? Your proposal basically implies the Big Bang didn't happen since you attempt to explain things the Big Bang theory already explains. If your explanation differs and you believe yours is the correct one, then the Big Bang Theory cannot be correct. If that is the case, then how did the universe get into its current state if not the Big Bang?

I'm sure I could go on and on, but hopefully you can see there are more than a few holes in your idea. No offense, but it takes years and years of studying to contribute to the forefronts of science. Ground-breaking ideas aren't going to be had by someone who read about a few concepts from Wikipedia or A Brief History of Time and decided they could come up with a better theory. That's the academic equivalent to reading about the rules of (American) football and deciding you can play in the NFL.


Why haven't Earth and Venus got any tiny moons? Or have they?

The strength of the Earth's gravitational field compared to the Moon and the Sun is not enough to capture and hold satellites - there are too many disruptive forces that would rip them away over time.

However there are some objects at the Lagrangian points - the points where the gravitational fields of the Earth and other objects are equal and so it is possible to have a (likely-meta) stable orbit.

This gives some details about what might be found at the various Lagrangian points: http://en.wikipedia.org/wiki/List_of_objects_at_Lagrangian_points


Does the astrology of constellations relate to its position during the year?

Yes, but no.

The basic idea behind the zodiac is as you stated what constellation the Sun is located in during the year. But the time assigned to each constellation (1/12 of the year) is not accurate, for several reasons. Firstly, because of modern constellation borders, some constellations are larger than others. This has also caused the ecliptic to pass through Ophiuchus, not in the zodiac. Secondly, axial precession has rotated the zodiac by almost an entire constellation over the last 2000 years. That is not accounted for in astrological dates.


How to view Jupiter with 4.5" Newtonian Reflector

Jupiter is a very bright object, so maybe the best procedure is to use your filters, they might help with the glare. However, I think you have either a case of low resolution or distortion. Generally, the larger the diameter of the telescope, the better is the resolution (more details here). Resolution defines how much detail you are able to resolve with the telescope.

Changing the eyepieces or using Barlow lenses can amplify the images, but it doesn't improve resolution (you'll just see a bigger blob - but still, it's cooler than just a small speck).  There are also other things to check:

Was it windy? Too much wind can, usually, mean a turbulent atmosphere, and it hampers observations. Another way to check for turbulence is to look at stars with the naked eye: if they are twinkling too much, the atmosphere is very turbulent
Was Jupiter near the horizon? If so, maybe you should try observing it when it's higher in the sky. When looking near the horizon, light has to pass through a large column of air (a parameter known as airmass by astronomers), and it distorts images
Is the telescope well collimated? Poor collimation (mirror alignment) usually results in tail-like structures in sharp objects, almost like a comet. This is probably not the case if the scope is new
What is the quality of the optics? Some telescope manufacturers ship their products with very low-cost, low-quality optical components (eyepieces, filters etc.)

Also, if your objective is to observe mainly solar system objects, I suggest using a refractor telescope, they are wonderful for that. Additionally, this video by Phil Plait on Crash Course might help you and give invaluable information.


What is the minimum distance from city that allow to see Milky Way plane?

The premise is certainly true. An exact distance isn't possible to determine since it would depend on how much light pollution is coming from the city, and how much haze (water droplets and particulates) is in the air. You could also be a "short" distance away but on a mountain with much greater elevation than the city.


What is wrong with my calculations of Jupiter's apparent magnitude?

I think that should be $+ V_{Sun}$ in your second equation, not $- V_{Sun}$.  Otherwise, a fainter Sun (larger magnitude) would give you a brighter Jupiter (smaller magnitude).   Those need to go in the same direction.
Applying that change (assuming the rest of the calculation is right) would increase your answer by $2 \times 4.83 = 9.66$, which gets you much closer to the right magnitude.
Your estimate will now be a bit on the faint side - not sure why - but at least a lot closer than before.


The point here is the "the solar spectrum" received from "the Sun" actually comes from different places depending on the frequency. The (stylised) smooth curve at optical and IR frequencies is pseudo-blackbody radiation from the photosphere. Pseudo-blackbody, because the radiation comes from different depths and temperatures in the photosphere, which gives rise to absorption features.
The photosphere is not hot enough to produce significant amounts of blackbody UV radiation, which accounts for the sharp "Wien tail" dying away into the UV.
The dashed lines in the UV and X-ray frequency range are emission that comes from the chromosphere and corona. i.e. They arise from a physically distinct region and thus there is no reason why they should form a continuous curve with the radiation from the photosphere.
The UV and X-ray emission is a combination of thermal radiation from hot plasma in the corona (at $\sim 10^6$ K), which produces continuum bremsstrahlung and recombination lines from highly ionised metal ions like Fe X or O VI, and plasma at $10^4$-$10^5$ K in the chromosphere and transition region that is dominated by discrete recombination lines produced by ions like Mg II and C IV.
The reason that a discontinuity can persist is that the photosphere, chromosphere and corona are not radiatively coupled. i.e. The underlying photosphere is not the source of heat for the chromosphere and corona. The heating agent is the solar magnetic field.


Current limitations in radio-astronomical spectrometry analysis of local interstellar cloud's hyperfine structures

The first thing to notice is that the Local Interstellar Cloud, in which the Sun is evolving right now, is a fairly diffuse region, with a typical density of about one to a few particles per cubic centimeters. Clouds with such low density are actually mostly atomic; as you can see on this plot (Snow & McCall 2006, adapted from Neufeld et al. 2005):

It is then quite challenging to observe molecules in this region.

Good news is, there is not only molecular lines to give informations about the physical properties (temperature, density, ionization, velocity structure and morphology) of the Local Interstellar Cloud. In particular, ultraviolet is a perfectly suited wavelength range to sudy this region in absorption, and there are some quite extensive studies of the subject (see for example Paper I, Paper II, Paper III and Paper IV of Redfield et al.).


What is the bright object above the moon in Sudbury, Ontario?

It's probably the planet Venus. You can use an online planetarium (or one of the many mobile apps) to identify objects. This link shows the sky this morning at 6:45am at your location:


This idea has been around for decades, so I'm not sure who first came up with it. Here's a reasonably sourced article on the involvement of supernova in solar system formation:Exploding Star May Have Sparked Formation of Our Solar System

  The shock wave from an exploding star likely helped trigger the formation of our solar system, according to a new 3D computer model, researchers say.
  The solar system is thought to have coalesced from a giant rotating cloud of gas and dust known as the solar nebula about 4.6 billion years ago. For decades, scientists have suspected a star explosion called a supernova helped trigger our solar system's formation. In particular, the shock wave from the explosion is thought to have compressed parts of the nebula, causing these regions to collapse.
  According to this theory, the shock wave would have injected material from the exploding star into the solar nebula.

So yes, material from supernova can end up triggering the formation of new suns, and material from supernova do end up mixed in with the nebular material that makes the new stars.


Since no one has posted an answer, I'll turn my comment into one, even though it is not going to give you a quantitative answer.
The reason that I can't give you a number is because the answer is simply, "lots."  Any crater that is on the north or south polar layered deposits (N/SPLD) are going to have permanent ice in them, by definition, since they formed in ice.  Since the NPLD is much younger than the SPLD, it has many fewer craters.
The largest (off the top of my head) on the SPLD is McMurdo, roughly 30 km across.  Korolev is larger at about 81 km across, but it is not on the NPLD.  Korolev itself is large enough that it has its own mini-climate with positive feedback mechanisms to keep the ice there, but smaller craters can't do that.
To get permanent ice in craters not in the N/SPLD, you need to keep the temperatures cold enough and pressure high enough for the ice to remain throughout that hemisphere's summer.  Since the northern hemisphere's summer is when Mars is near aphelion, getting 45% less sunlight than during southern summer, craters can be closer to the equator and still meet that requirement.  Also, the northern hemisphere is lower in elevation than the southern, so you also get more atmospheric pressure which helps keep the ice from sublimating.  You're also going to want a high enough rim and/or deep enough crater cavity to guard against sunlight as much as possible, so larger craters (like Korolev) are again going to be preferable to small ones.  But, Korolev is the largest crater closest to the NPLD, so that's why it's be best known for this sort of phenomenon.
So, are there others?  Certainly.  But, they're smaller.  And, unless an impact crater is scientifically important and has had a name nominated for it through the International Astronomical Union, it is not going to be named, so very few craters on Mars are named.
To answer your question about which is the closest to the equator, it is not something I'm sure has ever really been looked at.  One would need good, repeat mosaics at different points in Mars' orbit and simply do a visual search.  If you do do that, happy hunting!


What is a pupil slicer, and how does it work with anamorphic optics in VLT's ESPRESSO Echelle spectrograph?

In order to reach the stability required for planet detection, the majority of high resolution echelle spectrographs are mounted off the telescope in a stable environment. This involves pressure and temperature stabilization, often by housing the spectrograph in a vacuum vessel.

In order to feed the spectrograph with light from the telescopes, and to reduce the effect of image motion causing variations in the slit illumination and corresponding variations in the spectral line shape which would mask the tiny radial velocity changes     we are trying to measure, optical fibers are used to feed the light. However there are two disadvantages to this: 1) the fiber is now round (although octagonal fibers are the new hotness for their better image scrambling properties) and not a long slit, and 2) due to focal ratio degradation, the output of the fiber is wider (lower f/ratio) than the fiber input which decreases the spectrograph resolution.

In order to combat these effects and increase the resolution, which is needed to measure the tiny 1/1000th pixel shifts caused by low mass planets, image slicers are typically used to reformat the output fiber into a new more slit-like shape. The classic example is the Bowen-Walraven image slicer which uses a glass plate and prisms to slice the circular fiber image into 2 semi-circles and stack them on top of each other. Higher efficiency versions using mirrors or glass slabs have been made more recently; this ESO SPIE publication has some examples of alternative constructions and the resulting image shapes. There is also this page which has more details, including construction of a prototype.

I am not an expert on optical design or anamorphic optics but I suspect this is done because the beam is not the same size and shape in the spatial/cross-dispersion direction compared to the dispersion/wavelength direction and so equal power in the optical elements in each direction is not needed. Given the size of the input beam from the 8.4m VLT that will feed ESPRESSO, and the need to get the whole instrument into an affordable vacuum vessel that will keep vacuum for a long time, I would imagine the designers employed as many tricks as they could in order to keep the size of the instrument down; the Optical Design section of the ESPRESSO Overview paper talks a little more about this.


Comparing Star Formation rate in different galaxies

Not being an expert in star formation, I found a well-written paper summary from which I conclude that typical star formation rates range between $6 \ldots 24 M_\odot / yr$.
The blog quotes the following graph
 by M. Boquien, V. Buat, and V. Perret, see https://arxiv.org/abs/1409.5792

In this paper we investigate in isolation the impact of a variable star formation history on the measurement of the SFR.
We combine 23 state-of-the-art hydrodynamical simulations of 1<z<2 galaxies on the main sequence with the cigale spectral energy distribution modelling code. This allows us to generate synthetic spectra every 1 Myr for each simulation, taking the stellar populations and the nebular emission into account. Using these spectra, we estimate the SFR from classical estimators which we compare with the true SFR we know from the simulations.

In summary: To me, $0.2 M_\odot / yr$ looks rather small, but I cannot judge whether it is unrealistic for a dwarf galaxy.


Why does the Sun show different colour at midday and at morning?

Sunsets are red because the sky is blue.

Air, while it appears colorless actually scatters light just a bit. This is not the same as absorbing the light, but more like how light is scattered by fog.  If you are driving through fog with your headlights on, part of the light from their beams bounces off the fog particles and lights up the fog well outside the beam and some of it even bounces multiple times coming back to your eyes.

Air is much clearer than fog, but it does scatter light just a bit. What's more, it scatters blue light more than green, and green more than yellow, and yellow more than red.  So while the Sun's light in space is quite white, as it passes through the atmosphere on a sunny noonday a lot of the blue light gets scattered, while very little of the red does.  That blue light bounces many times and is the source of the blue sky light.  The loss of that blue light makes the sun appear redder.

At noon, the light comes down from high overhead and passes through a minimal amount of atmosphere and only some of the blue light is scattered. At sunset (and sunrise) the light comes in at a long, low slant and passes through much more of the atmosphere, and nearly all of the blue and even most of the green is scattered (and much light is absorbed, too), leaving mostly red and orange light left.

Hence the reddened sun.

See Why Is the Sky Blue? and Why Is the Sunset Red? for a bit more including some diagrams.


Are the Leonid meteor storms a thing of the past?

Wikipedia does not cite a source.

NASA used to make predictions, eg.:

  2009 LEONID OUTBURST FORECAST A significant shower is expected this year when Earth crosses the 1466-dust and 1533-dust ejecta of comet 55P/Tempel-Tuttle. According to J. Vaubaillon, the narrow (about 1-hr) shower is expected to peak on November 17, 2009, at 21:43 (1466) and 21:50 (1533) UT, perhaps 0.5 to 1.0 hour later

These are extensively studied studied, eg. List of all meteor showers  .

The great storms occur at ~33 year intervals. I can't find any prediction that this pattern will be unusually perturbed by Jupiter at this time.


Energy Source for Gamma Rays from Merging Neutron Stars

Not Nuclear fusion;
There is also a huge amount of nuclear fusion that creates heavy elements from all the iron there is in neutron star: they in fact are not only made of neutrons. But as said in comment, building of heavier elements rather consumes energy than it generates some.

Not sure scientists  has a clear agreement on how this works.

Gravitational collapse

For example I found this (rather old) abstract which states it could be a result of gravitational collapse, without singularity (since here the result of the merger might not be a black-hole, or the lightest ever: around 2.7 solar masses!)

  theoretical developments (string theory, quantum gravity, critical collapse), which suggest that complete gravitational collapse can occur without singularities or event horizons

Thermonuclear event again: fission

From Space.com, they say Kilonova energy could be explained by rapid atomic decay of heavy elements

  The mergers of dense cosmic bodies that are thought to cause short gamma-ray bursts can also blast out neutron-rich gas that rapidly generates heavy elements such as gold and platinum, scientists say. These "r-process" elements can undergo radioactive decay and release an enormous amount of energy — 1,000 times or so that given off by stellar explosions such as novas. These powerful events are thus known as "kilonovas"


Why, in the Solar System, all the mass seems to be concentrated at the centre?

It's because of the Sun.

It might be good if I give a quick overview on star formation before I get to the meat of the issue. Here's star formation in a few simple steps:

Giant Molecular Cloud forms. A large region of gas and dust, essentially a dense version of the interstellar medium, coalesces into an interstellar cloud. GMCs can be tens or hundreds of light-years across, enough to give birth to many stars. Within the GMC, some regions will be slightly denser than others.
A portion of the cloud collapses. A certain region of the GMC collapses, generally due to an outside disturbance. The most commonly cited cause is a supernova shockwave that compresses portions of the GMC, although close passes between galaxies have been known to incite star formation. My favorite example is the Cartwheel galaxy.
The region heats up. There is quite a lot of matter pressing in on what has now become a protostar, and so it heats up. Eventually, conditions become such that hydrogen fusion is possible. The protostar, now a pre-main-sequence star, begins to shine.
A protoplanetary disk forms. At this point, the star dominates this region of the GMC. Matter nearby is pulled towards it by the force of gravity, and a circumstellar disk forms. It may be composed of gas and dust. Eventually, small grains of dust collide and form bigger grains. Planetesimals form, then protoplanets, and finally planets.

The reason that there isn't more matter in a given stellar system is that the star dominates the surrounding area. It pulls in nearly everything around it during its early life. Much of the region of the collapsing cloud is made of molecular $H_2$, and so it is pulled in and used for fusion.

Now the question translates to 'Why isn't the protoplanetary disk more massive'? The answer is that when the disk formed, much of the matter that was in its inner reaches spiraled into the Sun. This is partly due to the Poynting-Robertson effect, where photons from the Sun pull dust grains in. Over billions of years, the star can accumulate much of the matter than was originally close to it in the disk.