What do gravitational waves allow us to understand? Before reading this question, you should read this paper.
From what I understood, we managed to detect gravitational waves for the first time.
Is this discovery going to help us understand something we haven't understood yet? Dark matter? Galaxy movements? FTL travel? Gravity manipulation, Interstellar style?
Though I understand the discovery, I'm a little confused about what it will actually improve for science.
So, what are the doors this discovery will open ?

I think the wikipedia page gives a reasonable overview of why gravitational waves give us a window on the universe that is either not observable or is complementary to the view we get from electromagnetic waves (or neutrinos).

But let's have a specific example. The potential of LIGO, as we have seen today, is to detect the gravitational wave signatures of merging black hole binaries.

The power radiated in gravitational waves strongly depends on the orbital separation of the black holes, it also depends on their masses. The frequency of the radiation will change as the black holes spiral together. The "noise" that this makes in the final few seconds as the black holes merge is the "chirp" that is detected by LIGO. Have a look (listen!) to what a chirp might "sound" like at this web page from University of Birmingham.

The exact characteristics of the chirp (duration, frequency etc.) can for instance yield the masses of the black holes and of their final configuration and may tell us about spin rates of the black holes. Yet these same mergers may produce zero electromagnetic wave signatures that could be seen by conventional telescopes.

Furthermore, because the amplitude and the frequency of the waves depend differently on the masses and distance to the GW source, these binary chirps acts as "standard candles" in a similar way to type Ia supernovae. In other words, measurements of the chirp independently gives the masses of the merging black holes and the distance to them.


GEO and HEO images of Earth I would like to see some GEO and HEO images of Earth. But I can't find a good source. There are a lot of LEO images of Earth but I can'f find any raw images from higher (preferably 30,000km+) altitudes. There should be at least 400 satellites at that height, according to Wikipedia.

Is there any website with those kind of images?

You might want to look at noaa.gov (https://www.nnvl.noaa.gov/view/globaldata.html in particular)

and similar sites for weather for other countries. In other words, the satellites in geostationary orbits (GEO) that take images are mostly weather satellite. I do not have a breakdown by type, but I would guess that a vast majority of the satellites in GEO are communication satellites, and they have no reason to take images.

I suspect that satellites in high earth orbit are there for astronomical purposes (to "get away" from the Earth, such as Chandra) or communication (such as the Russian Molniya satellites), so they are not imaging the Earth.


What is at the edge of the galaxy? The solar system is thought to have a heliopause which can be considered its edge for many purposes:

The heliopause is the theoretical boundary where the Sun's solar wind is stopped by the interstellar medium; where the solar wind's strength is no longer great enough to push back the stellar winds of the surrounding stars. This is the boundary where the interstellar medium and solar wind pressures balance.

  Heliopause: the boundary between solar wind and interstellar wind where they are in equilibrium.

Is there a similar phenomenon at the interface between space dominated by the Milky Way and intergalactic space?

What is at the edge of the Milky Way galaxy?

The short answer is: probably nothing much, because galaxies are very fuzzy objects without "edges".

If you look at the stellar disk, it just fades out in density, with no evidence for a sharp cutoff (this is true of disk galaxies in general). There may or may not be a "break" at some radius, but this just marks the beginning of a steeper falloff in density, not an "edge" in any real sense. The gas disk extends even further out (that is, further out than we can easily trace the stars in the disk), and doesn't show much evidence for a sharp cutoff either.

There's also a round halo of stars, which is low density but extends to at least 400,000 light years; two stars were recently discovered  which are plausibly part of the halo and located at distances of about 800,000 light years. (Note that there are other galaxies -- such as the Large and Small Magellanic Clouds -- which are closer to us and to the center of the Milky Way, so you have to accept that individual galaxies can be found "inside" other galaxies.)

And then there's the halo of dark matter...

I can think of two ways in which you might talk about the outer boundary of an isolated galaxy (which the Milky Way sort of is) from a theoretical perspective. The first is the idea of a halo "accretion shock", in which relatively cold gas falling onto the galaxy from intergalactic space runs into the galaxy's halo of hot gas ("hot" = millions of degrees), creating a shock where the infalling gas slows down and the local density of gas goes up. (This is a little bit analogous to the heliopause, though the direction of gas flow is the other way around: the heliopause is where the outflowing solar wind shocks into the more or less stationary interstellar gas.) The problem is that extensive, hot halos of gas are thought to form only around massive galaxies, and it's not clear the Milky Way is massive enough to qualify. It also won't work for galaxies in massive groups and clusters, where the individual galaxies aren't accreting gas any more (the cluster is what has the hot halo and the accretion shock).

The other possibility is a region where the infalling dark matter particles merge into the dark-matter halo (whose particles are orbiting within their common gravitational potential, and so are not as a whole falling towards the center any more). Simulations suggest that as one moves inward the local density of dark matter starts to increase rather rapidly at this point (and the average velocity of the dark matter particles changes), but it's still a fairly smooth process (unlike gas, the dark matter particles aren't "shocking" into each other). There's no way of determining where this is for the Milky Way, other than something really vague like "maybe 1 million light years"?


Say we were to bring Titan to Earth's orbit. How much would its atmospheric pressure change? I've heard one of the reason why Titan has such a thick atmosphere is because of its really low temperature. So say that were were to magically bring Titan to the Same orbit as Earth, and the moon starts to rapidly heating up. How much of its atmosphere would it lose? Would we still be able to stand there without a pressurized suit? Is it possible to terraform Titan to the extent that we can heat up its surface while still retaining its thick atmosphere?

Thanks

As Temperature rises, so would the pressure, this would work immediately, as heat from the sun reaches Titan's surface.

The atmospheric escape (and thus, pressure loss, as you describe it) would work on a much longer timescale.
We can make a few estimates to determine this timescale: On the most simplified level, the composition if Titan's atmosphere is that of Earth's - it's mostly molecular Nitrogen.
So the mean molecular weight $\mu$ would be the same. The temperature would be similar compared to Earth by assumption of your experiment, then the only important difference is the mass and radius of the two bodies, reducing the escape speed by a factor of ~10.

Titan has 2% of the mass of Earth, so the ratio of escape speed to thermal molecular speed at the exobase, from where molecules are lost, would approximately scale like $\sim 1/\sqrt{10}\approx 3.1$
To determine escape rates, those go roughly like $\sim \exp(v_{th}/v_{esc})$ and would thus increase by $\sim \exp(3.1)\approx 22 $, compared to today's level.

I don't know present estimates for the lifetime of Titan's atmosphere, but this factor would e.e. bring it down from 5 billion years to only 250 million years. That's really short, geologically speaking!

But of course it's not enough to affect you in your pressure suit on the surface. You'd rather be concerned about an overpressure than underpressure.


Space time and aging Would a more significant curvature of spacetime relative to earth (i.e. time on jupiter) effect the aging process? Basically would you age at a slower rate?
Or age faster on the moon?

Einstein's general theory of relativity explains time dilation. Wikipedia provides a concise summary:

  time dilation is a difference in the elapsed time measured by two
  observers, either due to a velocity difference relative to each other,
  or by being differently situated relative to a gravitational field. As
  a result of the nature of spacetime, a clock that is moving relative
  to an observer will be measured to tick slower than a clock that is at
  rest in the observer's own frame of reference. A clock that is under
  the influence of a stronger gravitational field than an observer's
  will also be measured to tick slower than the observer's own clock.

As one experiences more gravity, time seems to flow slower compared to (say) Earth. That means that "standing" on Jupiter, which isn't possible due to the gaseous surface, will cause you to move through time faster; but you do not age slower. Suppose your lifespan is 80 years. On Jupiter you still would live 80 years, but the time that has passed on Earth during your 80 years would be slightly more than that.

The gravitational time dilation on the Moon is the opposite: the weaker gravity means that an Earth clock ticks very slightly slower than a Moon clock.


How much time does the ISS take to repeat its orbit? I used to go to my roof to see the ISS, but it is not always visible. Then it appears again but does it appear with the exact same orbit as I saw before?
Thanks!

Objects in orbit pass over the surface above what's commonly called their ground track. For objects in low earth orbit, though they go around the earth every 1.5 or more hours, the Earth rotates beneath them so they don't trace a simple "circle" over the same points on land.

The orbit is around the Earth in a fixed plane, so we are likely (but not guaranteed) to see the satellite pass over 12 or 24 hours later.


How can tidal heating lower Io's orbit? This answer to the question Is Io a magic energy machine? suggests that the energy from the internal heating of Io due to tidal "squishing" as it moves cyclically closer and farther from Jupiter in its elliptical orbit will come from the energy of Io's orbit. A lower energy orbit is necessarily smaller, and that actually means that the velocity will be larger. (When you want to raise a satellite's orbit to a higher altitude, you actually use thrust in the direction of motion to slow it down.)

Given that tidal forces are a little complicated (cf. Why is the Moon receding from the Earth due to tides? Is this typical for other moons?), is it a priori certain that the heating will lower Io's orbit, causing it to speed up? (Consider that Earth's Moon's receding is due in part to Earth's liquid ocean, and Jupiter is a gas giant.) Is it just the perijove that will decrease, or the semi-major axis?

How can a (seemingly, naively, on average) radial force cause a tangential acceleration? Io is tidally locked to Jupiter so its rotation around its own axis is synchronous to its rotation around Jupiter.

edit: fwiw if the gravitational interactions between Io and Jupiter's other moons causes the problem to be too complex to answer easily, I'm more interested in the basic dynamics of tidal heating and effects on the orbit of a single moon, rather than specifically Io's situation.

How can tidal heating lower Io's orbit?

It doesn't, at least not to first order. The first order effect is that tidal heating acts to circularize Io's orbit. Counter to that, orbital resonances with Europa and Ganymede act to make Io's orbit more elliptical. This leads to a nice hysteresis loop.

Suppose Io is in a fairly circular orbit. This results in reduced tidal stresses, thereby making Io cool down. A cooler and hence more rigid Io is less susceptible to tidal deformations than is a warmer and hence more plastic Io. Given two bodies in the same orbit, one warm and plastic, the other cool and rigid, the warmer body will suffer more tidal deformations than will the cooler one. This is captured by the object's $k_2$ Love number. The inevitable lag in response means that the response will not be symmetric about periapsis/apoapsis for an elliptical orbit, and the greater the plasticity, the greater the greater asymmetry. This is captured by the object's tidal quality factor $Q$.

This cooling of Io as its orbit becomes close to circular enables the ever-present resonance effects to now dominate over the circularizing effects. Io's orbit slowly becomes more elliptical. That elliptical orbit increases tidal stresses on the cold, rigid Io, eventually making it start to warm up and become more plastic. The circularization effects grow as the orbit grows more elliptical and as Io's interior becomes more flexible and more plastic. Eventually the circularization effects dominate over the orbital resonance effect, making Io's orbit become more circular -- until the cycle repeats.

Rinse and repeat, at least as long as that three-way orbital resonance between Io, Europa, and Ganymede holds up. How long that three-way tidal resonance has existed and how long it will last is, as far as I know, unknown.


Why don't we have 2 Summers and 2 Winters? Due to Earth's elliptical orbit, its distance from Sun varies by almost 5 million Kilometers (147 million Kilometers at closest point & 152 million Kilometers at farthest point, i.e. almost 3% of the average distance).

As evident from the fact that that Venus has hotter environment than Mars due to their respective distances from the sun.

Why then Earth does not observe two winters (at farthest points) and two summers (at closest points)?

Additional Note:
I know that Earth's seasonal climate change is caused by its 23 degrees tilt that causes the sunlight density variations for the hemispheres.

But to me this 5 million Km distance seems more relevant than the 23 degrees tilt.

There are a few incorrect assumptions in your post, so it is difficult to answer as asked. But I can address the misconceptions.

1. The seasons are not caused by our distance from the sun
The seasons are caused by the 23.5° tilt in Earth's axis. When the Northern Hemisphere is tilted towards the sun (summer), the Southern Hemisphere is simultaneously tilted away from the sun (winter). So the seasonal temperature difference has little to do with the Earth's position in its elliptical orbit. Without this tilt, there would be no seasons and the temperature day to day across the globe would be relatively uniform.

2. Even the GLOBAL temperature is NOT consistent with our change in distance
As a matter of fact, the average temperature of the Earth globally is hottest when it is the furthest from the sun — hotter by about 2.3°C (ref). That's because there is a lot more landmass in the Northern Hemisphere facing the sun (when Earth is farthest away in its orbit). So even though there is less intensity of sunlight, the land is able to be heated up much faster than the vast oceans which have to be heated at perihelion.

This distance-temperature inconsistency isn't unique to the Earth. Look at the average temperature of the other inner planets as we move away from the sun:

Mercury (167°C)
Venus (460°C)  ← farther, but hotter than Mercury?
Earth (14.0°C)
Mars (-60°C)

Venus is actually warmer than Mercury because of the thick carbon dioxide atmosphere causing runaway global warming. So it isn't simply the distance from the sun that determines the average temperature of a planet.

3. There's only ONE aphelion/perihelion
The closest point of the Earth's orbit (perihelion) and the farthest (aphelion) only happens once per year; not twice. That is because the elliptical orbit of the Earth is such so the sun is at one of the foci, not the center (as illustrated below).

Note that the size of the bodies and the eccentricity of the orbits are greatly exagerated here.


M87. What was the black hole before? 10 seconds before the M87 black hole was a black hole, what was it? A star 10 times the size of our solar system?

We don't know (yet). It could have started with the explosion of a very large star, or a primordial black hole formed very soon after the Big Bang. See Wikipedia:

The origin of supermassive black holes remains an open field of research. Astrophysicists agree that once a black hole is in place in the center of a galaxy, it can grow by accretion of matter and by merging with other black holes. There are, however, several hypotheses for the formation mechanisms and initial masses of the progenitors, or "seeds", of supermassive black holes.
One hypothesis is that the seeds are black holes of tens or perhaps hundreds of solar masses that are left behind by the explosions of massive stars and grow by accretion of matter. Another model hypothesizes that before the first stars, large gas clouds could collapse into a "quasi-star", which would in turn collapse into a black hole of around 20 M☉. These stars may have also been formed by dark matter halos drawing in enormous amounts of gas by gravity, which would then produce supermassive stars with tens of thousands of solar masses. The "quasi-star" becomes unstable to radial perturbations because of electron-positron pair production in its core and could collapse directly into a black hole without a supernova explosion (which would eject most of its mass, preventing the black hole from growing as fast). Given sufficient mass nearby, the black hole could accrete to become an intermediate-mass black hole and possibly a SMBH if the accretion rate persists.
Another model involves a dense stellar cluster undergoing core-collapse as the negative heat capacity of the system drives the velocity dispersion in the core to relativistic speeds. Finally, primordial black holes could have been produced directly from external pressure in the first moments after the Big Bang. These primordial black holes would then have more time than any of the above models to accrete, allowing them sufficient time to reach supermassive sizes. Formation of black holes from the deaths of the first stars has been extensively studied and corroborated by observations. The other models for black hole formation listed above are theoretical.

(emphasis mine)


What would be the maximum theoretically possible angular resolution? I have studied some basic astronomy, but I have difficulty conceptualizing the physics of luminosity and optics.  We use electromagnetic spectra to detect existence and properties of distant planets, but I am curious about the extent of what could theoretically be optically captured.

(I am unsure if optical is the correct term, but I'm referring to what could be directly captured vs. computed.)

Assuming the use of technology far beyond what we currently are capable of, what is the maximum possible optical angular resolution we could theoretically obtain of a distant sky object?  Or, for example, of the surface topography of an outer planet/moon/dwarf planet?

What would be the limiting factor at the extreme end of possible angular resolution?

The answer that you are looking for rests on two main pillars. Are you limited in your ability to resolve objects because of the atmosphere like most ground-based telescopes, or because of the fundamentals of the wave nature of light (as per space telescopes)? I am assuming the latter in your question.

One of the biggest rule-of-thumb equations when it comes to astronomy is the equation that you are looking for in your answer. Astronomers define angular resolution with regard to the Rayleigh criterion: two point sources are regarded as just resolved when the principal diffraction maximum of one image coincides with the first minimum of the other (Wikipedia). See Airy Disk functions and the Wikipedia article on Angular Resolution for a better idea as to what this means.

The accurate, but still approximate, equation for the resolution of an object $\theta$ (radians), for a given wavelength of light $\lambda$, over some telescope's diameter $D$, is given below so long as the wavelength of light and the diameter is measured as the same length unit (i.e meters, feet, angstroms).

$$ \theta = \frac{1.22 \lambda}{D} $$

Obviously, the atmosphere is a pain, so, adaptive optics in most famous telescopes try and correct to this limit. To exceed this limit, major breakthroughs would need to happen in the wave nature of photons themselves. If your "technology far beyond" includes this, then, I don't think your question can be answered as you would hope aside from the standard "who knows". Currently, only space-based telescopes operate at this limit.

For the most part, this is really all you need. It does not matter what object you are observing, this still always applies.

Edited: Included unit specifications.


Does the observed color of the sun change based on the observer's location? A friend of mine visited Panama and claimed the sun appeared whiter. He's very color conscience and says certain shades of red looked different there. Could this be due to the position of the sun?

The Sun of course looks less yellow/red if viewed through less atmosphere; i.e. when it is overhead, which it never is in many countries (like the US and UK for instance).


Why are there no stars visible in cislunar space? It’s very puzzling that the moon landing had no stars in the background, the ISS clips have no stars in the background. I listened to multiple astronaut interviews speak on what it looks like up in space and about half of them speak of the “darkest black space”. I’m sure there is a very good explanation for this.

Is star light only visible through the medium of earth atmosphere? But once in the vacuum of space where there is no medium they disappear? What’s the explanation?

Minute 47-49 stars, press conference all three Apollo 11 astronauts

BBC interview with Neil Armstrong only

It is a matter of exposure and dynamic range. A sensor like a camera can only handle inputs in a certain range of intensities, and much of photographic skill (or smart presets) is about mapping the outside light onto this range so the details you care about show up rather than turn into white or black.

If you take a picture of a brightly lit scene, in order to make out the details of the bright parts (such as a lunar landscape, the Earth, the ISS etc) you will have to adjust the exposure making faint objects like the stars too dim to see against a dark sky background. You could try to set the exposure to show the stars instead, but now the landscape and Earth would be too bright (and likely also mess up the picture by causing flaring).

One can try to work around it by taking several pictures at different exposure levels and later digitally compositing them together. But this requires a lot of extra work.


I have seen so many articles but how can finding exoplanet density determine composition I have seen some articles and lectures that state but i cant seem to put my finger on on how does density affect composition and how are you able to determine composition from exoplanet density.

You can't get an exact composition just from density, but it is a clue.
In our solar system there are "rocky" planets with a density of about 5 to 6 g/cm³
And there are gas planets with a density of between 0.5 and 2 g/cm³
So if an exoplanet is found to have a density of 5.3 g/cm³  and a fairly small mass we can guess that the composition is rock (probably siliates with an iron core just like the rocky planets in our solar system)  And if the density is 1.1 g/cm³ we can guess that the planet is made of gasses like hydrogen and helium, perhaps with "ices" like methane or H₂O. If the mass is much greater than that  of Jupiter, then the planet is likely be be a (sub)-brown-dwarf.
You need both the mass and the density to make this judgement, as the density of gas giants depends on their mass, and larger gas giants have a greater density.


What would happen to a gas planet if its core mass goes beyond the Chandrasekhar limit? Hypothetically, let's say we had a gas giant that continued to accrete mass. I've heard that the cores of gas giants are electron degenerate. So if the planet continued to accrete mass and the core mass went beyond the Chandrasekhar limit, what would happen?

In white dwarfs, the result is dependent on the composition. Carbon-oxygen white dwarfs will undergo carbon fusion, leading to a type 1a supernova. Oxygen-magnesium-neon white dwarfs will undergo rapid oxygen fusion, leading to a rapid ignition and supernova but leaving behind a neutron degenerate core.

So would the composition of a gas giant's core play a similar role, if it went beyond the Chandrasekhar limit? What would happen if, say, Jupiter somehow accreted a core mass beyond the limit?

Gas giants like Jupiter consists mainly of Hydrogen and some Helium. If you gradually add mass to these planets then core temperatures will rise gradually and a stage will come where they will ignite like normal stars. Unlike white dwarfs where accretion of mass leads to type 1A supernova.


Is there an element of chance/chaos in stellar evolution? Since stars are an ideal example of macroscopic objects, is their evolution  determined by their initial mass and metallicity?

Are there any non-trivial random internal processes going on that may significantly affect a star's development and eventual fate? (It is quite evident that capture of another star or a brown dwarf is an external, exogenous event.)

EDIT/clarification: I'm looking for things that may shorten/extend the lifetime of a star beyond the "norm" prescribed by nuclear physics/gravity, change its composition, surface temperature. Solar flares/quakes and other instabilities come to mind first.

If you want to go into truly random stuff, you should look into quantum. The internal processes inside a star are not random, however they are bviously undetectable. Some factors other than mass and metallicity are temperature of the original dust cloud, or angular velocity. The temperature obviously affects the brightness, while the angular velocity will affect the gravity. I am not an expert, but I'd assume that any minor perturbation inside the star could cause a butterfly effect and result in, say, solar flares, so on average there would be stars who would be losing more mass than others with no  particular reason.
I assume there would be other factors linked with more complicated physics, too.


Why are blackholes generally not considered as solid spheres with an escape velocity FTL? I was reading Do Stars Vanish Into a Black Hole or Crash Against a Surface? A New Test Answers on space.com.
It says the following:

Another proposed alternative to event horizons is the "hard surface
theory," which suggests that matter within a black hole is destroyed
by smashing into a solid surface. Instead of a singularity with no
surface area, the black hole is a giant mass with a hard surface, and
material being pulled closer — such as a star — would not actually
fall into a black hole, but hit this hard surface and be destroyed. If
that were the case, the collision should create a large burst of
light.

If we focus on the last sentence:

If that were the case, the collision should create a large burst of
light.

If the escape velocity of black hole becomes at certain altitude above the say solid surface of a blackhole more than that of speed of light, would we still see a large burst of light when the collision happens? Black holes are incredibly dense wouldn't it make more sense from them to be solid?
Something like a dark star.
No one really knows what happens to the matter at the singularity. Wouldn't it make sense that the reason that a black hole gets larger is due to more matter being smashed into the singularity making it gain mass. It also seems that black holes can be hurled out their galaxies, it must be in some form of matter that it stays together even when hurled out?

The idea of a hard surface on a black hole is very much a minority theory, bordering on a fringe theory. The reason is that general relativity is fairly well tested, and does not just predict event horizons around black holes but also the Buchdahl bound on how small objects in hydrostatic equilibrium can be. Still, it is always worth testing the theory, which is what the paper proposes.
If you drop an object from infinity onto an object of radius $R$ the Newtonian kinetic energy at that moment would be $GM/R$ J/kg, much of which would be released as a flash. This is why accretion onto white dwarfs and neutron stars produce a lot of radiation beside the accretion disk: for white dwarfs about 0.0003 of the mass-energy would be released, while for a neutron star 0.147 of the mass energy would be released. For a black hole-radius object this crude estimate produces 50% efficiency of converting mass into energy.
However, the energy of that flash is reduced by the gravitational redshift. At the Buchdahl limit the redshift is z=2, halving the energy received (for neutron stars you only get 74% of the energy). But for a black hole horizon general relativity  gives infinite redshift, making the flash disappear altogether.
It does not make sense to see black holes as solid objects since the structure of spacetime inside the event horizon makes the inward direction behave like time does outside: you can only move inward, just as you can only move forward in time. Thinking of the singularity as a material object with mass is very misleading: it is not even point-like. Hence talk about the density of a black hole or imagining it as a sphere of something dense tends to end in confusion. Similarly talking about escape velocity is also tricky: it does not define the horizon as people usually say. The horizon is defined by being a trapped surface that can only be crossed in one direction.


Enhanced Star-Gazing with Special Glasses I watched a video yesterday on how telescopes not only magnify images but also increase the amount of light entering into your eye, allowing you to see things not normally visible with naked eye. Would it be possible to create a "telescope" with no magnification, a wide field of view... say ~190 degrees left/right, ~120 degrees up/down (the average human field of view), and small enough to wear? Essentially creating glasses that allow for better star gazing?

A side question is do night vision goggles let you see more stars? or does the increase in ambient light from earthly objects negate any increase.

Stereo Vision?
Optically, you'll need something like a couple big Fisheye lenses mounted on a helmet.
Looking straight through such optics yields horrible distortion, so you'd have to feed the lens' output into CCD/CMOS sensors, and massage that into flattened images your eyes can handle, on a video screen. Perhaps Google Cardboard?
Probably doable and light enough to wear.
A straight optical approach to correcting the fisheyes would probably end up too heavy to lift.


Is early life required for life? I was watching the new Cosmos and Neil DeGrasse Tyson said something that made me go hmmm...

He mentioned that the only reason that the Earth did not experience the runaway greenhouse effect like Venus is that life had evolved to the point at which it could feed on carbon and take it out of the atmosphere and deposit it in solid form as limestone.

The question is, if we were to find a planet in the Goldilocks zone, how likely is it that it would be habitable for life without already harboring life?  Would we expect that a similar scenario would have had to taken place on that planet to curb the greenhouse gasses in the atmosphere, thereby turning it into another Venus?  Can a carbon cycle exist without life?

To answer your question directly, it is quite unlikely that planets would be habitable without already having life. It would have to be in a near-perfect condition, which would be statistically unlikely. In case of planets already having life, the existence of life provides robustness to small changes and makes habitability possible in a larger range of conditions.

I am assuming 'habitable' here means habitable for man, trees and an ecosystem etc. Remember that there are extremophiles (or certain other hardy species) which completely change the perspective on habitability, and are often the key in making those places habitable for other forms of life.

This is also true for parts of earth which undergo a sudden change and are not 'habitable' for most forms of life till some hardy species takes over and changes the conditions, and consequently allows other species to be able to survive. See, for example, ecological succession (https://en.wikipedia.org/wiki/Ecological_succession), esp. primary succession and pioneer species (follow the links within the article).

Also, this is a long process. In case of the earth, there was also evolution that needed to happen, so it probably won't take as long as a few billion years, but even on earth, it takes a few years to make small disturbed microhabitats habitable. The atmosphere and other factors (soil, moisture etc., for the plants) need to be made suitable for living. Check this interesting article on terraforming: https://microbewiki.kenyon.edu/index.php/Terraforming

Hope this was helpful. I don't really know if a carbon cycle is possible outside of living organisms in some way.


Astromaster Celestron 130 EQ I brought a new Astromaster 130 EQ and collimated it using a laser. However, whenever I try to observe moon I get a perfect picture but with other planets I see only a bright glowing ball which increases and decreases in size as I adjust the focusing knob. Also, I see secondary mirror shadow in between that bright glowing ball. Kindly help me where I have gone wrong. I am using all kinds of eyepieces from 20mm to 06mm. I have a Barlow lens 2x also.

Subject Size
In angular dimensions, planets are tiny compared to the Moon.  The Moon is roughly 30 arc-minutes (about 1/2° ... varying slightly from apogee to perigee).  In real life they are, of course, MUCH larger than the Moon... but they are also MUCH farther away so they appear much smaller.
In comparison to the Moon's approximately 30 arc-minutes size, Mars is nearing it's closest approach (making it appear larger than usual) but is a still a mere 23 arc seconds.  Saturn is 17 arc-seconds across.
This means you are trying to resolve fine detail on an extremely tiny area and this is pushing the limits of what your telescope handle.
Collimation
Other factors such as optical collimation (alignment of the optical axis of the primary and secondary mirrors).  Portable Newtonian reflectors tend to need somewhat frequent collimation.  Collimation is easy to perform and will improve optical quality.  Also, if the temperature of the telescope mirror has not had time to acclimate to the ambient temperature, the mirror itself will reduce the quality of what you can see (e.g. if a telescope were stored in a warm house but taken outside on a cool evening).  Smaller telescopes will acclimate faster because the mirror has less mass.
Seeing Conditions
Seeing conditions will also have a large factor.  Weather fronts such as cold fronts, warm fronts, or the presence of the jet stream will impact seeing quality.  There is little you can do about this.  (Large telescopes can use 'Adaptive Optics' but this isn't a common thing in amateur astronomy.)
The best analogy I've come across to describe seeing conditions is to imagine placing a coin in the bottom of a pool or fountain.  If the surface of the water is perfectly flat -- no waves -- then you can easily see the coin.  With magnification you can see details on the coin.  But if a second person starts tapping the water surface to create waves... you can see the coin ... but not details.  The coin is optically distorted by the waves.  The atmosphere does the same thing when we use telescopes.  It need not be physical "waves" but can be things such as mixing warm & cool air in the upper atmosphere.
Infinity Focus
Everything in space is effectively focused to "infinity" for your telescope.  If anything is focused, then everything is focused.  This means if it makes things easier for you, focus your instrument on the moon and achieve the sharpest focus possible.  Then re-point the telescope to a planet and should not need to re-focus the telescope.  You will likely want to do this using your 6mm eyepiece (because changing eyepieces usually requires re-focusing the instrument.  There is such a thing as "parfocal" eyepieces -- which all share the same focus and you can swap eyepieces without refocusing.  Most eyepieces are not parfocal with other eyepieces.
Maximum useful magnification
There are some formulas for working out the maximum useful magnification of an instrument.
One such (rather simplistic) approximation is that the maximum magnification is 2x the aperture when measured in millimeters.  As you have a 130mm aperture, this would imply that 260x is the maximum magnification.  HOWEVER (huge caveats) this assumes flawless optics in flawless seeing conditions -- which almost never happens.  A more practical limit is roughly 1x of your aperture.  This becomes subjective as to when you decide that the magnification is making things worse instead of better.
It turns out mathematically... that the focal length of an eyepiece needed to provide magnification that matches 1x of your telescope's focal length in millimeters... will always be the same as the focal ratio of the telescope.
Since you have an f/5 telescope, a 5mm eyepiece will provide 130x magnification.
Both your 20mm and 6mm are fine and should not over-magnify the image ... you can use a 2x barlow with the 20mm, but you will not likely enjoy the views of the 6mm eyepiece combined with the 2x barlow.
There are more technical ways to discuss maximum focus such as the very simple Dawes' Limit or using Rayleigh criterion.  These methods discuss maximum resolving power of an instrument based on aperture and wavelength of the light.  But even these methods have a low-bar.  That is to say... their standard is whether two points of light with some amount of angular separation could be resolved as two points of light and not just one merged point of light.  They wont look sharp ... they'll just be blurry points that have noticeable separation.
One conclusion that can easily be drawn by looking at the formulae for maximum resolving power of an instrument... is that the bigger the aperture of the instrument, the greater the detail it will be able to resolve (which is why professional astronomers want to strive for larger and larger telescopes).
On a personal note, my first telescope had a 3.5" aperture.  I could see that Saturn had "rings" and I could see that Jupiter had "bands".  Then I got a 5" telescope... and on nights with better seeing, I could just barely make out that the ring system on Saturn had a dark band in it (the Cassini division) and that Jupiters belts sometimes had texture.  Over the years I would eventually get larger telescopes and, unsurprisingly, larger aperture telescopes allowed for viewing greater amounts of detail.  Have a reasonable expectation as to what you should be able to resolve with a 130mm (roughly 5") instrument.
Atmospheric Dispersion
When looking at anything low in the sky you may notice some "color fringing".  If a planet has a slightly blue edge on one side and a slight red edge on the opposite site, then this is typically a result of the atmosphere acting like a prism ... it's separation the light spectrum because the object is very low in the sky.  I live at fairly northern latitudes and this is true of observing outer planets during the summer months (when Earth's northern pole is tilted away from the outer solar system and toward the Sun ... from my latitude.  But southern hemisphere observer's are tilted toward the outer solar system, so they see these same planets very high in the sky where atmospheric dispersion doesn't impact them as much.  Basically outer planets appear high in the sky when observed during your hemisphere's "winter" season and low in the sky when observed during your hemisphere's "summer" season.
This dispersion will tend to blur the surface details of any planet.  It isn't really the fault of your instrument (there is a device called an Atmospheric Dispersion Corrector which is basically an adjustable prism and it is used to reverse the dispersion created by the atmosphere).


Do the number of moons a planet has affect the speed of the planet's rotation? Would the tidal forces of multiple moons interacting upon a planet speed up or slow down the day length of the planet? I was thinking that maybe the planet's day length would be slowed down due to all of the gravitational tugging, but on the other hand I was thinking that maybe all of those tidal forces could perhaps slingshot the planet ahead and make it spin at a faster rate. Would the day length even change at all? If the answer is yes, could all of those moons even affect the planet's precession?

Any moon exerts a tidal force on its primary, tending to cause the primary to bulge outward along the axis passing the moon and to narrow slightly in the other two directions. This effect is greater if the moon in question is larger and/or closer to the primary, but a solid primary may largely resist it, so that it changes shape little if at all. In the case of the Earth and its Moon, the solid Earth moves relatively little, while the water of the oceans is moved quite a bit. As a result, water has to flow from one place to another over the solid crust. That flow causes friction, which causes the "bulge" of water to lag behind the Moon and pull back on it by gravity. This process gradually slows the rotation of the Earth and drives the Moon further away.

This process acts, in general to bring the rotation of the planet and the revolution of the Moon to the same rate, so that the planet keeps one face to the Moon. Usually this means slowing the planet's rotation, but a few moons are so close to the planet that it would be the opposite. This process will be less pronounced on a planet which  has a deeper liquid layer, since there will be less friction, or on a planet which has a stiff solid structure, since there will be less movement.

The number of moons is not directly relevant. To a reasonable approximation they all work independently.


Estimate prevalence of ʻOumuamua-style interstellar obects inside Jupiter orbit now that C/2019 Q4 (Borisov) is found? Now we know two of them, so maybe it's not an outlier.

We have two points so we can draw a line. How many similar macroscopic objects should be zipping through space at ~30 km/sec so that we would see one of these passing inside the orbit of Jupiter once every two years? I don't really know what units this should be expressed with. Maybe it's 1 / (km^2 * year)  - the frequency of such a body coming through any random square kilometer of empty space in a year of time.

What's the "capture cross section" of intra-Jupiter orbit? I imagine that since the Sun affects trajectories of bodies coming near it, drawing them closer as they pass by, intra-Jupiter orbit will see much more bodies than a circle of same area in empty space. How large is this effect for ʻOumuamua-like bodies? I expect this is to be a unitless coefficient. Is it neligible? Is it 5x? 10x? 1000x?

Sorry if my question is not clear enough.

The enhancement of a cross-section due to gravitational focusing is given by
$$ \sigma_{\rm eff} = \pi a_J^2 \left(1 + \frac{2GM_{\odot}}{a_J\ v^2}\right),$$
where  $a_J$ is the semi-major axis of Jupiter's orbit (assumed circular), $v$ is the relative velocity (at infinity) and I have ignored the mass of Jupiter.

Thus, using $v=30$ km/s (as specified in the question) the term in brackets is the gravitational focusing enhancement of the cross-section and equals 1.38.

We now assume an isotropic velocity distribution and a homogeneous density of such objects of $n$ per unit volume. The flux of such particles is $f =n v \sigma_{\rm eff}$.

If $f = 0.5$ yr$^{-1}$, then $n \sim 5 \times 10^{12}$ per cubic parsec.


Existence of a "reflecting" star Wasn't even sure about what the title should be, but I had a thought and I wonder whether it may be possible or not.

Is it possible that there is a star which acts as a mirror and reflects back the light almost as it was received?

My though is that if there is something like that and let's say that the star is far from earth 50 light years, than we could see 100 years back to the past.

See this post about binary stars, which contains relevant information:

  Stars are far from perfect blackbodies due to scattering/reflection.
  This is especially true for hotter stars, because of all the free
  electrons, but even cooler stars can reflect a significant amount. For
  example, in aanda.org/articles/aa/pdf/2001/19/aa1009.pdf you will see
  that they use a reflection albedo of 0.30 for the K star and 1.00 for
  the F star, but the latter number is not meant to be taken seriously,
  they simply don't care if the light is reflected or absorbed and
  re-emitted because it isn't an important term. But the value of 0.30
  for the K star might be meant more seriously, though it is still not
  regarded as a critical parameter because it only affects the color of
  the light that is reflected, not the total amount of light (given that
  stars are in radiative equilibrium, so must ultimately return all the
  incident light, whether it happens by reflection or heating).

  Indeed, stellar emissions are often characterized by "effective
  temperature," to connect the surface flux of a star to the
  Stefan-Boltzmann formula for the emission of a blackbody by using a T
  parameter that is not necessarily the actual temperature. When using
  this notion, as is quite common for dealing with stars, there is no
  essential difference between heating of and reflection from the
  surface of the star in question. The details of the difference have to
  do with the shape of the spectrum, but that shape is generally not a
  Planck function anyway, so as soon as one is using the "effective
  temperature" concept one has already parted company from a detailed
  understanding of the shape of the spectrum. (When you do want the
  details of the spectrum, you will have to model the situation with
  some care.)

Is it possible that there is a star which acts as a mirror and reflects back the light almost as it was received?

That depends on what you mean by "as it was received". That post shows that the concept of albedo applies to stars as well; they can be reflective.


How to shift an AGN X-ray spectrum to rest frame I have limited information to shift a spectrum (in the X-ray 0.5-10 keV bandpass) from redshift $z=2$ to the rest frame. I have a plot of normalized (photon) counts s$^{−1}$ keV$^{−1}$ as a function of energy (keV). Is there a way to shift the spectrum I have to rest frame? Or do I really need luminosity distance, etc.?

The frequency is related to the redshift by $$\frac{\nu_{\rm obs}}{\nu_{\rm emit}} = \frac{1}{1+z}$$

Another useful relation is the fact that, for any redshift,

$$\frac{I_{\nu}}{\nu^3} = {\rm constant}$$

where $I_{\nu}$ is the specific radiative intensity.

The specific count rate (counts per area per time per energy interval) is proportional to $I_{\nu}/\nu$. (Do you see why?)

That should give you enough information to derive how the measured count rate changes with $z.$ Of course, to know the actual value, not just the function of $z$, you'd need to know the actual count rate measured, not just the normalized value.


How do the sun's light rays come to the world? How do they come to the world? One of my friends who is a flat earther told me about how the rays seem to gather at one point, which sort of proves that the sun is close to us and not very big, in his opinion. He thinks that the rays should come parallel, as the sun is much bigger than the world. We were also taught that they come parallel, as shown in the image.

However, what had me thinking is that the sun isn't that big from our point of view. When we look at it, it just seems like a small marble, and this makes it a small spherical light source. It being small makes it act like a point light source in my opinion, and this means the light rays do not come to the world as in the image, but with different angles. I also think that to see a spherical light source's light rays coming parallel toward us, the source must cover all of our horizon, but this is not the case for the sun since it seems just like a marble from the earth.
Can anyone please explain this to me? Is the image not the correct way to teach this?

The are parallel.  The picture is way off scale. Here is a scale picture of the sun and Earth

Oh dear! the Earth is too small to be seen!  Even the Earth and moon look to be in the same place.  Rays of light that are hitting your neighbourhood are coming in parallel. The light from the top of the sun and the bottom of the sun are not quite parallel (the lines in the diagram slightly converge) but light from on point on the sun will hit the all the places in your neighbourhood in exactly the same direction.
Let's zoom in

There's the Earth, and two rays from the sun.  Are they parallel? No there is an angle of 0.00052 degrees between them. The angle is only so large because the distance between the ends of the rays is a lot (about the distance from Mexico to Canada). If I'd put the ends of the rays closer together the angle would have been much less.  To all intents and purposes the rays are parallel.
What you describe is an optical illusion.  When the sun shines through gaps in the cloud you will see several parallel rays coming towards you.  Because they are coming towards you, they will appear to diverge, just like railway track appear to diverge as they come towards you.  But with railway tracks we can see that they are coming towards us, because they are on the the ground.  With the parallel rays of sunlight, there are no clues, and we see them as shining down, and so being non-parallel.  Its an optical illusion.


Parabolic or hyperbolic trajectories According to Newton's laws, the trajectories for the two-body problem are conics: either ellipses, or parabolas or hyperbolas. Of course periodic motions require Ellipses and in the Solar system these elliptic curves are a pretty good approximation of the trajectory of each planet.

However, it is possible that the trajectory of a very fast comet could be an hyperbola or a parabola with the Sun at a focus; in that case the motion would not be periodic and the comet would be visible near the Sun only once.

My question: was there ever any observation of a  comet on a hyperbolic (or parabolic) trajectory (with the Sun at a focus)? Same question for different stellar objects. It would be certainly very difficult to observe, since the comet would be visible only one time at its perihelion and would go at infinity after this with no return.

Yes, and it is not uncommon for an orbit have an eccentricity close to one. The wikipedia site, linked in a comment above, notes C/1980 E1, which entered the inner solar system with an eccentricity close to one, but had a close encounter with jupiter and was accelerated. It left the inner solar system with a eccentricity of 1.05, and so is on a hyperbolic trajectory, and will escape from the sun's gravity

Orbits that are highly hyperbolic are very unlikely. Comets formed as part of the solar system.

They are not really harder to spot than any other comet. A comet takes many months to make its passage through the inner solar system. There is plenty of time for them to be spotted, especially if you have probes like SOHO or NEAT


Does the accelerating expansion of spacetime mean that the pace of time is changing? Space expands everywhere, also here. And time is inseparable from space. Does this mean that time also "expands" as in changing its pace? Is the changing rate of time also astronomically observable? How did time behave during the radical inflation shortly after Big Bang?

To talk about 'the rate of time', we essentially need at least two different time coordinates. For example, this happens in special-relativistic time dilation, which is equivalent to $\mathrm{d}t'/\mathrm{d}t$ across two different inertial frames. Fortunately, we can do something similar here.

  Space expands everywhere, also here. And time is inseparable from space. Does this mean that time also "expands" as in changing its pace? ... In a similar way that the expansion of space is compared relative to, well, to itself I suppose.

A spatially isotropic and homogeneous universe has the metric in the form
$$\mathrm{d}s^2 = -\mathrm{d}t^2 + a^2(t)\mathrm{d}\Sigma^2\text{,}$$
where $a(t)$ is the scale factor and $\mathrm{d}\Sigma^2$ is the metric of an isotropic and homogeneous Riemannian manifold: the 'open' hyperbolic $3$-plane, the flat Euclidean $3$-space, or the 'closed' $3$-sphere (or real projective $3$-space, but that's usually not considered because it's non-orientable). If the scale factor is ever zero in the past, the cosmological time for this is conventionally chosen to be $t = 0$.

The cosmological time measures the proper time of an observer at rest relative to the bulk of the matter in the universe, so in some sense it's the most intuitive choice of a time coordinate, but like all coordinates, it's not sacred. We can, for example, define a conformal time coordinate $\eta$ such that $\mathrm{d}\eta = \mathrm{d}t/a$, in which the metric takes the form
$$\mathrm{d}s^2 = a^2(\eta)\left[-\mathrm{d}\eta^2 + \mathrm{d}\Sigma^2\right]\text{,}$$
and so all of the dimensions of spacetime are affected by cosmic expansion in the same way. Therefore, I think conformal time satisfies the requirements in your question, although it is not measured by any local clock.

  Is the changing rate of time also astronomically observable?

The scale factor is astronomically observable, and $\mathrm{d}\eta/\mathrm{d}t = 1/a$, so yes.

  How did time behave during the radical inflation shortly after Big Bang?

The conformal time essentially uses the particle horizon as a measure of time, i.e. the furthest distance from which an ideal lightlike signal could have travelled since $t = 0$ in order to reach the observer by the present time. During inflation, the particle horizon rapidly expanded.


Why is the Sun less massive than other G2V stars? The Wikipedia page for G-type main-sequence stars lists the expected mass and temperature for stars of each sub-classification:
$$\begin{array}{c|c|c|}
 & \text{Mass ($M_\odot$) } & \text{Temperature (K)} \\ \hline
\text{G0V} & 1.15 & 5980 \\ \hline
\text{G1V} & 1.10 & 5900 \\ \hline
\text{G2V} & 1.07 & 5800 \\ \hline
\text{G3V} & 1.04 & 5710 \\ \hline
\text{G4V} & 1.00 & 5690 \\ \hline
\text{G5V} & 0.98 & 5620 \\ \hline
\text{G6V} & 0.93 & 5570 \\ \hline
\text{G7V} & 0.90 & 5500 \\ \hline
\text{G8V} & 0.87 & 5450 \\ \hline
\text{G9V} & 0.84 & 5370 \\ \hline
\end{array}$$
Spectral type is only determined through a star's temperature, and thus the Sun with a temperature of $\text{5778 K}$ is unambiguously a G2V star.
However the Sun is noticeably less massive than other G2V stars are. Why is that? Or, another way of asking, why is the Sun hotter than other stars of the same mass (G4V)?

It isn't. You've just got  dodgy table from wikipedia.
A more modern (and well-used) version is here.
It lists
G1V  1.07 5880
G2V  1.02 5770
G3V  1.00 5720
This is an average relationship. The closest and most consistent relationship will be between spectral type and effective temperature and indeed the Sun is normally attributed a spectral class of G2V and $T_{\rm eff} \simeq 5780$ K.
The reason for any small discrepancy at the hundredth of a solar mass level with the mass in the table could be because the Sun has a slightly different composition to the average star that defines this table. The age of the Sun is unlikely to be a major factor. According to most models, the temperature of the Sun increases by just 100 K between a billion years old and around 8 billion years old and then cools a little bit. On the other hand, stars like the Sun do lose a little mass as they get older, mainly through a stellar wind. The Sun though is probably at around the average age for an early G star in our Galactic neighbourhood.


Why do most of the myths behind constellations originate from Greek? Why do most of the myths regarding constellations happen to have begun from Greek civilization? Why not other civilizations?

Most people who lived in the past era probably observed star patterns in the sky and created their own constellation myths.

Also, I would like to know more about some of the stories regarding the myths of those constellations.

Ptolemy was Greek.  He wrote an important book called the Almagest. In it, he lists and describes the constellations as used in Greece in the 4th century BC. Naturally, the Greeks used elements from Greek Mythology in their sky culture, just as Chinese sky culture uses elements from Chinese legend and myth.

Ptolemy's Almagest and Greek sky culture influenced the Hellenistic world, and through Rome, it influenced the whole of Western Europe.  Then through European expansion, it came to influence the whole world.

There are several additions to Ptolemy's system: The Southern Sky was divided into constellations by Europeans in the 15th century, and there are several additions to the Northern sky, such as Coma Berencies (Hair of Berenice II of Egypt) and Camelopardalis, the giraffe, (added in the 15th century)


How do telescopes "zoom" and change angle of view? Images from the Hubble Space Telescope have widely different angles of view. Is this only the result of composing multiple images, or can the telescope itself change its "zooming" optically, mechanically? How does the ability to change the angle of view differ between the major scientific telescopes of today and the near future, space and ground based?

And what about cameras on interplanetary probes? Can for example New Horizons optically change its zooming as it passes Pluto?

Telescopes tend to have a fixed focal length. What changes is the size of the sensor in the instrument used. If a small sensor is used, then a smaller section of the field of view is exposed, resulting in a narrower field of view being imaged than the equipment is capable of. If a larger sensor is used, more of the field of view of the telescope is utilised.

Additional optics in the light path that are associated with the specific instrument being used on the telescope will affect the field of view also.

Telescopes do not offer the capability of 'zooming' as you understand it from your consumer digital camera.


Stable polar solar orbit with the Earth continuously observable Is there a stable polar solar orbit such that the Earth is always in view and not eclipsed by the Sun?

As ganbustein says, this is not too difficult to imagine.  The simplest case (approximating with circular orbits and only the Sun, Earth and Satellite) would have the satellite orbit orthogonally to the Earth with a 1 year orbit.  The Satellite will pass the Earth orbit plane in two places, call these "down crossing" and "up crossing" points.

To minimize Earth - Satellite iterations, keep them 90 degrees apart.  Have the Satellite over the north solar pole when the Earth is at the "down crossing" point.  Then when the satellite gets to the "down crossing point" the Earth will be furthest from the Satellite plane.  When the earth is at the "up crossing point" the satellite will under the Suns south pole. And so on.

This would not be completely stable when we include Jupiter and the mutual interactions, but I think they should be small, allowing this to work generally.  If someone "does the math" and proves me wrong, I will accept that.


What causes fast moving pulsars to move so fast? This article investigates the traces left in the ISM by fast moving pulsars. Is there a mechanism specific to pulsars that causes them to move so fast, or are there just as many fast moving stars?

The article also mentions that

  Many fast moving pulsars quickly escape  the  host  supernova  remnant

This seems to indicate that something during the supernova makes the pulsar speed-up (or the remnant slow down). How does this happen?

The most likely scenario is that an asymmetry in the supernova explosion  imparts momentum to the proto neutron star at its core. The issue is not settled.

A recent study by Verbunt et al. (2017) models the
speed distribution of young pulsars as the sum of two Maxwellian distributions, one with an average speed of $\sim 130$ km/s and the other with an average speed $\sim 520$ km/s. About 30% of the population are in the low speed  population and only a few percent have speeds below 60 km/s.. A plot of the (model) distribution is shown in Fig.9 of that paper.

Why do some pulsars move so fast? Conservation of momentum. Pulsars are neutron stars with mass about $1.5 M_{\odot}$, born at the heart of core-collapse supernovae. A 500 km/s speed corresponds to a kinetic energy of about $4\times 10^{41}$ J and a linear momentum of $1.5\times 10^{36}$ kg m/s, but during the supernova, approximately $10^{46}$ J is made available when the core collapses from about the size of the Earth to a ball of neutrons 20 km across. Thus only a tiny fraction of this energy needs to be given to the neutron star to accelerate it to high speeds.

Most of the energy in a supernova is released as almost massless neutrinos from the core. In order of magnitude terms, the neutrinos carry away a linear momentum of $\sim E/c = 3.3\times 10^{37}$ kg m/s. If there were a small asymmetry in how these neutrinos escaped - i.e. more in one direction than another, then conservation of momentum would demand that the core moves in the opposite direction. To match the observed linear momentum of fast moving neutron stars would demand
a directional asymmetry of neutrino emission of $\sim 5$%, (which seems unlikely and may require magnetic fields of $10^{12}$ T -  Nardi & Zuluaga 2001 ). A better idea might be that in the initial stages of the collapse, the core material is opaque to neutrinos and it could be that there is an asymmetry in the way the neutrinos break out of the absorbing material (e.g. Nordhaus et al. 2012).

Alternatives are that there are instabilities in the final phases of nuclear burning, just prior to the core collapse. These instabilities cause the core to wobble back and forth and when the supernova happens, the core just happens to be travelling one way or another. There have also been suggestions that asymmetric radiation from the pulsar itself could gradually accelerate it to the speeds observed.


If the density of nebular distribution increases symmetrically in all directions, how does space curvature explain it? Edwin Hubble, in The Observational Approach to Cosmology, wrote

  Thus the density of the nebular distribution increases outwards,
  symmetrically in all directions, leaving the observer in a unique position. Such a favoured position, of course, is intolerable.

My first question is: do more recent observations still show a symmetrical nebulae density increase? Or did Hubble just do a miscalculation, misinterpretation of an observation etc.?

Apparently, Hubble can solve this problem with spatial curvature. Further below, he writes

  Therefore, in order to restore homogeneity, and to escape the horror of a unique position, the departures from uniformity, which are introduced by the recession factors, must be compensated by the second term representing effects of spatial curvature. - There seems to be no other escape.

I understand how an expanding Universe explains the symmetrical redshift, but I fail to understand how it explains the symmetrical increase of nebulae density.

Let me preface my answer by saying that you're reading a book from 1937 which references the scientific knowledge from the early 1900's. In case you're unfamiliar with astronomical history, I'll say that we've come a looong way since the early 1900's. For example, this book discuses "Nebula as Island Universes". At this point, astronomers had only just discovered that these mysterious "nebulae" were actually entire galaxies that were millions of light years away. Hubble is still referring to them as nebula though, rather than galaxies. That being said, it may actually be kind of difficult to "translate" some of this science from almost 100 years ago into modern theories and terminology. You may even find things which are flat out wrong. Hubble did make a lot of important discoveries, but there were many details he was mistaken on.

Do more recent observations still show a symmetrical nebulae density increase?

Again, nebulae here refers to galaxies, not what we've come to consider as nebulae. What you're asking here, and what Hubble was referring to, before it had an official name, is about the Cosmological Principle.

I think the appropriate answer to this question though, is to point out that I believe you're misinterpreting the text. In the Comparison of Observations with Theory section, Hubble is showing that observations of nebulae (sic, galaxies) indicate they are uniform through space and that his uniformity is easily explained by a static, non-expanding universe.

  If both of the extra terms (for recession and for curvature) were absent, the surveys would clearly fit the formula because the situation would be precisely that in a stationary universe.

The "formula" he's talking about here is the one which indicates

  nebulae are uniformly distributed through a non-expanding universe in which red-shifts are not primarily velocity-shifts, [and] then the numbers should be proportional to the volumes

However, he also knows that the Universe is expanding (he was the one to discover this after all) so he took the standard formula and threw in universal expansion. What he finds though, is that the equations now predict that

  the numbers of nebulae increase faster than the volume of
  space through which they are scattered

The important point here is that an expanding universe (with no curvature) predicts this is the case, not that it actually is the case. His previous sections and accompanying plot indicate that observations show the universe is homogeneous. Hubble makes the point (and you reference it) that this is discrepancy can be solved by including the curvature of the universe into the mix as well in which case the predictions now match up with the basic "formula" which didn't include expansion or curvature.

Just as an addendum, I'll expand on this and add that current observations do in fact show that galaxies are isotropic and homogeneous on large scales. One just survey showing this is the 2dF Galaxy Redshift Survey. Shown below is a plot from their results. While full statistical analysis is needed to says something conclusive, you can see that to the naked eye, the galaxy distribution does appear to be homogeneous and isotropic.

Note that this only covers part of the sky because the rest of it is blocked by the disk of our galaxy.

I understand how an expanding Universe explains the symmetrical redshift, but I fail to understand how it explains the symmetrical increase of nebulae density.

I'm interpreting this to mean, you're wondering how the "formula" with expansion included can produce the result that "the numbers of nebulae increase faster than the volume of space through which they are scattered". This I think is more or less a math question. If you're really interested in seeing how it was derived, feel free to look at Hubble's original paper: Hubble, E., Tolman, R. C., Astrophysical Journal, 82, 302, 1935. I think you'll find the summary equations in Section 12 (page 328 in the paper, page 27 in the pdf) with lengthy derivations before that.


On orbital mechanics of evaporating planets A planet orbits around its sun on an elliptic orbit, and loses mass slowly due to evaporation. How will the parameters of the orbital ellipse change as a function of time?
Could we do a generalisation and mathematically model it?

The mass of a planet does not affect its orbit significantly unless it is a very large planet.  On the opposite end of the spectrum would be a very small mass planet that was evaporating, and that is essentially what a comet is.  It's all Keplerian, though comets can have their orbits affected slightly by the tiny push they get from the evaporating gases.  So it's not the change in mass, but how the evaporation actually happens, but this is a small effect.  Even a large planet like Jupiter does not affect the Sun much (the Sun orbits around a point that is not even external to the Sun), so losing mass would not affect the orbit of Jupiter in any significant way either.


Distance to star using color index I'm doing the following question:

  A star is observed with UBV magnitudes $m_u = 16.31$, $m_b = 14.52$,
  $m_v = 13.76$. Spectral analysis gives $M_{bol} = 7.31$, $BC = -1.02$, $(U − B)_0 = 1.222$. Determine the distance to the star.

As $m_u - m_b ≠ (U-B)_0$, I gathered that the distance modulus can't be used directly, since extinction is present. From the bolometric correction (BC), we can determine that the absolute visual magnitude $M_v = 8.33$.

After that, I'm unsure of what to do; normally I think in these questions you can obtain the visual extinction $A_v = 3.0E_{B-V}$, where $E_{B-V}$ is the color excess, calculated by $E_{B-V} = (m_b - m_v) - (B-V)_0$. Then, the visual extinction can be added to the distance modulus equation to account for extinction in the visual band, and then we can easily obtain distance.

But, while we know $m_b$, $m_v$, and $M_v$, we don't really have a way of obtaining $(B-V)_0$ to my knowledge, unless there's some way we can relate it to $(U-B)_0$. Any help would be much appreciated!

There is a relationship between $E(B-V)$ and the reddening in any other colour. The exact value depends on the type of dust, the extinction value itself and the intrinsic spectrum of the star (as does the 3.0 coefficient mentioned in your question).

However, for the purposes of estimation, the canonical relationship is $E(U-B) = 0.72 E(B-V)$ (e.g. Pandey et al. 2003).

Thus you can calculate $E(U-B)$, then $E(B-V)$, then $A_V$, then $V_0$ and use this with $M_V$ to get the distance.


Is there a link between the amount of swirling and vorticity in a gas giant's atmosphere and its distance to its Sun? This is an empirical observation of mine:
I have noticed that out of the 4 gas giants in our Solar System, Jupiter's atmosphere has the most visible swirls and complex cloud patterns, followed by Saturn and then by Neptune (I have ignored Uranus here since I heard its heated more by the Sun than by its own internal heating)
These 3 planets also seem to be arranged in their distance to our Sun. I am assuming more heat from a Sun = more complex weather patterns due to interactions with the atmosphere
Does this mean that hot exo-planet gas giants would have extremely swirly, complex weather patterns?

Distance from the Sun is not a major driver for vorticity of gas giants in our Solar System
According to Yadav et al., Jupiter indeed has a higher vorticity than Saturn:

There is a stark contrast in the number of vortices between the two
planets: about 200 with 1000 km or larger diameter on Jupiter, while
only 10 to 50 on Saturn.  Note that while both planets also have
smaller vortices, the disparity in the numbers still persists.
Vortices are also present at or very close to the rotational poles:
Saturn has a cyclonic polar vortex at each pole , while Jupiter has a
cluster of cyclones at each pole

The authors claim the difference in the vorticity is mostly due to the differences in atmospheric make-up of the two planets (and their magnetic fields) and don't mention distance from the Sun as a factor.  The below image is from their paper:

The difference in vorticity between Saturn and Neptune is less clear. Vortices may be less visible on Neptune as there is less color contrast in the atmosphere. Neptune certainly has many vortices including its own Great Dark Spots.  It also has the highest winds observed in the Solar System.
The vortexes on Neptune are also modeled based on what we know about the atmosphere.  Hadland et al. model methane cloud formation in their paper: EPIC Simulations of Neptune’s Dark Spots Using an Active Cloud Microphysical Model.  Here is a picture of the Great Dark Spot (center) as taken by Voyager 2 in 1989.

You can contrast that image against this more recent image of Saturn from Cassini:

It certainly isn't clear to me which planet is more turbulent.
Reading the aforementioned papers, the vorticity of Jupiter, Saturn, and Neptune are due to:

The atmospheric makeup
The quantity of heat transfer in convective currents
The Coriolis Effects on the atmosphere due to the spin rate of the planets

Note that the ratio for power emitted to power absorbed by the Sun are 2.5 for Jupiter, 2.4 for Saturn, and 2.7 for Neptune, which means the convection currents are mostly driven by geothermal energy loss, rather than solar heating (as opposed to Earth's atmospherics).
Hot Jovian exo-planets are indeed expected to have "extremely swirly, complex weather patterns!"
Though the Sun doesn't play the primary role for our distantly gas giants, it probably plays an enormous role in the weather patterns of Hot Jupiters!  Most of the Hot Jupiters will be tidally locked to their stars since the time to tidal lock is proportional to $a^6$, where $a$ is the semi-major axis of the orbit of the planet.  Planets with a small $a$ tidal lock very quickly.
Hot Jupiters in tidal lock with their star have a much slower rotation rate (on the order of days) than our Jupiter's rotation rate (~10 hours).  That means the contribution to vorticity due to Coriolis Forces will be proportionally less.  However, heat transfer in the upper atmosphere will be much more dramatic since much of the heat absorbed on the "day side" of the planet will be emitted from the "night-side" of the planet. Skinner and Cho (2021) perform numerical simulations in their paper Numerical Convergence of Hot-Jupiter Atmospheric Flow Solutions and highlight that their solution:

features a dynamic, zonally (east-west) asymmetric jet with a copious
amount of small-scale vortices and gravity waves.

Here is one of the beautiful simulation images from their paper:


How to improve the quality of an image of the planets when taken through the eyepiece of a telescope with a dlsr camera I have a reflector telescope with a 114mm aperture and 1000mm focal length.  I find that to get the clearest image I can use a 4mm eyepiece, or with my 5x barlow a 20mm however, seeing that I am very interested in astro photography when I try to photograph Jupiter for instance, through the telescope eyepiece, being the size of about a green pea seen through the scope, there is not enough pixel data for my canon eos t2i rebel dlsr to capture a clear photo. Is there some way to enlarge the photo for the camera without blurring the planet's details from over magnification?

If you were using both a camera lens and an eyepiece (afocal method), try eyepiece projection.
In this method, the eyepiece is the only optical element between the prime focus and the detector.
You would need an eyepiece projection adapter tube to connect the camera body to the telescope's focuser.
A longer tube will increase magnification but also increase exposure time.
Any tube length which reasonably balances those concerns should be OK.

It's also possible to use a Barlow lens and no eyepiece to extend the effective focal length of the telescope.
If your adapter tube is wide enough to accommodate the Barlow, you may be able to use it this way too.

Astronomy Source has an article with more details about eyepiece projection.
Tele Vue has an overview of that and other methods, plugging their own products of course.


Is there a maximum size for a black hole? As far as I understand it black holes radiate Hawking radiation and probably gravity waves, which over time causes them to lose mass and eventually evaporate after almost unfathomable amounts of time.  I've also read that black holes eventually have difficulty gaining size after a certain point because gravitational forces working in a black hole's accreditation disk can eventually begin ejecting in-falling matter before it can be absorbed.

While I know black holes can become quite massive, that leads me to wonder if Black holes have a maximum possible size where they will begin to immediately radiate any additional mass that's added to it.  Or can a black hole effectively expand forever as long as the supply of matter is greater than the effects of radiation and ejection?

Is there effectively a size limit to black holes?

As David Hammen commented, the power emitted through Hawking radiation is proportional to $M^{-2}$. Thus the evaporation timescale for a black hole is proportional to $M^3$. This means that a more massive black hole is much more stable against evaporation than a lower mass black hole.

The other issue you mention is the limited rate that you can "feed" a black hole. There is inevitably a feedback; as gas is compressed towards the event horizon it gets hot and emits radiation. The pressure of this radiation can eventually balance the inward gravitational infall. For spherically symmetric accretion this leads to the Eddington limit, which sets the maximum spherical accretion rate, where $\dot{M}_{\rm max}\propto M$. That is, the maximum accretion rate is proportional to the black hole mass.

If accretion proceeds at the Eddington limit then the black hole mass grows exponentially with time and with a characteristic doubling timescale of around 50 million years (independent of the original mass - see this Physics SE page for some mathematical details).

If black holes were limited to this accretion rate (though there is some evidence from the presence of very luminous quasars at high redshift that they may exceed it), then the maximum black hole mass will depend on the age of the universe and the size of the initial "seed" black holes. If we assume an initial mass of 100 solar masses, a doubling timescale of 50 million years and that the seed black holes formed 400 million years after the big bang (all plausible, but contestable), then there have been 266 doubling timescales since and the black hole could have grown by a factor of $10^{80}$ !

Clearly there are no black holes with anywhere near this mass in the observable universe - the largest appear to be of order $10^{10}$ solar masses. Their growth is limited by their food supply. Supermassive black holes are found at the centres of galaxies. There is a poorly understood relationship between the black hole mass and the mass of the bulge of the galaxy it is in. The ratio peaks at about 1 percent for the most massive bulges (e.g. see Hu 2009; McConnell & Ma 2013). Since the most massive massive elliptical galaxies are of order $10^{12}$ solar masses, this appears to set the maximum mass of a black hole in the present day universe.

The future is speculation. If the cosmic expansion rate continues to accelerate, then galaxy mergers will become increasingly uncommon and the opportunities for further black hole growth will be limited.


How can we be sure that we have identified very distant stars correctly? From reading this question on calculating distance to stars and from a bit of background reading on the standard candle theory I still don't see how we can confirm that a star we see at one distance and a star we see at another distance (redshifted and at a different apparent luminosity) are the same type.

Beyond a certain distance, parallax is not possible, so how can we confirm star X and star Y are the same type therefore the difference in redshift and luminosity means Y must be at distance Z. How do we know it isn't a different type of star at a different distance?

Or are we just saying they look similar, so probably are?

We determine the spectral type (i.e. temperature) of a star using multicolour photometry, or (ideally) spectroscopy. By guesstimating the temperature, mass and radius of a star, we can say that two stars that have pretty similar observational properties probably are closely related to each other.

Cepheid variables, for example, display periodic pulsations that depend quite strongly on their intrinsic luminosity -- this is why they're reasonably good standard candles. Their characteristic variability makes them clearly identifiable as a Cepheid, and observations of their pulsation are backed up by data that place them in the same region of the HR diagram.

If it looks like a duck, swims like a duck, and quacks like a duck, then chances are it's a duck. If it's as hot as a Cepheid and pulsates like a Cepheid, then it probably is a Cepheid.

So to answer your final paragraph: yep. Though with no spatial resolution and often (in the absence of parallax measurements) only tenuous distance data, classifying stars is a rather messy business.


Average number and type of planets orbiting given star types I don't need "exact" numbers, but I'm trying to create an auto-generator for a stellar map to crate stars that are "somewhat" accurate.

I'm looking for numbers on the average number and type of planets around each type of Star, and whether they could be a good source for mining or are they good places for life?

So, like, I need an idea of how what is the average number of planets that are expected around a G class star, how many are expected to be Gas giants or terrestrial and what is the likelihood of them being in the habitable zone and containing life.

If I base it on Sol I would suspect about 10 planets, 50% terrestrial and 50% gas giants, with 1 to 3 in the habitable zone and a 30% chance of life developing. I'm looking for something similar to this type of information.

I assume this wouldn't be good for across the board or even for G class stars in general.

So I guess I'm looking for estimated planetary statistics based on spectral type? I don't want a list of exoplanet and stars that I have to look through and then make a bad guess at, but a good estimation of these numbers based on known facts.

This Question doesn't have a simple enough answer for me to grab onto to use effectively without just making too much stuff up anyways.

This Question seems to have pieces of information that I'd use to work something out, but it would likely by far more inaccurate than what other people would come up with and there might be better answer than that so I ask my question.

I wrestled with this one a bit, but because there's no real scientific answer to it, your best bet might to look at the 6 or 8 best known other solar-systems and build off that.   There's no right answer, so a base off evidence approach is probably the way to go.

Or, if you want to base it off nonsense, but sound impressive, you could use the Titius-Bode law.   But I think that's a bad idea, unless large gas giant planetary migration is kept to a minimum, because a migrating Jupiter would make mincemeat of that "law".

The easiest exoplanets to find are planets with short orbits and the easiest stars for us to find planets around are smaller stars.

With those limitations to your view, given that large planets are easier to see, it's hard to say how many smaller ones are out there or how many distant planets from their star.   There's basically zero information to build on regarding those 2 points.

A few generalities though, just for fun.

Rocky planets like the 4 inner planets in our solar system form inside the the Frost Line.  These planets are very low water by percentage.    Now, you could look at the Earth and say "there's tons of water on Earth", but there's really not, at least, not in terms of water to silicate ratio.   Much of Earth's water is on the surface, so we see lots of water, but Earth is basically Iron, Nickle and Silicates with less than 1/3 of 1% of water by volume (even less by mass).   By volume, (using the 860 mile diameter sphere pictured below and from this article).  Earth is about 1 part in 800 water by volume.

There may be as much or more water trapped in Earth's mantle than in the oceans, so the ratio might be closer to 1 part in 400 or there abouts, but the point remains the same.   If Earth is 0.25% water by volume, it's mostly made of stuff that isn't water.

Ceres, by comparison, may be as much as 25% water.  See here and here.  That's 100 times as much water to dry material ratio.   Outside the Frost-line you're going to get very different types of planets.

Over time, you have to figure atmospheric changes, which planets will lose their atmosphere and which planets will heat up like a greenhouse.

Now lets take 3 types of stars, one with 1 solar mass like our sun, one with 0.4 solar masses (red dwarf) and one with 2.5 solar masses (very bright star).

Our sun has a lifespan of roughly 10 billion years and a frost-line, currently at about 2.7 astronomical units (roughly Ceres distance from the sun), but when the sun was young and the planets were forming, our sun was some 30% less luminous, so the frost-line would have been (.7)^.5 * 2.7, or about 2.2 AU.   Now different frozen gases have different frost-lines, but this is just an approximation.   The fact that Ceres is about 25% water even though it's losing water to empty space implies that it formed outside the frost-line where frozen water was abundant.   Ceres is just one example.  All the large moons of the outer planets are also ice and rocky composites.

So, take our 0.4 solar mass red dwarf - a very common type of star.  It's luminosity (0.4)^4th power, is about 1/39th as bright, so it's frost-line would be a bit over six times closer in, less than 0.4 AU.   With less gravitation it might not have a much smaller disk of spiraling matter at the time of formation, so a much larger percentage of the material that forms our red dwarf's solar-system would probably form outside the frost-line, which would imply, fewer 99% dry rocky worlds and more wet (25% water) worlds.   We have many worlds like that in our solar system, but they're all moons or dwarf planets.   Ceres, Ganymede, Europa, Titan, Triton, many others are icy-rocky composites that formed beyond our solar-systems frost-line.

Many of the Kepler observed exoplanets have densities that suggest "water-worlds", many of them larger than Earth.   This fits with the red-dwarf, closer in frost-line argument.   We have no way of knowing how many rocky worlds smaller stars have, but I think it's a safe bet that they have a lower ratio of 99% or greater dry material worlds like our 4 inner planets simply because of the smaller zone inside the frost-line.

The reverse is true for the 2.5 solar mass star.   It also has a short lifespan of 10 billion / (2.5)^3, or about 640 million years, so there's less time for the planets to form, get past any early bombardments and cool down.    And the frost-line for our 2.5 solar mass star would be about 14 AU when the star is in it's early life, some 6 times further than the frost-line in our solar-system, so that's likely a much greater "dry" region for planet formation.   You probably get a higher percentage of rocky worlds around larger stars, so a star 1.5 or twice as bright as our sun could (in theory) have 6 or 8 rocky worlds of varying sizes ranging from hot to cold.  At least, I think it could, though I'm pretty sure this has never been observed.

Gas giants are fairly simple in nature.   All a gas giant needs to form is sufficient gravity to retain it's hydrogen and helium and a source of hydrogen and helium to collect.   A gas giant is more likely to form outside the frost line, but there's no reason why a gas giant couldn't form inside the frost-line.  You'd need about 8 earth masses of a rocky world at Earth temperatures to have a sufficiently high escape velocity that it could retain hydrogen and Helium and in theory, grow into a gas giant, but further away from the star where there's less solar heating, the amount of mass needed goes down with cooler surface temperatures, and with the additinoal mass of ices outside the frost line, it's probably far easier for gas giants to form outside the frostline than inside.

The next thing to consider is Planetary Migration.

Take our Solar-system for example.  There's a theory that Neptune and Uranus may have formed formed inside Jupiter and Saturn, but Jupiter and Saturn pulled them outwards as they drew inwards, perhaps because in the early solar-system there was a period when Jupiter and Saturn were in resonance.

It's also possible that there were 3 large gas giant planets in our solar-system initially.   (not counting Neptune and Uranus as "large" gas giants).   The 3 gas giant model helps explain the formation and water content of the 4 inner planets.

And it's also thought that Jupiter migrated inwards towards the sun, then back outwards.   If Jupiter had kept migrating inwards, which may be the case for several hot Jupiter planets that have been observed, then there's no telling what would have happened to the inner planets, perhaps scattered every which way, some out of the solar-system, pushed too close to the sun or swallowed by the migrating hot Jupiter.  A migrating hot Jupiter would wreck havoc with smaller inner planets as they crossed orbits.

As it is, our own Jupiter may have tossed a large gas giant planet completely out of the solar-system and perhaps made Neptune and Uranus switch places.    (all this is just numerical model based hypothesis, but several articles have been written about these ideas).

Here's a very cool video, if you have some time that runs models on planet formation on "sol" like systems, estimating planet size, location and including how much water the inner planets are likely to get from comets.   Earth, it's thought, got most of it's water from comets and asteroids, largely thanks to Jupiter's migrations.

If you skip forward to about 20 minutes 40 seconds in, you'll see he's computer modeled several different scenarios on planet formation with different gas giant combinations.   The chart shows eccentricity on the y-axis and distance from the star on the x-axis.  As eccentricity goes to one (top of the y-axis), the object is either sent outside the solar-system or close enough to the sun to get vaporized, so basically the dots you see flying up and out of the chart are leaving the solar-system one way or another.

There are, ofcourse other factors, mostly unknowns, like how much material is likley to be available for planet formation when a cloud of matter forms into a solar-system.   Our sun, for example, is something like 99.8% of the mass of the solar system with just 0.2% making up all the other stuff, but I don't know and I don't think anybody knows if that 0.2% is standard, higher than average or lower, and how larger stars might have different ratios than smaller onces, or how much of the material that gets blown off a star in it's young life gets captured by it's orbiting, forming planets.

It's entirely possible that more planetary material can lead to larger but fewer planets as larger planets tend to sweep out a bigger area where less planetary material over the same area might actually give you more smaller planets, but how many planets are likely to form in an average star system, based on size of the star, I don't think anyone knows.   But predictions can be modeled on what happens after the planets form.

What Kepler can tell us:

Most red dwarf stars have planets and at least 25% have planets in their habitable zone.   Source.   (Red Dwarfs are the easiest planets to look at and look for stars).

From the article:

  The new finds imply that virtually all red dwarfs throughout the Milky
  Way have planets, and at least 25 percent of these stars in the sun's
  own neighborhood host habitable-zone "super-Earths," researchers said.

A simple (2-5 inner, 3-5 outer) won't cut it if you're looking for accuracy, but you might be able to run some models, based on how much you (randomly) decide that the gas giants move around and how much material you randomly give the planets.   Heavier planets would need more space around them.

As for mining.  Venus would be a nightmare - too acidic.   Water worlds I would think would be terrible.   No solid platform to build on.   Ice worlds also not great.  Planets with past volcanic activity would be ideal and smaller planets are probably best, as most of the energy with mining probably goes into lifting the material into space, not actually the mining part.   Smaller planets could more easily build a space elevator.   Mars (volcanoes), maybe Mercury would probably be the best mining planets in our solar-system, unless you're mining for 3-HE, in which case, I'd look at the gas giants.   The moon is (I think), a terrible place to mine 3-HE, it's got so little of it, but the Moon's advantage is that it's close.

All that said, I'd just look up 6 or 8 fairly well studied solar systems and build based on those, add some common sense, like a hot Jupiter would remove half the smaller planets, and go with that, because there is no real knowledge on what the most likely scenarios and probabilities are.

Too long? / too many guesses?.  I think about exoplanets a lot.  It's one of my favorite subjects.  I'm very much looking forward to the James Webb Telescope's launch.


Time travel in past and future Why it is not even theoretically possible to travel in past but possible to travel in future ?

The thing about time travel is it's hard to define. Technically we're constantly traveling into the future.
Now, if you went at near-light speed for a long time and then stopped and came back, you would have the illusion of having time travelled into the future because time essentially went on without you. This is entirely physically possible, though not feasible of course.
But past time travel, what does that mean? Does it mean rewinding all time for everything? Or one entity aging backwards? Or time goes backwards while you remain the same age, like the reverse of the future travel?
In any case, unlike the future travel, there is no way, with our current model of physics, to do any of them.
And I must reiterate, future travel by the means I described is only an illusion. You didn't move though time, time just went on without you. Obviously, this won't happen the other way.


What is a "jumping trojan"? And what do their orbits look like? I was googling Neptune's trojan companions and found on Wiki this claim about  ~200 km diameter (316179) 2010 EN65:

  " the object is actually a jumping trojan, is jumping from the
  Lagrangian point L4 into L5 via L3."

So some asteroids not only oscillate between L4 and L5, between being trojans or greeks, but even go via L3, on the opposite side of the Sun? Are their orbits circular as Neptune's (in this case) or highly eccentrical? How could an object in the same orbit as Neptune have another orbital period than Neptune? Or how else can it migrate between L3, L4 and L5?

And are "trojan" objects expected to gather in L3 too?

EDIT:
I'd like to add these illustrations because I think they illustrate well how a regularly orbiting object seems to "stay" longer at L3, L4, L5. (I'm not sure whether "jumping trojans" have some significant other characteristics, though).

In short, most of the trojans stay orbiting arround L4 or L5. These can be called tad-pole orbit asteroids.

There are some trojan asteroids, however, that their orbit never get's too close to L4 nor L5 to get trapped and have a tad-pole orbit, or they do but they have too much energy to get trapped.

These trojan asteroids have larger orbits, following a path like:

L4 --> L3 --> L5 --> L3 --> L4 and so on. This kind of orbit is called horseshoe.

There is, however, a third kind of trojan asteroid. This one appears to follow a tad-pole orbit (I.E. arround L4), but numerical analysis proves they will eventually adopt a horseshoe-like orbit. When they reach the other stable point (L5) they  will get trapped again in a tad-pole orbit. This kind of orbit is very rare (rarity decreases as planet mass increases) and could be considered (personal opinion) as an hybrid tadpole - horseshoe orbit.

For more information, see:

"Jumping mechanisms of Trojan asteroids in the planar
restricted three- and four-body problems" from: Kenta Oshima and Tomohiro Yanao.