How big is the universe. How does it works? I watch this movie:

How big is the universe
https://www.youtube.com/watch?v=b34gwCKIM50#t=50m00s

I can't understand where is there triangle with 180 degrees.

What exactly is this red spot on the cosmic microwave background?

Is it a base of triangle? How does it appear that this spot is smooth surface but not a concavity?

There are features in the CMB, the distance and size of which can be derived from cosmological models (6-parameter Lambda CDM model). The expected size of the features can be predicted in terms of angles in the sky, depending on how curved large-scale space-time is. (The features are a statistical property of tiny temperature fluctuations in the CMB indicating the largest scale of causal connection - kind of sound waves - in the baryon-photon plasma before recombination 380,000 years after the Big Bang, called first acoustic peak of the CMB power spectrum. The angle should be about 1 degree for a flat space-time, in accordance with observation.) Things aren't quite straightforward, e.g. due to the way the universe has been expanding, therefore it's done with simulations.

Angles look larger in a positively curved space-time (e.g. a sphere) than in a flat space-time (e.g. a plane) than in a negatively curved space-time (e.g. a saddle).

The curvature of space-time follows the same principles as curvature of 2-dimensional surfaces. A triangle in an Euclidean plane has an angle sum of 180 degrees, while a triangle on a sphere has an angle sum of more than 180 degrees. Hence an object of a fixed size and a fixed distance looks larger (takes a larger angle) on a sphere than on a plane.

Here a sketch of a triangle on a sphere (may be interpreted as an observer looking to an object) and a triangle of the same size - meaning the same lengths of the sides in this case - in a plane:

(More on non-Euclidean geometry.)

If the observable universe is positively curved, it could be a fragment of the surface of a 3-sphere resp. 3+1-de Sitter space-time. A 3-sphere is finite. If the observable universe is flat (curvature 0), it could be a fragment of an infinite Euclidean space resp. 4-dimensional Minkowski space-time. That's plausible, but not the only possible extrapolation beyond the observable universe. An almost flat observable universe could e.g. be a fragment of a huge 3-spherical universe or of a huge 3-torus. Planck data don't indicate (in a significant way) that kind of structure outside the observable universe, but extrapolations become less valid the further we go beyond the observable universe.

According to the current (Lambda-CDM) model of the universe together with the best-fit parameters, the universe is flat within the limits of measurement. Hence it's plausible (by extrapolation), but not necessary, that the universe is either huge or even infinite.


Lunar eclipse above the atmosphere Would a lunar eclipse seen from low (or even high) Earth orbit look different to the naked eye than it does from the surface of the Earth?

The only image I could find taken from orbit was the photo by Alexander Gerst from the ISS.  "The slight hue of blue is actually the Earth's atmosphere, just before the Moon is diving into it."

It wouldn't look much different. The atmosphere absorbs some light and "seeing" reduces the effective resolution, but these have little effect on the visual impact of a lunar eclipse.

From a sufficiently high orbit, you might be able to see the terminator between the partially lit "red" side of the moon and the (nearly) completely dark side on the far side from the Earth (and the sun).

A lunar eclipse looks pretty cool from the Earth, and it would look equally cool from space.


When stars explode why can we still see them? This might be a silly question but if light travels at the speed of light and time is frozen in that speed then why the stars we see could be dead already and not just instantly disappearing from the sky the moment it explodes/dies?

Because we are not moving at the speed of light.

From our point of view, light travels at the speed of light, and so events on a distant star are not visible until the light reaches us.

From the point of view of the photon, the universe is 2 dimensional (it is flattened by infinite Lorentz contraction) and there is no passing of time (infinite time dialation). The star and you are at the same point. Photons have a weird point of view.

Fortunately we don't have to worry about that, because we have mass and so we are not moving at the speeed of light. We have a 3d universe and we have a dimension of time. Thank Higgs we have mass!


Cases of gravitational lensing resulting in a recognizable image of an extended object? There are several different classifications of gravitational lensing phenomenon.

Here I am asking for any examples of strong lensing where the lensed image of an extended object is magnified and recognizable as an extended object. Of course it may be distorted somewhat, but if the lensed object is a galaxy, then the lensed image should appear larger and "galaxy-shaped" even though distorted. If it's a tight pattern of stars or other objects, then the pattern should be larger.

I have a strong memory of reading about such a case in Nature or Science within the last few years, but I can not find it. I believe that the nearer, lensing object was a galaxy.

There are actually quite a few examples of this. A particularly nice one, where you can see star-forming substructure within the distant, lensed galaxy (the extended, vertical "snake" structure just right of center), is this HST image:

This is another HST-based example, in which the same background galaxy is lensed multiple times (indicated by white ovals) by an intervening galaxy cluster, with a reconstruction of the background galaxy in undistorted form shown in the lower-left:

https://www.space.com/14481-hubble-photo-brightest-galaxy-gravitational-lens.html

People have even obtained spatial resolved spectroscopy within the lensed galaxies, as discussed in this paper (which includes spectroscopy of the first lensed galaxy pictured above).


Does the luminosity of a star on its main sequence increase or remain approximately constant? From my understanding, the luminosity of a main sequence star should increase because, in its core, hydrogen is being burnt into helium which means that the number density of hydrogen decreases and the temperature increases and from the Stefan–Boltzmann law, the temperature is proportional to the luminosity so the luminosity of a star should increase while it's on the main sequence phase of evolution.

Please correct me if my reasoning is incorrect.

The luminosity of a star remains approximately constant during its time on the main sequence. There is a slight increase over time, which is, as you guessed, related to the changing composition of the star due to fusion.

The so-called Vogt-Russell theorem tells us that a star's mass and composition are the only two factors that affect its structure and, by extension, its luminosity.$^{\dagger}$ Most main sequence stars have negligible mass-loss rates (at least, compared to evolved stars like AGB stars), and so therefore compositional changes should be the only thing dictating luminosity evolution.

It turns out that the luminosity is related to the mean molecular mass $\mu$ by (approximately)
$$L\propto\mu^4$$
which is not insignificant. Fusion turns hydrogen to helium in the star's core, and hence there should be an increase in $\mu$ and thus in luminosity (roughly a factor of two). The change is small compared to the orders of magnitude by which two main sequence stars may differ from one another, but it isn't zero.

As an aside, there is indeed a change in the central temperature (though I would note that your use of the Stefan-Boltzmann law requires a change in the surface temperature) to accommodate the increase in luminosity, but the energy generation rate is very sensitive to changes in temperature, particularly for stars using the CNO cycle.

$^{\dagger}$ This is, strictly speaking, not true. Rotation, as Rob Jeffries mentioned, is also important for certain stars, and it can have a role on the evolution of a star's luminosity.


What can be seen with a 4.5" telescope I just got a 4.5" Newtonian reflector.  The skies haven't been clear where I live lately so I've only been able to use it to see the moon and Jupiter (I was also able to see the Galilean moons).  A friend of mine with a similar telescope says he can see Saturn with its rings and the phases of Venus with his telescope.  I am wondering what else I can see with a telescope my size, specifically which Messier objects I can see with my telescope.  I live in a suburban area near a small urban area and so light pollution is a concern but I have access to darker skies close by.

The aperture of your 4.5" telescope is one thing, it's also important what focal length you have. Is it a f/5 or rather a f/8? The f/8 would be suitable for viewing the Moon, Jupiter, Saturn, maybe even Mars and Venus. You can also buy a good solar filter, attach it in the front of the optical tube assembly, and view the sun. But be careful with that, and inform yourself beforehand! Your eyesight might be in danger otherwise. For the Moon it is advisable to buy a neutral grey filter, because it is also very, very bright.

As for the Messier objects: you can probably view the larger ones. The Ring nebula (M57) will be tough, because it is very small and faint. But open clusters, globular clusters and Andromeda's core will be possible. A few bright nebulas will also be possible, like M42 (Orion Nebula).

There is a good list of all Messier objects over at Astropixels. You should try objects of magnitude 4 or better, and that have a size of more than 5 arcminutes. Otherwise they may be too dim or small to find.


Are Gamma Ray Bursts of galactic or extragalactic origin? I read about the 1995 Lamb-Paczynski debate on whether GRBs are galactic or extragalactic in origin.  With our current experimental evidence, have we found whether GRBs are galactic or extragalactic?

Based on our understanding of what might be possible causes for GRB, there's nothing to suggest that this phenomena is isolated to other galaxies alone, but we have so far only detected GRB originating from outside of the Milky Way. Good that we did too, because if any of them happened in our cosmic neighborhood and was pointing towards us, it would be the last thing we'd ever see and would effectively sterilize our planet. More information is available on Wikipedia on Gamma-ray burst, it's actually a pretty good article presenting extensive information on GRB (I guess that's why it's featured there).


How hard is it to find the Sun's "sisters?" As @ProfRob stated in his excellent answer regarding the ejection of the Solar System's fifth gas giant,

It is for similar reasons that, even though the Sun was probably born in a cluster of $\sim 10^4$ stars, none of those siblings have been firmly identified.

So why is it so difficult to find such stellar siblings?
NB: Maybe it's because open clusters tend to disassociate quickly and the stars would be scattered everywhere. But wouldn't stars with similar spectra, age, metallicity, etc. be found easily?

Here are the problems/issues:
Most stars are born in clusters/associations but a cursory investigation of cluster demographics with age reveals that the vast majority of clusters do not survive to old age. The majority either are never gravitationally bound to begin with or become unbound in the first 10 Myr.
The Sun was likely born in a cluster of $10^3-10^4$ stars (Adams 2010). If it dispersed more than 4 billion years ago, then its members would have had time to spread all around the galaxy by now. That is because although the members would be kinematically coherent to begin with, the velocity distribution of stars in the Galactic disc becomes "heated" as stars scatter in the potential of giant molecular clouds and pass through spiral arms (Wielen 1977). They attain a significant velocity dispersion which means they could now occupy positions over a broad swathe of the Galactic disc and be displaced above/below the disc by $\sim 200$ pc. If we argue that the Sun's siblings could be in an annulus, with width $\pm 1$ kpc and thickness 400 pc, then if the solar cluster was $10^4$ stars, then the nearest sibling is expected to be at a distance of 160 pc.
Another way of looking at this: The density of stars in the Galactic disc is around 0.1 per cubic parsec compared to the expected density of solar siblings of $2.4\times 10^{-7}$ per cubic parsec.
Thus only about 1 in 400,000 of the local stars might be a solar sibling.
How could they be found?
Cluster members would have a similar age and a similar chemical composition.
We know the age of the Sun precisely and accurately. We don't have that information for any other star. Age estimates of field stars are imprecise, model-dependent and are of indeterminate accuracy. In the best cases - solar type stars and a little more massive - asteroseismology and the HR diagram position might give an age to about $\pm 0.5$ Gyr. But you need good data to do that and we don't have asteroseismology for the nearest 400,000 solar-type stars (in order to find ONE solar sibling). Even if we did, it would only narrow the candidates down by a factor of 10.
What about chemical abundances? There are now big spectroscopic surveys that have observed large-ish numbers of stars. Again, the most robust data comes for stars like the Sun, so that a differential abundance analysis can be done. The more numerous cooler stars have spectra which are more difficult to deal with and there may be systematic abundance errors when comparing with the Sun. Giant stars are bright, with narrow spectral lines, which is good, but their abundances may have been modified during their evolution. Thus we are limited to looking at solar-type field stars. No spectroscopic surveys (yet) have detailed spectra of 400,000 potential solar siblings.
Chemical abundance may also not be that discriminatory. In the solar neighbourhood, stars have an abundance dispersion of about a factor of two , centered quite close (a bit below) the solar metallicity. Good quality spectroscopic analysis can give the metallicity to 10%, so enough to resolve the distribution, but it would only whittle down the candidates by factors of a few.
Very high quality spectra could look at the detailed abundance mixture, but is only available perhaps for a few thousand stars. The majority also have an abundance mixture that is not very different to the Sun. Thus whilst the evidence is that the detailed abundance dispersion in a cluster is much smaller than the dispersion in field stars (Paulson et al. 2003), it does not look like the Sun is that unusual or has any unique chemical "markers" (Bensby et al. 2014). Some hope may be offered by the detailed mix of s- and r- process elements; the former may be age sensitive (e.g. Jofre et al. 2020), while the latter might reveal some peculiarity associated with contamination by nearby supernovae in the Sun's natal environment. At the moment, although candidate solar twins can be found, it is unclear by how much that narrows down the one in 400,000 figure, especially when you consider that abundance peculiarities may also be imprinted by later accretion events or some process associated with planet formation (e.g. Melendez et al. 2012) or that the abundance dispersion in a cluster may not be exactly zero (e.g. Liu et al. 2016).
In summary, the space density of solar siblings is likely to be very low compared with unassociated field stars. The properties of those siblings are not that unusual compared with typical field stars and we lack precise enough measurements of age and chemical composition to have anything more than a  list of candidate solar twins at the moment. It's like looking for a needle in a huge pile of other needles.


Effects of a rogue planet passing between the Earth and the Moon? The plot of Thundarr the Barbarian got me thinking about the science behind

  the passage of a runaway planet between the Earth and the Moon

and its effect on the Earth and Moon themselves, as well as their orbits.

For the following scenario:

planet has half the mass of Earth, and is moving at 16km/s
moving perpendicular to the plane of the ecliptic
passes directly between the Earth and the Moon with closest distance to Earth of 192,500 km

What sort of effects, if any, might this have on Earth and those of us residing there during the passage in later months and years?

It doesn't look good.

Tidal effects. The passing planet will certainly cause disruptive tides as it passes. The exact height of the tides would be hard to calculate as it depends on how the tides flow around the land masses, but the effects would be much greater than lunar tides. The tidal effect could also have consequences for the earthquakes.

Disruption to the orbit of the moon. The moon's orbit will be significantly altered. It could cause the moon to enter an elliptical orbit (with consequences for tides).  There would not be enough disruption to cause the moon to leave Earth orbit immediately

Disruption to Earth's orbit.  The orbit of Earth would also be significantly changed, it could enter a significantly elliptical orbit, this would change the amount insolation over the year and greatly change the Earth's climate

If the disruption were significant enough, it could bring the Earth's orbit uncomfortably close to that of Venus, this could result in further disruption to the moon's orbit

Fortunately space is big, and even if there are a lot of rogue planets out there, it would be a very rare event for one to pass so close to star


The colour of blue dwarf stars The paper "M dwarfs: planet formation and long term evolution" describes blue dwarf stars, a hypothetical next-stage in the lifespan of red dwarf stars within a certain mass range, after which they become white dwarves.

(Hypothetical because the universe is not old enough for any red dwarves to have reached this stage.)

The Hertzsprung Russell diagram on page 917 of this paper, if I've interpreted it correctly (I'd never seen one of these until recently!), shows red dwarves in the 0.14-0.16 solar mass range progressing further away from the "red" end of the spectrum and in the direction of the blue. But it does not actually depict their surface temperature reaching - or indeed exeeding - 9000K (spectral type A, instead of the B or O-type that are normally considered blue enough to justify the name.)

Am I correct that "blue dwarf" stars would not, according to this paper's H-R diagram, actually ever get past "white", and are thus named because they've moved a long way from the red end of the spectrum toward the blue? I have seen different colour charts depict different levels of blueness for the O, B and A types while researching this question, although the majority consensus seems to be that A types are almost entirely white with only a very small amount of blue.

(The same Hertzsprung-Russell diagram is also shown on page 424 of the 1997 paper "The End of the Main Sequence", if that helps at all.)

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

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

and one of them replied:

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

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

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


How can gravitational lensing makes a quasar appear brighter? How can gravitational lensing makes a quasar brighter than it would in the absence of a foreground galaxy?

The quasar gives out light in all directions. The light spreads out in space. Only a very small amount of that light would be pointed exactly in the direction of your telescope.

But if a large galaxy or galaxy cluster is between the quasar and us, it bends some of the light towards us, making the quasar brighter (it would also distort the shape, but quasars are too small for their shape to be seen) This makes it brighter for us (and dimmer in other parts of space which would have got the light that is now bent towards us.)


How close are we to having the technology to measure planetary obliquity for exoplanets? As far as I can tell, we do not yet have the precision to even put reasonable bounds on an exoplanets obliquity, but wikipedia seems to indicate that this may be possible in the "near future." It seems like this would have to be accomplished by direct imaging, either by directly observing rotational flattening of an exoplanets, or by looking for moons and assuming that the planet is tidally locked to the same plane as its satellite.

How close would you estimate we are to this kind of precision? Are there other approaches to measuring planetary obliquity?

Obviously, I'm not expecting a definite answer. Just wondering if anyone knows of any research in this area or has any thoughts about it.

Carter & Winn (2010) suggest that the most promising means of detecting exoplanet obliquity would be through miniscule signatures imprinted on the transit light signal at ingress and egress (~ 200 parts per million for a planet as oblate as Saturn). Zhu et al. (2014) use this technique to make the first tentative detection of exoplanet obliquity from a Kepler object, the 18 Jupiter mass brown dwarf Kepler 39b (KOI-423.01). They measure an oblateness of 0.22±0.11. They also place some upper constraints on the oblateness of other planets in the Kepler catalogue.

Transit signal for KOI-423.01 over 12 orbits. The residuals of two models, one with oblateness and one without, are plotted at bottom. The Oblateness model is a better fit to the data.

Oblateness variations are thought to be conducive to exoplanet habitability by regulating temperature modulations, so I expect that measurements of this property over time will be a priority in future exoplanet observations for astrobiology and SETI studies.


How much matter was ejected when the Solar System formed? Assuming the accretion disk model for the formation of the Solar System, the most important problem, according to wikipedia, is "how the material, which is accreted by the protostar, loses its angular momentum."
If angular momentum is conserved, then as our Sun lost angular momentum in formation, excess gas and dust in the disk must have gained angular momentum.  How much matter (if any) reached escape velocity and was ejected from the Solar System?  When compared to the total mass of the Solar System, was this a significant portion?

It is actually the other way around:
First a massive accretion disc can form, through which material looses angular momentum and accretes onto the star radially, hence being angular momentum poor.
However, during the initial free-fall phase, before the disc forms, infalling material can be 'rejected' at the star, either via high pressure gradients or magnetic interactions. This causes a polar jet to form around the protostar, which emits material back into the interstellar medium. Measured jet mass-loss rates are up to 1/2 the measured accretion rates.
Furthermore, the remaining fraction of material that did not form planets is ejected at the end of the disc lifetime via photoevaporation by the young stars' X and UV photons. What fraction this is in comparison to the mass in the planets is unknown, as the overall planet forming efficiency is unknown.


Was time different before the great inflation? In time different during the first second after Big Bang than it is now? Inflation had a dramatic effect on space, and spacetime is one thing. Was the properties of time affected too? Curved spacetime around black holes cause funny effects for outside observers, infalling objects appear to never reachthe event horizon. The very early universe was even denser. When we talk about the first second, are such effects accounted for?

Food for thought on density and time dilation.  Density isn't gravity.  We tend to think it is, but it's not.  Variation in density gives us gravity.

If you have an infinite universe, very young, hot and dense, but it's uniform, then you have no time dilation.  One way to think about this is to ask if light passing through the universe is red shifted or blue shifted.  If the universe is uniform and infinite, it's the same in all directions around the photon, so the photon is neither red nor blue shifted, so, contrary to what our intuition about relativity tells us, there might not have been a great deal of time dilation in the very young universe.

Of-course the ray of light passing through expanding space is enormously red-shifted, but that doesn't affect time dilation.  The gravitational red or blue shift in the very young universe might still be close to zero meaning very little time dilation anywhere.

As the early universe grew less uniform then you had time dilation variations in denser parts of the early Universe but with FTL expansion and gravity limited by the speed of light, it's unclear if there ever was massive time dilation in the young universe (at least, unclear to me, if somebody here knows 100%, feel free to post and/or correct me).

Now if we assume the universe is finite and flat and the big bang happened at a point, which, generally isn't the model most people like these days, then you could run into enormous time dilation inside the tiny young and dense universe, but it still expanded FTL, so the calculations get weird and too hard for me.   If the expansion of space happens faster than gravity can keep up, gravitational time dilation might not apply, at least not until after the rate of expansion slowed down enough for gravity to permeate the local regions.  I couldn't even begin to run the math on this and you'd have different answers for different models too, I'd think.   I agree with Andy though, it would need to be accounted for or the models wouldn't be much good.


What is the difference between wind, jet and outflow? For jets, I found a pdf file here

  Jet: collimated beam of matter of high velocity

  sources: young stars, active galactic nuclei, $\mu$-quasars, gamma ray bursts, planetary nebulae, pulsars

  jet sources host accretion disks

How about winds and outflows? Can somebody make some clarifications for the three concepts， their correlation and difference?

I'm not sure there are very clear official definitions, but here is my take on accepted usage in the star formation community:

Outflows - general term describing both winds and jets.

Jets - collimated outflows along magnetic poles.

Winds - outflow from the stellar surface in all directions, not just along the poles.

Stellar winds are what comes from individual bright stars. Jets can be protostellar jets from young stars, or on a larger scale from galactic nuclei.


Will Triton have a thicker atmosphere as the Solar System ages? With an average temperature of around 34 kelvin, Triton is extremely cold. Currently, it has a thin mostly nitrogen atmosphere with a pressure of around 1 Pa. However, its surface has large deposits of nitrogen ice. This leads me to a few related questions.

Do we know how much nitrogen ice is on Triton?
If all the nitrogen ice on Triton thawed, how thick would its atmosphere be?
Will Triton thaw naturally, and have a thicker atmosphere, in the future as the Sun's luminosity increases?
If so, would its atmosphere be stable over a long period of time?
In the far future, perhaps as the Sun turns into a red giant, would Triton be warm enough to have liquid water?

Triton's orbit is decaying due to tidal interactions, it is predicted to reach Neptune's Roche limit in about 3.6 billion years (Chyba et al., 1989) where it would likely be disrupted, possibly forming a ring system. This timescale is shorter than the timescale for the Sun to become a red giant.
Even before that, Triton's orbital decay will bring it into the region of the inner prograde satellites. There's a possibility that it could experience one or more major collisions (since Triton is in a retrograde orbit, the collision velocities for an impact with a prograde satellite will generally be higher). Such collisions would likely have an effect on the inventory of volatiles on the surviving objects.
This makes prediction of the future evolution of conditions on Triton extremely difficult.
Even if this weren't the case, there would still be a question of whether a world as small as Triton could maintain liquid water. Arnscheidt et al. (2019) provide a conservative estimate for the lower gravity limit for waterworlds to maintain a stable atmosphere at around 1.48 m/s2. Triton's gravity of 0.78 m/s2 is below this threshold, putting it in the non-habitable "comet-like" regime. They also note that deglaciation of an icy world into a long-lived habitable state is unlikely: except at very low albedos, the required stellar flux is sufficiently high that the moon transitions directly to a short-lived, high temperature state.


Where does the Solar System end? This is a question I've heard many times in the past, and a quick search of the site says it hasn't been asked here, so I figured I might as well ask (and answer) it. I know that it is rare for someone to ask and answer their own question, but I think it could work here, and I welcome input (including other answers) from anyone and everyone here.

The Sun is roughly 4 light-years away from the closest star system, the Alpha Centauri system. The planets in our Solar System, however, aren't even close to that far away from the Sun. Where does our Solar System end? Is the edge considered to be the orbit of Neptune, the Kuiper Belt, the Oort Cloud, or something else?

Note: this question on Physics SE is similar, but the answers posted here go in different directions.

According to the Case Western Reserve University webpage The Edge of the Solar System (2006) an important consideration is that

The whole concept of an "edge" is somewhat inaccurate as far as the solar system is concerned, for there is no physical boundary to it - there is no wall past which there's a sign that says, "Solar System Ends Here." There are, however, specific regions of space that include outlying members of our solar system, and a region beyond-which the Sun can no longer hold any influence.

The last part of that definition appears to be a viable definition of the edge of the solar system.  Specifically,

valid boundary region for the "edge" of the solar system is the heliopause. This is the region of space where the sun's solar wind meets that of other stars. It is a fluctuating boundary that is estimated to be approximately 17.6 billion miles (120 A.U.) away. Note that this is within the Oort Cloud.

Though the article above is a bit dated, the notion of the heliopause has been still of interest to scientists, particularly how far away it is - hence, the interest in the continuing Voyager missions, which states on the website, that it has 3 phases:

Termination Shock

Passage through the termination shock ended the termination shock phase and began the heliosheath exploration phase. Voyager 1 crossed the termination shock at 94 AU in December 2004 and Voyager 2 crossed at 84 AU in August 2007.

(AU = Astronomical Unit = mean Earth-sun distance = 150,000,000km)

Heliosheath

the spacecraft has been operating in the heliosheath environment which is still dominated by the Sun's magnetic field and particles contained in the solar wind.
As of September 2013, Voyager 1 was at a distance of 18.7 Billion Kilometers (125.3 AU) from the sun and Voyager 2 at a distance of 15.3 Billion kilometers (102.6 AU).

A very important thing to note from the Voyager page is that

The thickness of the heliosheath is uncertain and could be tens of AU thick taking several years to traverse.

Interstellar space, which NASA's Voyager page has defined as

Passage through the heliopause begins the interstellar exploration phase with the spacecraft operating in an interstellar wind dominated environment.

The Voyager mission page provide the follow diagram of the parameters listed above

It is a bit complicated as we do not know the full extent of what the dynamics are like out there, a recent observation reported in the article A big surprise from the edge of the Solar System, reveal that the edge may be blurred by

a strange realm of frothy magnetic bubbles,

Which is suggested in the article could be a mixing of solar and interstellar winds and magnetic fields, stating:

On one hand, the bubbles would seem to be a very porous shield, allowing many cosmic rays through the gaps. On the other hand, cosmic rays could get trapped inside the bubbles, which would make the froth a very good shield indeed.


Moon's negative greenhouse effect? Using the standard formula for effective temperature of a planet, Venus has T(eff)=220K, Earth has T(eff)=255K and Mars has T(eff)=212K (using albedo for Venus a=0.7, Earth a=0.367, Mars a=0.25). Average surface temperatures of 730K, 288K and 218K respectively are easily explained by differences in greenhouse effect. The moon however with an albedo of a=0.1 should have a T(eff) of about 270K, but the average surface temperature is about 250K.
Here is where I got the T(eff) formula and here is where i got the average temperature of the moon. (the latter is a new citing and I have edited the mean temperature value) I have revised my planet temperatures using this reference.
What explains this negative difference?

You don't say how you got your average temperature. If it is a straightforward average, then I think I have your answer.

The temperature of the moon is highly non uniform, ranging from around 100 K on the night side to 370 K on the sunlit side. This gives a crude average of 235 K.

https://space.stackexchange.com/questions/3290/what-is-the-temperature-variation-between-the-lunar-day-and-night-on-the-moon

However, in terms of blackbody radiation, if we treat both hemispheres as separate blackbodies, then together they radiate as much energy as a hotter blackbody because of the $T^4$ factor in Stefan's law. The "effective temperature" will be
$$ T \simeq (0.5\times 100^4 + 0.5\times 370^4)^{0.25}= 311\ K$$
So this is more like your equilibrium temperature and a more appropriate area weighting and/or tweaks to the exact range of temperatures could bring it into close agreement.


Why do telescopes use hexagonal mirror pieces instead of pie slice shaped ones? Some new large telescopes in the near future, on Earth and in space, will use multiple mirrors. The individual mirror pieces will be hexagonal in shape. I wonder why this shape is prefered over the circle sector shape (like pie slices). I would think that corners and joints between mirrors cause practical problems. And a circle sector slice has half as many corners and two rather than three or six neighboring pieces, and shorter interfacing edges with neighboring pieces overall. So shy is the hexagonal shape prefered?

The ideal shape for the mirror is round. It's the easiest to make. It's the best-behaved while in use.

The hex tiles are already harder. The mirror is a revolution surface generated by a conic curve (circle, parabola, hyperbola, ellipse), which needs to be machined with a precision greater than 0.1 microns. That's extremely difficult already with a round mirror, where the surface can be easily distorted near the edge in the process of manufacturing.

With the hex tiles, maintaining that precision near the corners is very hard - corners are like the edge but exponentially harder. Unless you take special precautions and unless you perform extra work, you're guaranteed to end up with surface errors near the corners (the surface is either too raised, or too low, or has a more complex distortion). Based on my experience making round mirrors, I would guess the surface near the corners would tend to be turned down (too low relative to the rest), which is a defect that's extremely hard to correct - one of the hardest, in fact.

With a pie slice, all problems mentioned above increase greatly in magnitude. The blunt angle of the hex tile gives you some support in machining the surface, but the sharp angle of the pie slice gives you almost none. I can't even begin to imagine the difficulties one would encounter while making a high precision surface on a pie slice. The sharp end of the slice would be almost guaranteed to be worse quality than the rest.

What most people don't realize is that maintaining the precise shape of the mirror while in use is difficult too. You can't just lay it on a hard surface - the uneven support would distort the precise shape. Mirrors are supported on the back by a precise mechanism, with a number of support elements precisely sharing the weight in equal amounts (or, if not equal, then deduced from finite element analysis), and located in places carefully calculated.

With a round or hex tile this is, if not easy, then at least a well-understood and manageable procedure. A pie slice would be very difficult to support in the same even manner near the sharp tip. You can't rely on the symmetry of the shape to provide the even load on the support points. The support force would have to be specially adjusted there. It would probably be doable, but harder.

This is only an issue with terrestrial telescopes, which operate under gravity. Space telescopes don't suffer from this issue.

Alternatives to hex tiles could also be square tiles, or triangle tiles. These are worse than hex tiles for all the reasons shown above - the corners have sharper angles which make everything more difficult. The blunt angles of the hex tiles alleviate these issues somewhat.

TLDR: Non-round mirrors are hard to make anyway, but hex tiles are less hard compared to the alternatives.


Standard Big Bang model and space curvature Why it is said that in standard Big Bang model space curvature grows with time when the Universe expands? My intuition is that it should be the opposite.

I saw this in a book talking about the problem of standard Big Bang model and why we need inflation theory. It says that the Universe is observed to the nearly flat now. And because the space curvature grows with time, it should be even flatter in the past, which cannot be explained. But the inflation theory solves the problem because even if space is initially far from flat, inflation will smear out the curvature and make it flat.

What exactly did the book say? It all depends on what you mean/define as "curvature". What you describe appears to be a description of the behaviour of $\Omega$. Inflation does indeed drive $\Omega$ towards unity and simultaneously flattens space because the radius of curvature grows exponentially bigger.

If $\Omega < 1$ at some early epoch then it should decrease quickly with time such that $\Omega << 1$ in the present day - this means that the universe has negative curvature, but does not mean it is becoming more curved.

In the Friedmann equation, the curvature parameter $k$ is a constant $(1,0,-1)$
$$H^2 = \frac{8\pi G\rho}{3} - \frac{kc^2}{a^2}$$

Here, the spatial curvature is $k/a^2$ and the radius of curvature is $a$ if $k=+1$. Thus as the universe expands and $a$ gets larger, any curvature becomes smaller.

In a little more detail - one can write the above equation in terms of the density parameter $\Omega$, the ratio of density to the critical density $3H^2/8\pi G$:
$$(\Omega ^{-1}-1)\rho a^{2}={\frac {-3kc^{2}}{8\pi G}}$$

During inflation, the energy density $\rho c^2$ remains constant as $a$ grows exponentially. In order to keep the left hand side equal to the right hand side (which is just a collection of constants), then $\Omega$ must be driven very close to unity, while $k/a^2$ will tend towards zero.

After inflation then $\rho$ will vary with $a$ depending on whether the expansion is dominated by matter ($a^{-3}$) or radiation $(a^{-4})$. In both these cases $\rho a^2$ will decrease as the universe expands, such that if $k \ne 0$, then $(\Omega^{-1} -1)$ must increase, which means that $\Omega$ must either grow or shrink away from unity. But $k/a^2$ continues to get smaller as the universe expands.


Is it true dark matter was discovered whilst looking at the rotational speed of galaxies? Just a little something whilst a dark matter pioneer moves onto a better place.

This commentator writes:

  My understanding is that dark matter was "discovered" when trying to find out why stars in the outer edge of a galaxy rotates with the same speed as the inner. A ten-fold increase in number of galaxies doesn't seem to affect this.

When reading the history - this simple explanation doesn't quite come across. Perhaps the statement above is oversimplified. For example:

mass in the galactic plane must be greater than what was observed (doesn't quite talk about comparative rotational velocity)
estimated its mass based on the motions of galaxies near its edge (doesn't quite talk about comparative rotational velocity)
some unseen matter provided the mass and associated gravitation attraction to hold the cluster together (doesn't quite talk about comparative rotational velocity)
measurements of galaxy rotation curves (what is a galaxy rotational curve? Shouldn't it be a straight line if they're rotating at the same angular velocity?)
gravitational lensing of background objects by galaxy clusters (not talking about comparative rotational velocity?)

My question is: Is it true dark matter was discovered whilst looking at the rotational speed of galaxies?

What you're possibly missing here, judging from your questions, is the link between the mass distribution of a galaxy and the rotation velocities.

The simplest way to obtain a prediction for a tangential velocity component is to look at the Kepler problem, i.e. a central mass, dominating another smaller mass, orbiting it.
Newton's force-law $\vec F = m \dot{\vec{v}}$ relates acceleration and acting force, which is given by gravity.
All acting forces then sum up to change the velocity of a test-particle $\dot{\vec{v}} = \sum_i \frac{\vec F_i}{m}$.

Then we get a number of cases, depending on how many summands there are, and how they are distributed spatially:

Kepler problem: Only one central $F_i$ exists, which dominates the system's behaviour. For a circular orbit one gets the well-known tangential velocity $v_t = \sqrt{\frac{GM}{r}}$, with $M$ being the mass of the central object and $r$ the distance from it.
A Galaxy: In a galaxy the visible mass distribution is very different from a stellar system. It is spaced out more equidistantly and thus would give rise to a peak in $v_t$ and then a decrease again, after one gets far away from most of the mass. This is however not observed, and calculating the measured velocities of visible mass backward to the true mass distribution leads to the postulation of dark matter.

A related problem is the virialisation of galaxy clusters. When a bunch of mass particles interact with each other gravitationally for long enough, in this case galaxies, their averaged kinetic energy $<T> = <\frac{1}{2}mv^2>$ becomes half the available gravitational potential energy $<V>$. Thus, under the assumption of virial equilibrium one can measure the total mass in a system by measuring the velocity dispersion. Because galaxy clusters are very old objects, it is usually assumed they display this equilibrium. Departures from this are still ongoing research and for reasons I don't remember the milky way is usually not assumed to be virialised.
Zwicky 1933 realised that the Coma cluster then needs to contain as much as 400 times the observed mass, to explain it's observed velocity dispersion.


Planned telescope to detect alien waste-heat I remember watching a talk by someone who designed a telescope to view a single star at a time.

The purpose of the telescope was to detect waste-heat which would presumably be emitted by any civilization utilizing a large percentage of their planet's solar energy, due to the second law of thermodynamics. By focusing on a single star, it would be able to detect when the planet crossed the path of star-light, and the additional energy emitted by the planet - or something like this.

Anyone know who this might be?

This would be the SETI's Colossus telescope project, that aims to build a high-resolution, multiple-mirror instrument with ability to directly image the heat generated by other civilizations on planets orbiting stars near us:

    Artist's impression of the proposed SETI's Colossus Telescope (Credit: Innovative Optics/Colossus Corporation)

  As Earth-like civilizations evolve, they use more power. For example,
  in Roman times, we estimate Ω [the ratio of a civilization’s power production to the amount of solar power it receives] was about 1/1000 what it is today.
  Humans’ global power consumption is growing by about 2.5 percent per
  year, even though the world’s population is growing at less than half
  this rate. In contrast, our knowledge base (the combined total of all
  recorded information) doubles in just two years. As cultures advance,
  their information content also must grow, and the power required to
  manipulate this knowledge eventually dominates a civilization’s total
  power use.

  Using a sensitive coronagraph to remove scattered light that would
  obscure an exoplanet, Colossus would be able to find hundreds of
  Earth-sized or larger planets in the habitable zone including any
  civilizations on their surfaces.

  Source: Paul Gilster for Centauri Dreams quoting Jeff Kuhn (University of Hawaii), Svetlana V. Berdyugina (University of Freiburg), David Halliday (Dynamic Structures, Ltd., in British Columbia), and Caisey Harlingten (Searchlight Observatory Network, Norwich, England)

Here is a Jeff Kuhn's, Institute for Astronomy, University of Hawaii, talk on The Colossus Telescope and the search for ET, and a quite descriptive blog post by Brian Wang on Technology for 77 meter primary mirror ground based telescope exists today and it could survey earth sized exoplanets out to 60 light years advocating the project from a technology perspective.

A bit more can also be read on the Innovative Optics Ltd. web pages, that are sadly under construction, but they do give a hint that an article about it was written in June 2013 edition of the Astronomy Magazine, titled How to find ET with infrared light (PDF), by Jeff R Kuhn, Svetlana V Berdyugina, David Halliday, Caisey Harlingten. A nice digest is also available in this Centauri Dreams blog post.


How can I calculate how far through the day the prime meridian is of different planets I'm trying to create a widget that shows the 'time' on different planets. It will show how far through the day/night cycle (as a percentage) a point on the planet is. It has been easy to scale down the cycle from 24 hr to eg ~10hr day of Jupiter however I am struggling to work out how I can 'set' the time.

For Mars this has been straight forward, using the comparison of MTC and UTC of when the Curiosity rover landed but I can't find similar data for other planets to anchor time from earth to the other planets.

Is there a data base for this kind of information?

NASA's Navigation Ancillary Facility (NAIF) publishes planetary constants kernels (PCK) which are basically text files containing pole orientations for the largest known bodies.

PCKs includes the parametric orientation of their prime meridian in agremeent with IAU standards (meaning datum is J2000.0).

The latest PCK dates from 2011 and is actively used by most operational interplanetary flight projects across the world.

Using the NAIF SPICE library (available in Fortran, C, Matlab and IDL) you can load this kernel and read the orientation of the prime meridian for your body and date of interest.

Time offset between bodies can be reconstructed as angular offset between meridians. But you may find some time-related functions within SPICE which can make your task easier.


Visible Stars in Andromeda Galaxy So when I look at images taken of Andromeda, I see a lot of individual stars.

Image by André van der Hoeven

It seems to me that the actual individual stars that far away would be too small to resolve, even with a big scope like the Hubble. So, I have to assume that these points of light that I see are either a) stars in our own galaxy, or b) other distant galaxies, like we would see in the Hubble Deep Field:

So I decided to think a little about this ... so I chose what I presume is big, bright star: R136a1. This one is about 30 times the size of the sun, and 8.7 million times as bright. We can barely see this thing with a telescope, and it's 163,000 light years away. Andromeda however, is 2.5 million LY away, over 15 times as far, which would make the light ... what ... 15 squared... 235 times as faint?

I have to imagine that the glow from the galaxy comes from the scattering and reflecting of all the collective starlight inside the galaxy off the dust and gas and whatnot contained therein, and that the actual individual stars would be kind of like individual droplets of water in a cloud. Almost kind of like when you can briefly see the form of a cloud when lightning flashes inside it at night (even though the light really isn't coming from the droplets)

Am I even close to correct in thinking this?

Thanks

You are right that most of the dots of light that you see in the at image of Andromeda are stars in our galaxy that happen to be on the same alignment.

However we can resolve stars in the Andromeda galaxy. (Here I am understanding "resolve" means "to see as individuals and not just a haze")

https://www.spacetelescope.org/images/heic1502a/zoomable/

Even without the Hubble telescope, individual stars had been identified in the Andromeda galaxy, and (since the brightness of some of these stars can be determined) the distance was calculated. This was also done by Hubble, but by the man, not the telescope.  He found that the Andromeda galaxy was not part of the Milky Way, but much further away.

Hubble's photograph from 1923 can be compared to a modern skysurvey image.

The light in the image that you show is the combined light from billions of stars. They are too dim to be seen at the resolution of your image, but combine to make what looks like a shining cloud.  Just like a real cloud is made of lots of dots of water that are too small to see.

There are background galaxies. Some can be seen on the high resolution view I link above. One surprising thing is how small the area of the sky in the Hubble Deep field image is. It would be only a few pixels across on the scale of the image you have of the Andromeda galaxy.

You could expect that many galaxies to be in every few pixels, but too dim to be seen in the image of Andromeda.


Would Adaptive Optics be Useful in Radio Astronomy? This Question and Answer got me thinking. If atmospheric seeing at visible wavelengths is the result of refractive index inhomogeneity, would it also be a similar problem for mm to cm wavelengths? From a quick search, the index of refraction of air at STP is about 1.0003 (visible) and 1.0002 (radio).
If it is not, is there a way to understand quantitatively why it is not a problem?

Sources: 1, 2

In fact, the techniques of adaptive optics are already being used in radio astronomy.  They are implicit in the basic imaging algorithms (e.g., CLEAN) used to produce maps from radio interferometers.  In those cases, they are usually being used to correct for the artificial structure introduced by the way the interferometer samples the sky, rather than for structure imposed by the intervening material.  But at low frequencies (1 GHz and below, certainly) they are also used to correct for the artificial structure imposed on the incoming radio wavefronts as they pass through the ionosphere.  Current large low-frequency instruments (such as the LWA and LOFAR) rely heavily on these methods.


If earth changed its orbit, what would happen to the moon? Let there be an accelerating force acting on earth over an arbitrarily long time to change its orbit around the sun (e.g. by asteroids repeatedly passing by close to earth (intentional or not) or whatever). For this question consider only the effect of earth's gravity on the moon (and vice versa), not other influences (e.g. not the immediate effect the asteroids passing by have on the moon's orbit).

If such perturbations are weak enough yet of sufficient duration to change earth's orbit around the sun, how does it change the moon's orbit around earth? My considerations:

Since the moon remains in orbit around earth even as the earth goes around the sun there obviously is some lower limit to how fast earth can accelerate. However, that force wanders around earth once a year, hence its effect on the moon's orbit is evening out - and the effects from the sun are supposed to be ignored here, anyway, so let's have the force go in a constant direction.

The force acting on earth can be decomposed into $F_\perp$ perpendicular to and $F_=$ coplanar with the moon's orbital plane. $F_\perp$ moves earth out of the plane of the moon's current orbit, so the moon's orbit will adjust to find a new plane: if the force is continuously applied in the same direction the moon's orbit will change until $F_\perp = 0$, so this factor can be neglected.

$F_=$ will cause the moon's orbit to become very elliptical, the moon passing closer on the side toward which earth is accelerated and being further away on the other side. If the force is indefinitely sustained something will happen to the moon, but under which circumstances will which scenario happen?

the moon remains in orbit,
the moon gets tidally torn apart,
the moon crashes into earth,
the moon leaves orbit of earth (though the moon will probably say that it's earth which ran away...),
anything else interesting I forgot.

Aside from the fact that it's 81 times easier to move the Moon than the Earth, so, in such a scenario, the Moon could be moved too with an extra 1.23% of time/money/energy, so, it really would make sense to move them both, not just move the Earth and risk losing the moon or worse, crashing into it.

But (lets credit the need to save 1.23% to a congressional budget committee) and just move the Earth, as you propose.   Would the Earth lose the Moon?  . . . It depends, but not necessarily.

The first, idea to get out of the way is that there's no gravitational string connecting the Earth and Moon, so if the Earth was accelerated fast enough (say, launching millions of very high velocity rockets off the same side of the earth at the same time) there's no attachment that would pull the Moon with the Earth.   This is one of those scenarios where the rubber sheet analogy works quite well.  Accelerate the Earth and the corresponding gravity well moves away from the Moon and the Moon moves corresponding to the decrease (or increase) in the slope of Earth's gravity well, so the Moon's velocity carries it relative to the new slope.  But that's the argument for a single acceleration.   For multiple gravity assists, you have to account for the moon being in different positions so the relative movement wouldn't all be in the same direction.

Asteroid Gravity Assist - how close to the Earth?

A passing asteroid would affect both the Moon and the Earth, but for optimal Earth movement, you'd want it pass within, say, a few thousand KM of Earth's surface, outside of the atmosphere but much closer to the Earth than the Moon, where it's gravitational tug on the Earth would be over 1,000 times the tug on the Moon at closest pass.  The entire path wouldn't be a 1000 to 1 ratio, but with a close enough pass we can effectively say the Asteroid is giving the Earth a much larger gravitational tug, where the tug on the Moon is somewhat negligible.  In effect, moving the Earth's orbit but not moving the moon's orbit nearly as much.

Asteroids passing that close would be inside the Roche limit and probably would begin to break apart, but that wouldn't change the gravity assist or be a problem for the Earth if the velocity was sufficient to pass through and not remain in a near-Earth orbit.

If it was a single asteroid of high mass with a near-Earth pass that effectively moved the Earth but not the Moon, Then any of your scenarios are possible.  The Earth could be moved sufficiently where it could be pulled away from the Moon (a change in velocity of about 1,500 km/hour in the right direction would do that) or the Earth could be pulled into the Moon (a change in velocity of about 3,600 km/hour), or the orbit could be sufficiently jiggled where one of those two scenarios would happen eventually if not right away.

To change the Earth's velocity that much, with a single asteroid pass, you'd need that asteroid to be, (if my math is right), a few times the mass of the Moon, and an object with that mass passing within a few thousand KM over the Earth's surface, lets just say that would be a bad idea for a number of reasons. - so, it's better to do it the way you suggested.  Many asteroids, over a long time.

Many asteroids - what would happen to the Earth-Moon system

Each asteroid, passing within a few thousand km of Earth would move the Earth slightly, but as the Moon moves around the Earth, many of those movements would cancel out.   They would move the Earth towards the Moon when the Moon was on the same side of the Earth as the asteroid, and away from it when the Moon was on the opposite side.  Similarly, eccentricity could be increased or decreased.   There's no one answer as to whether the Earth would lose the moon without adding up the position of the moon and averaging it out.     Moving the Earth could be timed, where, in effect the Moon would be carried along with it.  This works both ways too.   We could move the Earth's orbit by properly timed thrusters or explosions on the surface of the Moon, sometimes moving the Moon away from the Earth, sometimes closer, but gravity assists are probably easier with less energy involved, as Jupiter could be used to accelerate the asteroids, which would reduce the energy input needed.

The net effect is that you can move the Moon with the Earth, or the Earth with the Moon, but pushing on just one of them.   That's possible with gravitationally bound objects.

So, depending on the timing of the asteroid gravity assists, you could create any of your four scenarios, but without specific timing, there's at least a pretty good chance the Moon stay with the Earth.  The 2nd scenario, the Moon getting tidally torn apart, that would only happen if it got very close to the Earth.


Blackbody curve in RGB for objects less than 1500 K? We know the colors of stars that have a temperature greater than 1000-1500 K, shown here. However, I am wondering about those stars/brown dwarfs with surface temperatures of less than 1500 K. Is there a blackbody curve for these temperatures, and are there any set RGB values for them?

So I use the following logic:

Define 'red', 'green' and 'blue' light in terms of the wavelength ranges those colours encompass (from here)
Calculate the average spectral radiance across each wavelength range, for a defined temperature
Define the RGB value to be the relative ratios of each colour's spectral radiance with 255 defined as the colour with the largest spectral radiance

I made a Python script which you can find here to calculate, display and show the appearance of the corresponding RGB value. Within the script, just change the value of the stellar_temperature variable to see the RGB values of stars of different temperatures.
The script is then finished off with a simple plot to show the appearance of that RGB value.
Now there are a couple of assumptions of course:

RGB values can be defined in terms of radiance/luminosity/flux ratios at each wavelength... This obviously breaks down if you have a detector which gets saturated at certain flux levels! I presume the human eye might fit that description.
Stars can be modelled by perfect blackbody spectra. I believe this to be a pretty valid assumption when the accuracy level needed is differentiation of different RGB tones...
No foreground extinction/absorption by atmosphere/dust etc.


How can something infinitely big have expanded from an infinitely small? Please help me reconcile what I see as contradicting theories:

The universe began with the Big Bang and expanded from an infinitesimally small point.
The universe is infinite.

How can something infinitely big "expand" from an infinitely small point? There has to be some sort of a 'blast wave', right?
Also, if we think we know the total amount of matter the Big Bang must have produced - how can a limited amount of matter fill an infinitely big universe?
P.S. One idea I have is that the universe may be infinite, but the Big Bang didn't create it - it created matter within the infinitely big universe. This would explain the expansion we're observing now: the matter will continue being distributed across the infinitely large universe. So I guess my question is more of a "why this assumption is incorrect"... :)

The universe started with "big bang" is a slogan for "There was a time when the universe was hot and dense, and this time may be considered to be the start of the universe, and the start of time."
The universe has (as far as we know) always been infinitely large.  That's not certain, but we have no evidence contradicting it.  The universe was never an infinitesimally small point. It was always infinite at every time t>0.
We know how much matter the big bang has produced in the observable universe, and we can model this. (We don't really know why it produced this much matter, but we have enough parameters in our models to get a universe like ours).
We also think that the universe is kind of the same everywhere.  Again, there is no proof of this, but nothing contradicts it, and so there would be an infinite amount of matter in the universe.
There was no "blast wave".  Because the whole universe was hot and dense at the same time.  The whole infinite universe, filled with an infinite amount of matter, which then expanded. (and yes, an infinite thing can expand, it just means that things within it get further apart.)
As for t=0 or for t<0  We have no idea.  I don't know if those are even things that we can talk about. It seems that we can talk about the state of the universe at time t=1 second.  But we can't talk about the state of the universe at t=0 seconds, at least, not with the mathematical and physical knowledge that we currently have. Time t=0 is a singularity.


What is the Milne-Eddington Approximation? In this paper: Planet temperatures with surface cooling parameterized it states in the "radiation model" the following:

The Eddington–Milne approximation relates $T_0$ and $T_e$ through the
gray IR optical depth $\tau$:
$T_0=T_e(1+\frac{3}{4}\tau)^{0.25}$

I looked this approximation up on google, and found it was more commonly known as the Milne-Eddington Approximation. However, this approximation seems to (mainly) be applied to stars, and I can't exactly see the connection between it and the temperature of a planet. (I also don't completely understand what an "optical depth" is.)
What is this approximation and why can it be applied to approximate the temperature of a planet with an atmosphere?

I don't have time to write up a full answer with derivation, but you might want to have a look into the standard radiation transport literature (e.g. the book by Mihalas&Mihalas) or the radiation transport in stellar interiors (e.g. Kippenhahn) or literature for irradiated exoplanets (e.g. Guillot (2010)). The ME-approximation is a standard result for grey radiation transport at optical depths >1, when the radiation flux is diffusive, i.e. $\rm F_{rad} = c/(3\rho \kappa_R)\nabla E_{rad}$.
Then you can couple the equations for $\rm E_{rad}$ and $\rm E_{gas}$, integrate and solve for $\rm E_{gas}$, which is $\rm \rho c_vT$. This gives you the ME relation, which is valid for the diffusive radiative transport in gases, and precludes interesting things like the greenhouse-effect, temperature inversions, etc.


Possible to use tachyons to explore black hole? I read on a Wikipedia article lately that tachyons are theoretical particles which always travel at or above the speed of light. That means that when one passes us, we see two images, a blue shifted one and a red shifted one.

Black holes on the other hand have gravity so strong that light gets pulled in. However, I haven't heard that black holes can exert a gravitational pull that can pull and object that is travelling greater than the speed of light.

So now, I am wondering that if it is possible to use/make tachyons and control those tachyons, could we send them into a black hole and use them like a "echolocation" thing, except the sensors would be on the other side of where the tachyons are first produced?

Let's look at the validity of tachyons first. Travelling faster than light, as said by userLTK, would create time travel, which would create the famous paradox, the tachyonic antitelephone. The tachyonic antitelephone is a violation of causality, and thus most likely, tachyons would not exist.

Now, take a look at another assumption. Wikipedia is right almost all times, but sadly, it has some wrong information. Such is with tachyons. It gives us some contradictory statements of tachyons too. It is wrong to assume that tachyons always move faster than light. A tachyon, is a particle with an imaginary number as its rest mass. This, however, does not mean it can travel faster than the speed of light, nor that there's any conflict between their existence and the special theory of relativity.

The main idea here is that the typical intuition we have about particles -- them being billiard ball-like objects -- just fails in the quantum world. It turns out that the correct classical limit for quantum fields in many situations is classical fields rather than point particles, and so you must solve the field equations for a field with imaginary mass and see what happens rather than just naively assume the velocity will turn out to be faster than light.

Leandro M. wrote on physics stack exchange, that

  a good way to think about tachyons is to imagine hanging several
  pendulums on a clothesline, one after the other. If you disturb one of
  them, some amount of force will be transmitted from one pendulum to
  the next and you'll see a traveling disturbance on the clothesline.
  You'll be able to identify a "speed of light" for this system (which
  will really be the speed of sound in the string). Now you can make a
  "tachyon" in this system by flipping all the pendulums upside down:
  they'll be in a very unstable position, but that's precisely what a
  tachyon represents. Nevertheless, there's absolutely no way that you
  could send a signal down the clothesline faster than the "speed of
  light" in the system, even with this instability.

This means that tachyons don't actually move faster than the speed of light, and your assumption is wrong.

Furthermore, StephenG wrote in a comment that tachyons essentially can't exist in a black hole.

user106422 wrote in the linked question on physics stack exchange that

  in a nutshell, creating a tachyon itself would lead to some form of
  a spontaneous phase transition in which the tachyonic mode no longer
  exists. So from a rigourous QFT + GR setting, I don't think tachyons
  exist the way it is portrayed in simpler QM models. So no, tachyons
  will not escape the horizon simply because the theory will not allow
  for them to exist.

Thus, no, even if they exist, they don't really travel faster than the speed of light, and even if they do, that can't really "travel" through a black hole. So, it is not possible to use tachyons to explore a black hole.


Can moon set after being up when due north? (pseudo circumpolarity) I'm in the northern hemisphere, facing north, and notice that the moon
is due north (azimuth 0) and is still above the horizon, albeit barely.

Does this mean the moon is necessarily circumpolar (doesn't set), at
least for the next few hours?

As the moon moves away from due north, it's altitude/elevation
normally increases. However, it's possible that the moon's declination
is decreasing so rapidly that the moon's elevation actually decreases,
and the moon sets.

Is this possible?

This question is tangentially related to my question "libnova odd behavior for 89.5 degrees north latitude" on Stack Overflow.

EDIT to answer questions: I am facing true north. I am referring to the Earth's true moon, but not necessarily in any given time frame. In other words, if something like this happens 10,000 years from now, that's fine.

EDIT: OK, I believe the moon CAN set even if it's up when due north. Example:

You are at latitude 89.5N
The moon's declination when due north is +0.5N. This means the
moon grazes the horizon when due north.
If the moon's declination were constant, it's highest elevation
for the day would be 1 degree.
Since the moon's declination can change more than one degree per
day (average of 1.5 degrees/day), it's quite possible for the moon's
declination to go below -0.5N, at which point it would have set (it
will actually set before this point unless it happens to reach due
south).

In theory, this could happen with any object whose declination
changes, provide you're close enough to the North Pole.

I'll leave this update open for critiques.

EDIT: Actually, this whole question is just asking whether the midnight sun/moon can set at any position other than due north, which is fairly obviously true. Reasoning: once the moon/sun finally sets not due north, it was obviously still up the last time it was due north.

Yes - here is a good explanation of the situation. Just as it's possible to have continuous daylight for days or weeks on end, you can have continuous moonlight too.

The Moon's orbit is tilted at (a maximum of) just over 5 degrees to the ecliptic, however this tilt has an oscillatory precession with a period of 18.6 degrees. This precession means that our "lunar arctic circle" will vary in latitude over time.

For example, if the moon is sitting exactly on the ecliptic (latitudinally speaking), it would remain above the horizon until it is at a sufficiently low phase of illumination that its current ecliptic longitude is below the horizon. Of course in reality the moon only crosses the ecliptic twice during each lunar cycle (it's these two points that precess). Stellarium is a cool program to visualize this on if you turn on the ecliptic grids.

One important thing to note is that this phenomenon is dependent on both the time of year and the phase of the moon. In the summer months, new and near-new moons are the ones that can remain visible for days or weeks on end. Conversely, at the North pole, you might not see a full moon at all for a few months!


Since the Universe is expanding, is it accurate to say that a galaxy is 5 billion light years away? Isn't it better to say that the light from the galaxy took 5 billion light years to reach us and it is a very old picture of it? However, if light travelled back to the galaxy at the constant speed and an observer was stationed to record it wouldn't it take longer to reach because of the expansion of the Universe?

Also if it still exists after 10 billion years or not we could not predict. So is the picture of the Universe more of a timeline of events rather than like a conventional map that shows distance between points.

How do current day theories tackle these issues?

I'm not 100% sure if I'm understanding what your asking, but if your question could be rephrased as "how do we measure distances in an expanding universe?", then I can try to answer that.

Depending on what astronomers measure they use different distance measurements. For example the comoving distance between two objects takes into account the expansion, and so does not change with time. If you know the redshift of the galaxy, for example by measuring the spectrum, and have a cosmological model, then you can calculate the comoving distance. Here cosmological model means constraints on the amount of dark energy, matter (both dark and regular) and radiation. The current accepted model is that the universe is around 70% dark energy and 30% matter, most of which is dark (with negligible radiation). The percent here refers to the fraction of energy density. Note that these values change over time, mostly since dark energy is like a property of space and so increases as the universe expands.

For some more info see:
https://en.m.wikipedia.org/wiki/Distance_measures_(cosmology)

Note that light years is a definite measurement, and so we can use it a valid unit for all distance measures.


What is the ratio of "real" stars in the sky? When you look at the sky without any utilities like binocular or telescope, what is the rough ratio of "real" stars to other objects like planets, the moon, asteroids, satellites?

90% stars - 10 % others?
99% stars - 1% others?
Almost 100% stars - apart from a very few you can easily name as a hobby astronomer?

It's almost 100% stars.

In good conditions, you can see perhaps 2000 stars. (There are about 6000 naked-eye visible stars; of these, 3000 are above the horizon at any time, and about 1000 are hidden because they're too close to the horizon and blocked by the atmosphere.)

The number of non-star objects you can see without assistance is tiny in comparison:

The Sun (obviously not at night, and of course it's a star)
The Moon
The International Space Station, but only a tiny fraction of the time
The visible planets: Mercury, Venus, Mars, Jupiter, Saturn (and maybe Uranus if you have excellent conditions and better eyes than mine)

A handful of other artificial satellites might be visible, but only rarely. Comets can be very visible, but again that's rare. Visible asteroids are even rarer. Vesta, a large asteroid, may be barely visible, but I've never seen it.

Note that some of these objects are quite obviously not distant stars just based on their appearance.

Some galaxies (Andromeda, and the two Magellanic Clouds if you're far enough south) are visible, but they don't look like stars. A few of the brighter nebulas and globular clusters might be visible; the latter are groupings of stars, so I don't know how they'd count.

Meteors and aircraft can be visible, but they're within the atmosphere, and probably not covered by your question.


How much overlap will the Andromeda galaxy and the Milky Way have when they collide? Measurements of Andromeda's blue shift let us conclude that the distance between the Andromeda galaxy and the Milky Way is decreasing and in a few billion years they will "collide".

The blue shift only yields the radial component of Andromeda's velocity vector. It is my understanding that measuring the tangential component is crucial in determining whether a "collision" will actually happen (in a gravitationally bound two body system, for point-like bodies to collide, the relative velocity component must point exactly towards the other body, i.e. the tangential component must vanish).

Now, galaxies are not point-like, so some small nonzero tangential component might lead to a collision where at least some galaxy arms intersect.

Has the tangential velocity been measured? If so, how? How central is the collision (bulge into bulge, bulge into arms, arms into arms)?

This page, from June 2012, contains a fairly detailed summary of three papers that considered the tangential velocity and collision problem.  I'll quote a few choice bits from that page:

Andromeda (M31) and the Milky Way are the two largest galaxies in the small group of galaxies called the Local Group. At the moment, M31 is about 770 kpc away from our galaxy, but Doppler measurements of the line-of-sight velocites of its stars have long shown that it is inexorably falling toward us. The exact nature of the collision, however, has so far remained unkwnon. Will it be a miss, glancing blow, or head-on smashup? This depends on the proper motion (sideways motion) of Andromeda in the sky, which is extremely hard to measure.

At last, the authors of this study manage to collect extraordinarily accurate Hubble Space Telescope observations of the tangential motion of M31 over a five-to seven-year period, and these data remove any doubt that Andromeda is destined to strike and merge with our Milky Way in four billion years. The Triangulum galaxy M33, the third most massive galaxy of the Local group, which is bound to M31, will likely join in the cosmic boom (with a small chance that M33 will hit the Milky Way first).

The final result is that M31 has a radial velocity with respect to the Milky Way of about  -109 km/s, and a tangential velocity of about 17.0 km/s (<34.3 km/s at 1-sigma confidence). These numbers clearly imply that the velocity vector of Andromeda Galaxy is statistically consistent with a radial (head-on collision) orbit towards the Milky Way. This means that the Milky Way-M31 system is bound, and that the two galaxies will merge, as investigated further in Paper III.

The simulations show that the Milky Way and the Andromeda galaxy will merge, consistently with the radial (head-on collision) orbit deduced in Paper II for M31, and  that the first “pericenter” (closest approach) will occur at around 4 Gyr from now. For our Milky Way,  the encounter has 72.2% probability of being prograde (the galaxy spins in the same direction as the flyby). In 41.0% of the Monte-Carlo orbits M31 makes a direct hit with our Milky Way, where the authors define a “direct hit” as an encounter with a first pericenter distance less than 25 kpc. The two galaxies will eventually merge after 5.9 Gyr, and the radial mass profile of the merger remnant will be significantly more extended than the original individual profiles. Roughly speaking, this profile will follow the $R^{1/4}$ law characteristic of elliptical galaxies, in agreement with the predictions from the numerical simulations of major mergers of spiral galaxies.

I'll note that $25 \text{ kpc} = 25,000 \text{ pc} \cong 81,540 \text{ ly}$, and that the Milky Way is only about 100,000 ly in diameter, so the "direct hit" definition is quite a substantial distance here.


At what annual rate are new exoplanets being recognized? How does it compare to new asteroids? I just read the BBC News article Exoplanet tally set to pass 4,000 mark
. It makes me wonder about the annual rate  that new exoplanets being recognized, and how it compares to the rate of new asteroids.

I'm also wondering if there is any chance there will be a crossover in the rates in the next few years. TESS has found it's first exoplanet, and hopefully WFIRST will be on schedule as well.

At what annual rate are new exoplanets being recognized? How does it compare to new asteroids?

Assuming exoplanets have been discovered at a constant rate since 1995 (not very true) then the rate is very approximately 117 exoplanets a year. Comparing to the Minor Planet Center (MPC) archive stats which are plotted below:

which shows that approx. 761,000 asteroids of all types have been discovered since 1995 April or roughly 22,000 a year. (The lower black line is for the smaller number of asteroids that have been seen enough times and the orbit is secure enough that they can be numbered).

Exoplanets suffer from magnitude and volume-limit problems in that to get a large enough number on the sky to discover large numbers of them, requires going faint. Since confirming an exoplanet and ruling out other explanations such as blended background stars and M dwarf or brown dwarf binaries (which give similar transit depths but different radial velocity amplitudes) requires a large additional effort and high precision spectroscopy to confirm them, this becomes the bottleneck requiring tens or more of hours of large (4m) telescope time to confirm each of the fainter exoplanet candidates. Additionally the most numerous exoplanets in the 2-15 times of the Earth range are very tough to confirm as the RV amplitude is very small (few m/s or smaller depending on the orbital period).

  I'm also wondering if there is any chance there will be a crossover in the rates in the next few years.

Because of the limitations discussed above, the chances of there being a cross-over in rates any time soon is slim to none.


Could an Earth-like magnetic field protect life at exoplanet Proxima Centauri b? I took a look at Wikipedia's page for Proxima Centauri b, the exoplanet that orbits Proxima Centauri, where it is said it is expected to receive 2000 times of stellar wind pressures than on Earth.

It does not say anything about Proxima b having a magnetic field, but I found this paper where a magnetic field for the planet is predicted:

  In our simulations, most Proxima b analogues develop intrinsic dynamos
  that last for 4 Gyr (the estimated age of the host star). If alive,
  the dynamo of Proxima b have a dipole moment . These results are not
  restricted to Proxima b but they also apply to earth-like planets
  having similar observed properties.

My question is if an Earth-like magnetic field, if Proxima b has one, could protect life as it does on Earth, or, conversely, habitability could not be possible due to stellar wind.

Jorge I.Zuluaga, Sebastian Bustamante (2018): "Magnetic properties of Proxima Centauri b analogues". Planetary and Space Science.
Volume 152, March 2018, Pages 55-67

According to Garcia-Sage et al. (2017) "On the Magnetic Protection of the Atmosphere of Proxima Centauri b", who assume that Proxima b has a magnetic field strength identical to the Earth, the situation does not look promising:

  With an O+ and H+ escape at 1600 km altitude of 4.2×109 cm−2 s−1 as found for thermospheric densities of 3×T,
  the total mass-loss rate is 4.3×105 g s−1 over the dayside
  hemisphere. Using a total atmospheric mass of 5×1018 kg
  (Trenberth & Smith 2005) results in a loss of the entire mass of
  the atmosphere over 365 million years.

(T is the thermosphere temperature of the Earth)

They go on to note that Proxima would have had higher EUV and X-ray emission in the past, which would have made things worse. Ongoing outgassing of volatiles might be possible to create habitable conditions but the resultant situation would be very different from the Earth.


Where does the Milky Way end? I was reading this article
 and it says the following:

  Researchers measured the mass of the Milky Way and found that our galaxy is approximately half the weight of a neighbouring galaxy known as Andromeda which has a similar structure to our own.

So I was thinking, if we consider a galaxy neighbor to us, then our galaxy should be having an endpoint and the neighboring galaxy should be having a start point. So how do we know which is the starting and ending point of a galaxy, and how do we calculate it?

Here's a rough sketch of the Milky Way and the Andromeda galaxy,* showing their approximate sizes and distance from each other to scale:

What the picture (hopefully) illustrates is the incredibly vast gap of empty space — around 2.5 million light years, to be exact — between the galaxies, each of which has a diameter of only(!) around 100 thousand light years or so.

While both galaxies are shaped pretty much like "fuzzy whirlpools" of dust and gas (and, apparently, dark matter), with no precisely defined sharp outer edge, they are still pretty unambiguously separated.  While we may not be able to point to a specific line in space and say that "the Milky Way ends right here", it's still clear that the Milky Way is over here, while the Andromeda galaxy is over there, and there's a huge gap of pretty much absolutely nothing at all in between.

(Of course, there is some stuff even in intergalactic space, including some very diffuse gas, a little bit of dust and even the occasional stray star.  Still, compared to the galaxies themselves — which, from a human viewpoint, are already pretty full of empty space — the intergalactic medium can be pretty well described as empty.)

*) The little specks in the picture around each major galaxy are meant to represent their smaller satellite galaxies, such as the lesser and greater Magellanic clouds. Their relative positions and distances, alas, are probably not very accurate.


Do we know a star that is similar to the Sun when it would be a red giant? In about 5 billion years the Sun is predicted to become a red giant and have more than 200 times its current size, reaching a radius of about 5 AU when largest.

I wonder what spectral class the Sun would have then, I think somewhere from M1III to M5III. Do we know a red giant star that is similar to what the Sun is predicted to become?

Models for the future behaviour of the Sun do vary, mainly as a result of uncertainty of mass loss during the red giant (H shell burning) and asymptotic red giant (H+He shell burning) phases.

A highly cited paper by Schroeder & Smith 2008 claims that the Sun will reach its maximum size of about $256 R_{\odot}$ (1.18 au) at the very tip of the red giant branch (and not at the end of the asymptotic giant branch phase, which is suggested by some other models). This maximum size will occur 7.6 billion years in the future (not the 5 billion years of popular literature), when the Sun's mass will be reduced to about $0.7M_{\odot}$ and have a surface temperature of 2600 K (or about 2300 Celsius). This would have a spectral type of M6III, or perhaps even M6I.

Do we know of a star similar to this? It depends what you mean by similar, but there are unlikely to be any stars like this in our Galaxy. The reason for this is that star formation began in our Galaxy about 12 billion years ago. But a 1 solar mass star like the Sun requires about 12 billion years (or a bit more) to reach the tip of the red giant branch. Even were this just about possible time-wise and we were to find a red (super)giant star of about $0.7 M_{\odot}$, it would be highly unlikely that the star would have a similar chemical composition to the Sun. That is because stars born early in the life of our Galaxy would have very low concentrations of metals like iron and nickel that are only produced inside stars and only present in the interstellar medium when a generation of stars have lived and died.

So my perhaps pedantic answer, is that there aren't any big red giants we can see now that started life as 1 solar-mass stars and have a similar chemical composition to the Sun.


Future of CMB observations: How will our knowledge of the early universe change? The Planck satellite has been presented and awaited for a long time as the ultimate experiments for measuring temperature fluctuations in the cosmic microwave background (CMB) over the full sky.

One of the big questions that still need answer and that Planck might help clarify is about the dynamics and driving mechanisms in the first phases of the universe, in particular in the period called inflation.

Thankfully there is room for improvements at small scales, i.e. small pieces of sky observed with extremely high resolution, and more importantly for experiments to measure the polarisation of CMB.
I know that for the next years a number of polarisation experiments, mostly from ground and balloons, are planned (I'm not sure about satellites).

For sure some of these result will rule out some of the possible inflationary scenarios, but to which level?

Will we ever be able to say: "inflation happened this way"?

This is a great question. I know of a couple of really big things about inflation people want to be able to nail down by using the cosmic microwave background.

The first is measuring what are known as E- and B- modes, which are the curl-free and divergence-free components to the modes of cmb radiation:

Essentially, measuring large scale Gaussian B-modes from primordial gravitational waves will help constrain the energy scale of inflation. It may also be able to rule out most ekpyrotic and pure curvaton/inhomogeneous reheating models (same source).

The other thing people are looking at is this idea of primordial non-Gaussianity, which are second order corrections to the Gaussian fluctuations present in the cmb (review article; early planck results). Measuring a parameter called $f_{nl}$ (deviation from Gaussianity) has been a fairly crucial part of current and future studies and will also help rule out various inflationary models. This $f_{nl}$ parameter is defined as follows:

    In this case the multipole coeﬃcients $a_{lm}$ of the CMB
    temperature map can be written as
    $$a_{lm} = a_{lm}^{(G)} + f_{nl} a_{lm}^{(NG)} $$
    where $a_{lm}^{(G)}$ is the Gaussian contribution and $a_{lm}^{(NG)}$ is the non-Gaussian contribution.


What is the probability of seeing a neutron star as a pulsar? Pulsars are neutron stars that emit a beam of electromagnetic radiation that is not aligned with its rotation axis. If the Earth passes through that beam of radiation, we see a pulsar. Pulsars are only observable if the beam crosses the observer's line of sight. Otherwise, we can only see a regular neutron star.

For a pulsar with random orientations, what is the probability of seeing its beam from Earth? Out of 100 pulsars, how many will have a beam that crosses the Earth?

Out of 100 pulsars, how many will have a beam that crosses the Earth?

About twelve.

"The beaming fraction f , that is the mean value of the fraction of observable pulsars or the mean probability of observing a normal pulsar, is 0.124 ± 0.004." M. Kolonko et al.: On the pulse-width statistics in radio pulsars


Does liquid water on Mars means life? We need to figure if liquid water is present throughout a Mars year, and how long the planet has been at its current distance from Sun. That will give us the length of time that liquid water has been present.

We can then compare this with Earth's data to figure out how long life would have had to evolve and what state it may have reached. In particular would there have been enough time for humanoids to evolve?

Would the different composition of the atmosphere and surface gravity produce life that looks different to that on Earth today?

I don't think applying Earth data to Mars makes much sense, well, except perhaps at the very beginning.  The reason I say that is that life on Earth took a long time to get what we might consider "interesting", for lack of a better word.

Source - and, OK, it's a children's book, but I like the picture.

4 billion years ago - simple cells.
3.5 billion years ago - photosynthesis.
2 billion years ago - cells with Nuclei
1 billion years ago - bacteria.

So the Earth took 3 billion years to make - bacteria.   Granted it's only one planet as a sample, but if that's standard, then, arguably, most of the life in the solar system might be 1 celled and, you know, kind of boring to you and me, though I'm sure scientists would love to study 1 celled organisms from other planets.

If planets need a few billion years before things like plants, fish, insects, etc, evolve, then many planets won't stay in the Goldilocks zone that long.  . . . or, option B, maybe things happened slower on earth than other planets, but for now, we just don't know.   Finding life on Mars or records of past life, if there was any, could help answer some of those questions.

Mars may have lost it's oceans fairly quickly, in less than a billion years.   That's not a long time for life to evolve, at least based on the Earth Model.

Now, low gravity, probably not a big deal.   Animals and trees on a low-G planet grow grow taller and thinner/weaker - thinner bones, smaller muscles for example.   High-G, just the opposite.  Shorter and stronger with thicker bones.    Prior to lungs, Insect size is determined by Oxygen content in the atmosphere much more than gravity.   (Fish-Fin size point removed as it probably wasn't correct).

Probably none of this happened on Mars cause I doubt life evolved that far but in theory on a low G planet you might get very large animals, perhaps the size of 10 story buildings, because size is a good evolutionary defense mechanism.  (Fun to think about, right?)

Thin Air, that's a bigger problem cause thin air leads to evaporating oceans and once the oceans evaporate, life would have a hard time continuing the evolutionary process   Life needs water, at least here on Earth.   Life can adapt to living with small amounts of water but life needs water.  In ice, primitive Life hibernates, but it doesn't continue to evolve.

Now it's possible that Mars' thinning atmosphere coincided with it cooling off and it could have had oceans frozen at the top but liquid below that for some time, while heat from inside the planet maintained liquid water and life was able to survive in that.   This happened to the Earth, when the Earth was covered by ice during the snowball earth period and when Snowball Earth ended, the Cambrian explosion started.   The problem on Mars was, if Mars had a snowball with liquid water below the ice period, it never ended.   It never went back to liquid oceans and that's a problem for evolution.

It's possible that snowball earth (limiting the sunlight and atmospheric gases available to life inside the ocean) forced bacteria to evolve, hunting for food rather than simply absorbing it via sunlight and air, but that's just speculation on my part but the timing was pretty consistent.  The Cambrian explosion followed snowball earth.

Humanoids on other planets (assuming we ever find any) would probably have characteristics adapted to that planet.  We stand upright because our ancestors found it helpful to run.   That might not be the case on other planets, perhaps that have thicker brush and no open planes.  That's just one example, there's probably others.   Our height likely developed out of the optimal height for hunting.  If we just were gatherers and trappers, not spear throwers we might be quite a bit smaller with shorter arms cause there's be no evolutionary advantage to being bigger or longer arms if we climbed trees to get away from predators.  You can clime trees higher if you're small for example and be safe that way.   Humanoids might have tails on other planets if they had a use for them, like, impressing the opposite sex with them or for balance for tree swinging/jumping.   There's a variety of possibilities that go way beyond gravity (which might just have an effect on body size and shape) or air pressure, which might affect things like wings for gliding, running (as thick air might reduce running speed) and lung size.

On red dwarf planets for example, plants and people might be significantly different colors.  Plants might be blue or black, to absorb more red light, Animals, for example, might have colors into the Infra-red spectrum that we don't see.   One blue sun planets, plants could be red and animals might have colors into the UV spectrum.   (Some birds on earth have UV spectrum colors that we don't see but they do).  Thicker air pressure might affect sound as well, they might talk much quieter perhaps higher pitch and have smaller vocal cords and smaller ears, where as, thinner air, bigger animals might make thunderous yells when they communicate.

There's a variety of possible factors. . . . hope I haven't gone too deep into speculation here, but speculation is fun sometimes.

Personally, I don't believe Mars ever came close to any of the ideas I mentioned above.  I don't see how it could.  it wasn't habitable for long enough.


Comparing different magnitudes. Is this statement correct? I have two methods which allow for a detection of a signal that is at most of magnitude x. If method 2 can detect signal that are half a magnitude larger, i.e. fainter, let's say x.5 mag, is it correct to say that method 2 can detect signals that are about 60% fainter than what method 1 can detect?

Is the 60% correct? I got this number by converting the magnitudes $m_i$ to flux $f_i$, i.e.
$$100^{(m_1-m_2)/2.5}=\frac{f_2}{f_1}\approx 0.40$$
$$\Rightarrow f_2=0.40 f_1\sim 40\% f_1$$

Thus, $f_2$ is about $40\% f_1$ which means about $60\%$ fainter. I have never worked with magnitudes before, so is this a valid statement?

Textbooks typically express the flux vs. magnitude relation something like this:

$$m_2 - m_1 = -2.5 \log_{10} \frac{f_2}{f_1}$$

which we can transform into this:

$$\frac{f_2}{f_1} = 10^{(m_1 - m_2) / 2.5}$$

so the original version of your formula was correct.

If m2 - m1 = 0.5, then f2 / f1 = 0.63.
Some readers find comparisons like "x% fainter" confusing, so I would say method 2 is more sensitive than method 1 by a factor of 1.58.


Which database of celestial objects do stargazing apps use? Stargazing apps such as Star Walk must have a database with a list of celestial objects, their names and details and each of their celestial coordinates.

I am interested to know which database these apps use as I am looking to build my own stargazing app for a computing project.

It would be great if someone could help me with this.

Thanks!

The Hipparcos is probably all that's really needed.  A lot of them add in portions of the Tycho catalog as well.  But even the Hipparcos catalog has more stars than what most armatures will need, and it's generally impractical memory wise to use the whole thing.  To really go crazy, a torrent for the NOMAD catalog is available.  All of those list only individual stars.  For things like galaxies and nebula the NCG catalog should do, but there are also the Index Catalogue, and Hershel Catalogs.  The most popular catalog would be the Messier, which has no official distribution sources (that I know of), but databases are available if you search this one for example.

If you don't care about the original sources, Stellarium has their star catalogs on their wiki.