space time - How far into the future can we go by traveling close to a black hole?

The way that you have specified the question, the answer is as far as you like. You simply put your spaceship into any orbit around the black hole and wait.

A more sensible question is what is the largest time dilation factor that can be accomplished - i.e. that maximises your travel time into the future for a given amount of proper time experienced on the spaceship.

This in turn is governed by how close to the black hole you can come and still tolerate the tidal forces. If you don't put a limit on this (your first case), then the answer is again infinite; you can hover as close to the event horizon as you like, using an enormous amount of rocket fuel, and the time dilation (see below) can be arbitrarily large.

Your second case is more realistic. Roughly we can say that the tidal acceleration across a body of length $l$ is given by $GMl/4r^3$, where $M$ is the black hole mass and $r$ is the distance from the black hole. If we make this acceleration equal to say $1 g$, and your body length $l sim 1$m, then for a $5M_{odot}$ black hole $r simeq 2500$ km (well outside the Schwarzschild radius of 15 km).

If you could "hover" at this radius, then the time dilation factor would be
$$frac{tau}{tau_0} = left( 1 - frac{2GM}{rc^2}right)^{1/2},$$
where $tau$ is the time interval on a clock on the spaceship and $tau_0$ is the time interval well away from the black hole.

For $M=5M_{odot}$ and $r = 2500$ km, this factor is 0.9970.

If the spaceship is in a circular orbit, the factor is $(1 - 3GM/rc^2)^{1/2} = 0.9955$.

These factors are perhaps not as big as you might have imagined!

interstellar travel - Detecting motion

It is part of General Relativity that if you are in a (small) closed box, you cannot tell the difference between acceleration and a gravitational field.

I suppose you could argue that you would explain Earth's gravity to the occupants of the biosphere as a 1g acceleration away from the Earth for 50 years, a slow swivel of the spacecraft, and then deceleration at 1g for 50 years.

It is hard to say whether such a deception is possible without more details, but in principle it could be done if you have some way of obscuring the initial part of the journey - launch etc, where you would think some non-uniform acceleration would be inevitable.

There is also the question of how far you are going and whether there is a feasible propulsion system. An acceleration of 1g for only a year gets you up to relativistic speeds. You could easily travel to other galaxies in 50 years at this acceleration. So, if the destination was supposed to be a nearby star then the deception fails miserably, unless you try to convince the passengers that you are executing some sort of weird trajectory to get there.

Additionally, how big is the biosphere? What about tides due to the Sun and moon? Any sizeable body of water would show up tides (and indeed possibly the coriolis force due to the Earth's rotation).

star formation - How to tell a nebula from a galaxy?

Galaxies are a large organised collection of stars (& nebulae) outside of our own galaxy, very distant. They shine by their own light.

Nebulae are clouds of gas & debris from, usually, a stellar explosion (Nova, supernova, etc), within our own galaxy, lit up by nearby stars (maybe internal ones) - but the gas is not glowing with it's own light, generally.

So a galaxy is going to be a bright clump of glowing stars, regular in shape - be that elliptical, barred or other, generally they will appear symmetrical & regular. A nebula will be much more amorphous & patchy, possibly with shapes from the clouds of gas (c.f. Horsehead, Orion), and you will be able to see individual stars in it - unlike a galaxy where they are too tightly packed & distant to make out individual stars.

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

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

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

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

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

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

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

-J

How do we know which elements are in a galaxy spectra?

Because the wavelength ratio of the lines remains constant despite any Doppler shift.

For example, if the redshift is $z$, all the lines are shifted redward in wavelength by a factor $(1+z)$. This means that a pattern of lines can still be recognisable.

We also have a pretty good idea of what the spectra should look like, which chemical elements will produce visible absorption features with what relative strengths and so on (see below). This usually makes identification of line features straightforward.

Of course if there were just a single line visible in the spectrum (it does happen, usually in high redshift quasars) it can be difficult to pinpoint the redshift.

In terms of analysing what's in a Galaxy, well usually the light is dominated by the mixed spectrum of billions of stars. This spectrum is interpreted and modelled using galaxy evolution models and population synthesis models that predict a spectrum from a given ensemble.

If a Galaxy is near enough, the chemical abundances of its interstellar medium can be estimated from resolved spectra of emission nebulae.

In comparison, interpreting spectra from an individual star is trivial. Hundreds if not thousands of absorption lines can easily be identified and matched with the predictions of very detailed stellar atmosphere models to estimate chemical abundances. These models contain up to millions of possible radiative transitions as well as the various line strengths and broadening processes that affect the spectrum.

surface - Could Pluto and Charon have extra-Solar origin?

(Edit, I think my original conclusion here was wrong, having read up about it).

While it seems probable that Pluto and Charon were formed by collision, I gather it's unlikely that this collision was so recent as to explain their lack of craters and young surface. The Collision, by most articles I've read, happened when the solar system was young, not in the last 100 million years.

Now, it's possible that none of this is certain, but I retract that part of my original post.

But, the creation of Charon by giant collision remains likely See here, and here. That would suggest formation within our solar-system, not from outside.

Pluto/Charon are also among a fairly common orbital region called Trans-Neptunian objects.

According to Wikipedia they suggest the collision that formed Charon happened 4.5 billion years ago.

Sedna (love the story, by the way), has a very elongated and distant orbit which seems more likely with capture of an object. I agree with everything James Kilfinger said. Rogue planet/Rogue object capture may happen from time to time, but the Rogue would need to get quite close to the sun for the sun to have sufficient gravitation to achieve the capture. Highly elongated orbits would seem likely for solar-system orbital capture. Pluto is only slightly elongated and not a good candidate. More massive suns should have significantly greater capture numbers, but that's kinda obvious I suppose.

gravity - Gravitational red hift vs Doppler redshift: Is the universe really expanding?

Ultimately this is an application of Occam's razor

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

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

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

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

galaxy - Distribution of Stars in Milky Way and globular cluster analogy

Particles in a gas approximate to point-like objects that interact roughly elastically through short-range forces when they collide, but are otherwise non-interacting.

Stars interact gravitationally over long ranges, occasionally with each other, but always with the overall gravitational potential of the system.

Sometimes people do talk thermodynamically about star clusters. You can discuss the "temperature" of stars when you are referring to the velocity dispersion in a cluster. The concept of heating or cooling a cluster also has some merit.

gravity - Where does Jupiter's gravitational force come from? Why don't Jupiters gasses fly away?

You are confusing the "mass" with "solid". All matter has mass, and all mass produces a gravitational field. That includes gasses, liquids and plasmas.

Although gasses are much less dense than solids, gasses also have mass, and if you have enough gas it will have a measurable gravitational field.

Jupiter is big, it is composed of lots of Hydrogen and Helium (and some other gasses), and deep within the planet, the gasses are compressed into strange states. There may even be a rocky core, but it is under such extreme pressure that it is not much like "rock" as we understand it. But it is not necessary for a planet to have a solid core to produce a gravitational field, because all matter has mass not just solid matter.

Will the Universe end by time stopping?

There are several theories on how the universe might end by time stopping. The problem with cosmology and some other parts of theoretical physics is that it cannot be proven, nor reproduced or tested. This makes it often more a faith/religion than a science. So, if you notice some irony in my answer, please, it's because of this.

There are two types of theories which fantasize about the end of the universe by end of times. I freely call those type the formula type and transcendental type theories.

The first theory I will only briefly describe, because they end up transcendental anyway. There are several models on the universe that will describe what the universe (or universes) looks like and how they will evolve in time. The problem with these models is the variable time. If you have an endless time or an endless amount of universes, you end up with an endless amount of possibilities, which will result in all things will eventually happen. So, somewhere in time or a universe we will all become filthy rich and marry a gorgeous, intelligent, funny, friendly, etc., woman/man that never says no (to you). Because of this anomaly scientists have started to theorize that time must end at some point. If you believe these models to be correct, the scientists might be right. The problem in this lies that you first must believe the model is right.

The transcendental theories are a bit more difficult to explain and I will briefly leap out of astronomy into philosophy. In the 18th century a great philosopher wrote a book on the critique of pure reason (Kritik der reinen Vernunft). In this book he was looking for a transcendental doctrine of method and elements. The transcendental part of his doctrine was that it had to be build up on a priori knowledge that was not based on experience. This was his pure reason, because the elements and the methods are not tainted by (personal) experience from an observer. They are true in itself.

Why is this interesting? Because Kant (that great philosopher) said that there were two transcendental elements, space and time. I will skip space, but must say something on time, because someone thinks it might end. Kant states that time is an a priori element of knowledge in pure form. Kant uses five reasons, why time is universal and not empirical. They all can be brought back to the fact that we cannot see things/phenomena to coexist together or successively when there is no concept of time. Therefore, time is an a priori element of pure form.

Now, what has this to do with the ending of the universe in respect to time? The theory you mentioned as heat death is such a transcendental theory. The theory states that the universe expands until the universe is too big to be heated by the energy provided by the matter in the universe. This theory models that the universe follow the same rules as any thermo dynamic system and therefore at a certain point in time all energy, matter and temperature are evenly distributed in this huge universe. Because all is evenly distributed no stars will be created and all processes come to a grinding halt. Since the state before, now and after are the same, the scientists now determine this as the end of time. The formula theories also end up making some theory that time will end.

The problem with these theories is that time will never end. According to Kant time is an a priori element of pure reason and will be there despite of what we observe. Because the state of the universe doesn't change, doesn't mean that there will be no time. Time has just stopped. Theories that state that time will end, do not comply with Kant's critique of pure reason, which states that time is the formal condition of all phenomena whatsoever.

If it didn't entirely answered your question, I hope it was entertaining and educational.

Kind regards,
MacUserT

cosmology - What do cosmologists mean when they talk about "the running of the spectral index"?

The spectral index $n_s$ describes how the clumpiness of stuff varies on various scales. If you observe the CMB and take its power spectrum $P$, this is a function of the wave number $k$ (where $k=2pi/lambda$ with $lambda$ being the physical scale), predicted by many inflationary models to be:
$$P(k) propto k^{n_s-1}.$$
If $n_s=1$, the fluctuations are scale invariant.

If $n_s$ is not a constant, but instead changes with $k$, i.e. if
$$frac{dn_s}{d ln k} neq 0,$$
it is called a "running spectral index". And in fact it seems that that $n_s$ does chance with $k$, see e.g. here.

The term "the running of the spectral index" refers to the quantity $dn_s,/,dln k$.

black hole - Collapse of a star below the mass of Chandrashekhar Limit

The Chandrasekhar mass is a theoretical maximum stellar mass that can be supported by ideal electron degeneracy pressure.

It was originally calculated by Chandrasekhar using polytropic equations of state for white dwarf stars of various compositions.

It is found that if the equation of state is $P propto rho^{4/3}$, which is appropriate for ultra relativistic electrons, then equilibrium is only obtained for $M_{CH} = 5.8 mu_e^{2} M_{odot}$, where the density becomes infinite and $mu_e$ is the number of atomic mass units per electron in the gas.

Typical white dwarfs are carbon and oxygen with $mu_e= 2$, and $M_{CH}= 1.45M_{odot}$, but in the core of a supernova progenitor made of iron-56 it would be lower - around $M_{CH}=1.25M_{odot}$.

In more recent years, the Chandrasekhar limit has evolved to colloquially mean the maximum possible mass for a white dwarf. The main corrections to the ideal case considered by Chandrasekhar are Coulomb corrections, the possible onset of inverse beta decay (electron capture) and the instability at a finite density predicted by using GR rather than Newtonian gravity. The latter probably sets the "Chandrasekhar mass" for carbon white dwarfs to be $1.38M_{odot}$.

A carbon white dwarf that had a mass less than this could be supported by electron degeneracy pressure and would not collapse.

If your question is asking for a derivation of the Chandrasekhar mass, then I suggest you look at the stability analyses that are presented in a standard text on the subject like "Black holes, white dwarfs and neutron stars" by Shapiro and Teukolsky. An approximate result can be obtained using the virial theorem assuming a uniform density star.

General question on Solar Eclipse

Let's assume 'solar eclipse' occurred

Now, at what degree 'moon' will be in 'with reference to' earth (and) at what degree 'moon' will be in 'with reference to' sun

In other words, by 'how many degrees' (out of 360 deg) the moon would have orbited 'earth' and 'sun' in the event of 'solar eclipse'?

cosmology - The largest discrepancy in the history of science

There are roughly two possibilities: either there isn't a large vacuum energy, this would imply that there is something missing from quantum field theory. We don't know what it could be.

Or the zero point energy really is as large as QFT predicts, but there is something else that prevents it from having a large cosmological effect. We have no idea what that could be.

We might get more of an idea if we find out what Dark Matter consists of, or a good quantum theory of gravity we might know more.

software - Notifier about visible ISS passes and/or Iridium flares for Ubuntu PC

I am trying to find application that would be capable of notifying me about
visible ISS pases for specified location and/or visible Iridium flares for specified location.

This software must be capable of running on Ubuntu.

I strongly prefer active open-source projects.

I know that there are multiple mobile apps but I want something that may run on Linux PC.

To avoid "this is subjective" - I will be happy about any software fulfilling this requirements and criteria are not subjective.