Meaningful theories of the shape of the universe

Normally, when people say "the universe is infinite" they generally mean something like "the observable universe is locally flat, it is easy to assume that it is flat way beyond the observable universe, I don't know what lies beyond that, I won't talk about that, that is enough for practical purposes" (or any other proposition implying infinity in any direction and assumed for simplicity's sake while actually focussing on a small region of the space, the observable universe). So, "the universe is infinite" does not seriously mean that physical space goes on forever because this simply makes no sense at all, "infinite" is not a number, it is not a magnitude, it is not a property of real things (if you disagree with this premise please explain how the notion of infinity can be seriously applied to any direction of physical space, i.e. how you can seriously think to extend, sic et simpliciter, such a property of your mathematical model to the real world). (Personally I don't think this should be counted as a theory of the shape of the universe at all).

On the contrary, "the universe is finite and unbounded, compact, closed in all directions" is indeed a meaningful and in principle acceptable theory because it can be thought, described, discussed for what it actually implies. Of course, we don't know what lies beyond the observable universe but the idea of a compact universe makes sense and it seems to me this is the only meaningful explanation currently available of what "could" be (it is not necessarily the right, true explanation, of course).

Is there any other meaningful alternative (which can be thought, described, discussed)? Is there any alternative to the dichotomy "finite universe" vs "infinite universe"? Is there anybody out there working on models that overcome this dichotomy?

earth - Are we made of the stuff of one star or more stars?

It is highly unlikely that we're made out of stuff from only one star. The simplest reason for this, is that we have gold on earth. Gold is (we believe) created by the collision of two massive stars (neutron stars probably).

If there was only one predecessor to the sun, it would be extremely likely that all of its mass would still be nearby. The total mass of the entire solar system is much to small to have formed for example nickel and copper in any noticable amount. You would have to have a star of about 5 times the mass of the solar system. That mass doesn't go away.

You could, of course speculate that a couple of neutron stars at 2-3 times the solar system initially created everything, then split up into around 2-3 different solar systems. But we have quite a lot of chemical elements such as hydrogen and helium in the sun, which there would not be a lot of in neutron stars (due to it having to have fused into heavier elements).

All stars go through a few stages from their inception to their death:

Initially, the theory is that hydrogen was the prevalent chemical element. It's the "simplest" chemical element. When helium is compressed, due to the gravity of a star it's temperature will rise up. Once it reaches around 10 million degrees, fusion starts. Fusion of hydrogen creates helium.

Helium, being heavier than hydrogen will sink to the center of the star. Later, you will have helium fusion, if the star is massive enough to compress helium enough. Helium will generate oxygen and carbon.

A very massive star, multiple suns in mass, is able to fuse oxygen and carbon - which creates a lot of different chemical elements; neon, sodium, magnesium, sulfur and silicon. Later reactions transform these elements into calcium, iron, nickel, chromium, copper and others.

Eventually, many stars will explode into a supernova. In that process, a lot of these materials will be ejected into space, where they will gather due to gravity again.

The sun was probably created in a messy universe, where hydrogen and perhaps helium came together in a region where there was a lot of these other chemical elements.

Sources:

astrophysics - Good Introductory Textbooks

I have a more mathematical background but have always been interested in astrophysics, cosmology, astronomy, etc. There are a lot of popular books on the subject, but I am getting more interested in looking at a more rigorous approach to it.

What are the best introductory textbooks on the subject? (Calculus+ and assuming introductory courses in Mechanics and Heat and Electricity and Magnetism, etc.)

Is it just coincidence that the Moon follows the ecliptic?

It is not a coincidence at all! (There was, however, some statistical chances involved.) A key question to answer before answering your question, though, is Why is there an ecliptic at all? It is fair to see all the planets and a majority of the smaller bodies existing in a nice flat plane (the ecliptic) and think that it didn't have to be that way. Why not have different planets orbiting in different planes, or even backwards? To get the answer, we have to go back to the origins of the Solar System, when it was still a collapsing cloud of interstellar gas and dust. As gravity collapsed the cloud, the small amount of angular momentum it had became more significant, much as an ice skater pulling her arms in while spinning will make her spin faster. So, with the help of friction, the early Solar System flattened and had a 'spin' in a preferential direction.

As the Solar System evolved, planets formed, and all of them had ingrained in them this spin. Today, we see that in not only the existence of the ecliptic and the fact that planets orbit in the same direction, but in the fact that most planets rotate in the same direction as the sun does (Uranus and Venus being notable exceptions) and most large moons orbit their planets in the same direction (Triton around Neptune being a notable exception).

What about the moon? A leading theory for its formation is that it formed from the debris that resulted in a collision between a still-forming Earth and another planet-sized object. Statistically, both these objects would be most likely to have similar angular momenta to that of the overall Solar System (though it was by no means guaranteed), so their resulting debris would have it as well. When that debris coalesced into our moon, it too would also keep the original angular momentum 'signature,' and its orbit would thus be comparable to that of the ecliptic.

Of course, this is all a very chaotic and statistical process. While angular momentum is always conserved, there are ways of exchanging it between bodies (via gravitational interactions & collisions). Consequently, there are variations away from the ecliptic: the moon is inclined 5 degrees from the ecliptic; Earth's rotation is inclined 23 degrees from it; smaller bodies like comets will sometimes orbit well outside the ecliptic; etc. But the general trend holds, and is a marker you can see present throughout the solar system.

As an interesting aside, while all major planets in our Solar System lie roughly along the ecliptic, that is not always the case for other planets in other star systems. Wasp 17-b, for example, is observed to have a retrograde orbit around its host star, while others have been observed to orbit outside of their own system's ecliptics entirely.

What are the differences between a Black Hole and a Supermassive Black Hole

The mass of a black hole is not infinite. In fact, if a black hole is created that is big enough to survive evaporation, its mass will be its starting mass, plus any mass swallowed up, minus the radiation that leaves it.

Which is why you hear phrases such as "A black hole with ten times the mass of our sun" or in the case of a supermassive black hole, "...of millions of suns"

universe - Sources of astronomy-related dataset?

You have plenty of choices!

I am specialized in X-ray astronomy, then I can suggest you many facilities: they usually give at least some of their data publicly available. Tipically, you have data for light curves (photon count rates versus time), and/or spectra (that is flux versus energy).

I suggest you to work on the light curves: they are easily available, already reduced (you don't have to play with the data to make them usable, you can directly use them), and they fit your request of conforming to a regression model. Also spectra are enjoying, still I know some theoreticians who are not familiar with spectra, plus they usually need some more knowledge, because of response files, spectral fitting packages, etc. It is up to you (and your available time)!

Here a list of some facilities with available data:

Rossi X-ray Time Explorer

Swift/BAT

INTEGRAL

Chandra

MAXI

Also here you can find a list of many facilities with NASA participation, so the list is much larger.

Of course you can also use other kind of data (optical, infrared, radio) by the MAST project, but I have no experience on those. I guess, in the optical band, the Hubble Space Telescope will have a huge amount of data!

If you need a hand, beyond the SE vote up/vote down neurotic fashion, let me know. Good luck!

galaxy - What is a Galactic Eclipse?

Definitely a hoax as other commenters have said.

Dark rifts exist in the galaxy - large clouds of dust, several can be made out by eye, overlapping the milky way, in ideal conditions. See for example the Great Rift. However these are so large it would take far longer than three days for a solar system to pass through them. Probably thousands or millions of years. So this is definitely incorrect information.

observation - Stellarium 0.10.4: planet orbits change over time?

Edit (I looked, unfortunately most of the sources are astrology, not astronomy), but Mars last went in Retrograde March 2014 and it's not due to go again till May 2016 (every 2 years, 2 months). My guess below was incorrect (though it's kind of cool, I'll leave the picture up).

Mars does have a tilted orbit compared to earth and that could be the reason. That and the angle from the earth changes too.
Source

Mars, from our point of view, slows down, temporarily reverses direction then returns to it's original direction and continues on. The entire "S" motion takes maybe 3-4 months and your 2 photos are 24 days apart. (but this won't happen till May 2016)

Source of photo and explanation here:

Which is the most early type star with a planet discovered by radial velocity method?

The answer to this, and other questions of its kind about exoplanets, can easily be found at the website http://exoplanets.org/ This site contains a very authoritative catalogue of exoplanet discoveries and has tools to enable tables and plots of many variables to be constructed.

For example, to handle your question, I produced the following plot for exoplanets discovered using the doppler radial velocity technique. This shows effective temperature of the parent star on the x-axis, versus projected exoplanet mass $Msin i$. The the hottest star with an RV-identified exoplanet (on the website, you can click on the points) is HD113337, an F6V-type star discovered by Borginiet et al. (2013). The next hottest is HD103774, which is given a slightly earlier spectral type of F5V. These two are joint hottest within their uncertainties. Just a touch cooler is Tau Boo.

It is difficult to find exoplanets around high-mass main sequence stars using the doppler method because of the paucity of strong, narrow spectral lines. Most of what we know is from observations of subgiant stars - i.e. stars that would have been early-type stars on the main sequence, but which have cooler photospheres after they have left the main sequence. HD102956, mentioned in another answer, is an example if this - i.e. it was an early-type A star on the main sequence.

naked eye - Is the moon only 60 pixels?

It doesn't seem so far-fetched to me. Sure, you might be off by a few pixels, due to differences between the human eye and a computer monitor, but the order of magnitude seems about right — the detail in your images, viewed closely, more or less matches what I see when I look at the full moon.

Of course, you could fairly easily test it yourself: go outside on a dark night, when the moon is full, and see if you can spot with your naked eye any details that are not visible (even under magnification) in the image scaled to match your eyesight. I suspect you might be able to see some extra detail (especially near the terminator, if the moon is not perfectly full), but not very much.

---

For a more objective test, we could try to look for early maps or sketches of the moon made by astronomers before the invention of the telescope, which should presumably represent the limit of what the naked human eye could resolve. (You needed to have good eyesight to be an astronomer in those days.)

Alas, it turns out that, while the invention of the telescope in the early 1600s brought on a veritable flood of lunar drawings, with every astronomer starting from Galileo himself rushing to look at the moon through a telescope and sketch what they saw, very few astronomical (as opposed to purely artistic) drawings of the moon are known from before that period. Apparently, while those early astronomers were busy compiling remarkably accurate star charts and tracking planetary motions with the naked eye, nobody really though it important to draw an accurate picture of the moon — after all, if you wanted to know what the moon looked like, all you had to do was look at it yourself.

Perhaps this behavior may be partly explained by the prevailing philosophical opinions at the time, which, influenced by Aristotle, held the heavens to be the realm of order and perfection, as opposed to earthly corruption and imperfection. The clearly visible "spots" on the face of the moon, therefore, were mainly regarded as something of a philosophical embarrassment — not something to be studied or catalogued, but merely something to be explained away.

In fact, the first and last known "map of the moon" drawn purely based on naked-eye observations was drawn by William Gilbert (1540–1603) and included in his posthumously published work De Mundo Nostro Sublunari. It is quite remarkable how little detail his map actually includes, even compared to a tiny 40 by 40 pixel image as shown above:

^{Left: William Gilbert's map of the moon, from The Galileo Project; Right: a photograph of the full moon, scaled down to 40 pixels across and back up to 320 px.}

Indeed, even the sketches of the moon published by Galileo Galilei in his famous Sidereus Nuncius in 1610, notable for being based on his telescopic observations, are not much better; they show little detail except near the terminator, and the few details there are appear to be inaccurate bordering on fanciful. They are, perhaps, better regarded as "artist's impressions" than as accurate astronomical depictions:

^{Galileo's sketches of the moon, based on early telescopic observations, from Sidereus Nuncius (1610), via Wikimedia Commons. Few, if any, of the depicted details can be confidently matched to actual lunar features.}

Much more accurate drawings of the moon, also based on early telescopic observations, were produced around the same time by Thomas Harriott (1560–1621), but his work remained unpublished until long after his death. Harriott's map actually starts to approach, and in some respects exceeds, the detail level of even the 60 pixel photograph above, showing e.g. the shapes of the maria relatively accurately. It is, however, to be noted that it is presumably based on extensive observations using a telescope, over several lunar cycles (allowing e.g. craters the be more clearly seen when they're close to the terminator):

^{Left: Thomas Harriott's lunar map, c. 1609, based on early telescopic observations, via Wikimedia Commons; Right: same photograph of the full moon as above, scaled down to 60 pixels across and back up to 320 px.}

Based on this historical digression, we may thus conclude that the 40 pixel image of the moon, as shown in the question above, indeed does fairly accurately represent the level of detail visible to an unaided observer, while the 60 pixel image even matches the detail level visible to an observer using a primitive telescope from the early 1600s.

Sources and further reading:

Why does Astronomy still use the Anno Domini system for Time Synchronization

Hopefully this answer isn't redundant.

Astronomy is done over huge orders of magnitude. To make things manageable, we try to keep numbers under a thousand - it's both more practical and more intuitive. This is reason #1.

The second reason why we don't set our zero point to the beginning of the Earth is because it's a measured quantity with an error. If you set your clocks to the 'beginning' of the Earth (which by the way is not a well-defined statement since the time of the formation of the Earth is actually an inclusive range of times), you would have to report the year as:
$$ 4,540,002,013 pm 50,000 text{ years} $$
Though the zero-point is certainly arbitrary, it at least defines a point in time where we can use clocks to measure from.

Lastly, why do you think the age of the Earth is the relevant zero-point? Why not use the beginning of the Universe?

special relativity - How is the universe is experienced at light speed?

No, not a bi-dimensional space. A photon can intersect with photons coming from every direction, so it senses a three-dimensional space. But since time does not happen for the photon, it experiments all the events at the same time. Everything happens to it together.

distances - Does Tobler's First Law of Geography Apply to Star Composition?

There have of course been extensive observations of clusters of stars. To all intents and purposes, to the limits of experimental accuracy, it looks like stars that are born in the same open cluster or star-forming region are all born with the same composition. e.g. http://adsabs.harvard.edu/abs/2014A%26A...567A..55S , http://adsabs.harvard.edu/abs/2002AJ....124.2799W , http://adsabs.harvard.edu/abs/2007AJ....133.1161D

There are of course various photospheric abundance anomalies in some stars, but these are normally ascribed to mixing processes or nucleosynthesis within the stars, not their birth composition.

The situation in globular clusters is not so clear cut. Multiple populations distinguished by their chemical compositions have been found. Possibly as a result of ancient mergers. So this does not perhaps represent a violation of Tobler's law since these stars would actually have been born in different environments.

Once stars leave their birth environment then they very quickly become mixed around the Galaxy. A star with a peculiar velocity of only 1km/s will travel a parsec in a million years. Stars born in the same place are probably widely distributed around the galaxy in a billion years or so. Most of the mixing is in azimuth or vertically, rather than Galactocentric radius.

Nevertheless there is a radial dependence (Galactocentric radius) of chemical composition (e.g. http://adsabs.harvard.edu/abs/2010A%26A...511A..56P ). Thus stars with similar Galactocentric radii have similar gross chemical compositions (with some scatter). But then this does violate Tobler's law because it means there is a similarity between objects that are on opposite sides of the Galaxy but with similar distance from the Galactic centre.

cosmology - Cosmic microwave background radiation

If the big bang is true, after the emission of light from the hydrogen plasma, the universe was still expanding. Why would we expect to see uniform radiation if earth very well could have formed outside of this hydrogen plasma. Then we would expect to see bits of background radiation coming from one direction. People sometimes answer this question by saying that the big bang happened everywhere and that where the earth is right now was a haze of hydrogen plasma 13.7 billion years ago. I do not see how one can assume this as since the universe expands we could have formed outside of the plasma and therefore should not expect to detect uniform background radiation.

fundamental astronomy - How might Thales have predicted a solar eclipse?

I recently read the relevant parts of the Cambridge Concise History of Astronomy and I'd suggest it was partly good observation, partly luck.

Good observation in that Thales would have noted that the movements of the Sun and Moon were such that eclipses were possible on certain dates, and luck in that the shadow of the eclipse he suggested was possible passed over him or those to whom he had suggested the eclipse took place.

I very much doubt he had the observational data (about the size of the Earth for instance) to have been precise about the shadow path - but would have had the data to show when the Sun and Moon were in alignment.

general relativity - Does gravity propagate?

Gravity is sometimes described as a curvature in space-time. Due to relativity, doesn't this imply that gravity doesn't propagate?

There's a fairly precise sense in which gravity propagates: if you have a spacetime and you perturb it a bit, then you can think of the new spacetime as the old "background" spacetime with a small change on top of it. Then it makes sense to discuss the speed at which this change propagates.

But in the general case, the speed of propagation of gravity has no particular meaning. This is sensible: to talk about speed, you need some standard to compare it to, and hence a background spacetime. But gravity is nonlinear, so to have an objective answer to that question, the changes to that background need to be either small or tightly constrained.

If a black hole was moving toward you at the speed of light ... [would you] experience something similar to a supersonic blast, except its a gravity blast, ...

Not analogously to a supersonic (so here, superluminal?) one, no.

For an electric charge, the ultra-relativistic limit of its electromagnetic field is a plane wave that's impulsive, an infinitely-thin Dirac delta profile. This travels at the speed of light. The gravitational analogue of this (for a Schwarzschild black hole) is the Aichelburg-Sexl ultraboost, which is a spacetime that's axially symmetric and everywhere flat except for an impulsive plane wave.

... and it would allow you to remain unaffected until you arrived at the very centre of the black hole?

No.

If you were able to turn around, just before you arrive at the center, and travel away from the black hole at the speed of light you would never notice it, even though you would be travelling at the same velocity as the black hole in the same direction?

That's the same thing as saying you're stationary above the black hole. Hence, you would notice it because you'd need to be accelerated to stay stationary. Plus, if you're turning around after passing the horizon, it's far too late.

Is our universe included inside a black hole?

There's a lot to pick apart in everything you try to propose, as it includes a lot of far fetched (or at least rather non-standard) claims. I am frankly not up to attempting to address every one of them, if for no other reason than that it makes the question as a whole rather too broad for my taste (and perhaps more in the territory of Physics.SE, which has quite a lot of answered questions concerning black holes).

There is, however, the following simple and amusing observation: current estimates of the mass-energy of the observable universe tell us that it is too dense to be a black hole. That might sound a little weird if you're not familiar with black holes. In fact, the density of a (non-rotating, Schwarzchild) blackhole is inversely proportional to the square of its mass, and the radius is directly proportional to the mass. More explicitly:
$$r=frac{2 G M}{c^2},$$
$$rho(M) = frac{3 c^6}{32 pi G^3}cdot frac{1}{M^2},$$
where $r$ is the radius, $rho$ is the density, $M$ is the mass, $c$ is the speed of light, and $G$ is the gravity constant.

The order of magnitude estimate for $M$ is $10^{54}$ (and $Mgeq 10^{54}$ in particular), which makes the universe ~3 times too small at least.

A key fact here is that the universe is not static with respect to itself. See this Physics.SE Q&A in particular. I'll quote the end of Lubos Motl's answer, in particular:

Our Universe, dominated by the dark energy, is already rather close to an empty de Sitter space which is, from many viewpoints, analogous to a black hole except that the interior of the visible part of the de Sitter space is analogous to the exterior of a normal black hole, and the analogy of the interior of a black hole is everything that is behind the cosmic horizon - where we don't see. It is misleading to create the analogy with the static black holes directly because our Universe is not static in the normal cosmological coordinates.

In other words, there are lots of important and sometimes subtle issues with the whole "the universe is a black hole" concept.

solar system - Why natural satellites (moons) of all Planets are Solid?

To answer this, we have to consider the definition of an atmosphere. I'll go with Miriam-Webster's online definition: "A mass of gases that surround a planet or star". By that definition, we can say that gas giants are really just planets that are massive enough that they have really massive atmospheres (incidentally, Wikipedia's article on gas giants seems to agree), because deep down, they have a rocky core - although not a core similar to the "rocky" inner planets in our solar system.. So now we can reduce the question to "Why do most natural satellites not have extremely large atmospheres?"

This comes down to mass. The more massive an object is, the more gravitational pull it has on objects around it. This means that a very massive object traveling through a cloud of gas would attract the gas more than a less massive object would. In the early solar system, this was the case, and it is why Jupiter and the rest of the gas giants have such large atmospheres compared with the smaller bodies in the solar system - namely, the natural satellites. Moons can't hold a lot of atmosphere (at least, not enough the consider them as gas giants) because they are very low-mass; therefore, they cannot become gas giants.

I hope this helps.

Definition: http://www.merriam-webster.com/dictionary/atmosphere

atmosphere - Would a high albedo reflective substance cool down Venus?

Eventually, yes.

Interesting information about Venus: Venus is hotter than Mercury, despite being nearly twice as far from the Sun. Earth, despite being further from the Sun, receives more
energy from the Sun than Venus, due to Venus's very high albedo.

As you might guess by this information, the major factor that keeps Venus hot isn't how much energy it receives from the Sun, but rather its inability to rid itself of energy. While adding a cloud of some high albedo substance to the atmosphere may effectively prevent the Sun from heating Venus, it would also likely prevent infrared radiation from leaving Venus, thus keeping it warm.

As you know, Venus already has a very high albedo. It's thick atmosphere prevents energy from leaving the planet, which is what caused the temperature to rise far above the Earth-like temperatures we believe it once enjoyed. This is caused by IR radiation being emitted from the surface and being reflected back down towards the planet by the atmosphere more detail, which plays an essential part in the greenhouse effect.

In my opinion, a more effectual method in terms of making it habitable would be to find a way to drastically lower the albedo of Venus to allow all the excess energy to escape.

gravity - What would happen if a body were to fall into a neutron star?

Let's assume that what is falling onto the neutron star is "normal" material - i.e. a planet, an asteroid or something like that. As the material heads towards the neutron star it gains an enormous amount of kinetic energy. If we assume it starts from infinity, then the energy gained (and turned into kinetic energy) is approximately (ignoring GR)
$$ frac{1}{2}m v^2 = frac{GMm}{R}, $$
where $m$ is the mass of the object (which cancels) and $M$ and $R$ are the mass and radius of the neutron star (let's assume typical values of $1.4 M_{odot}$ and 10 km respectively).

This results in a velocity as it approaches the neutron star surface of $1.9 times 10^{8}$ m/s - i.e. big enough that you would have to do the calculation using relativistic mechanics actually.

However, I doubt that the object would get to the surface intact, due to tidal forces. The Roche limit for the breakup of a rigid object occurs when the
object is a distance
$$d = 1.26 R left(frac{rho_{NS}}{rho_O}right)^{1/3},$$
where $rho_{NS}$ and $rho_O$ are the average densities of our neutron star and object respectively. For rocky material, $rho_O simeq 5000$ kg/m$^{3}$. For our fiducial neutron star $rho_{NS} simeq 7times10^{17}$ kg/m$^{3}$. Thus when the object gets closer than $d= 500,000$ km it will disintegrate into its constituent atoms.

It will thus arrive in the vicinity of the neutron star as an extremely hot, ionised gas. But if the material has even the slightest angular momentum it could not fall directly onto the neutron star surface without first shedding that angular momentum. It will therefore form (or join) an accretion disk. As angular momentum is transported outwards, material can move inwards until it is hooked onto the neutron star magnetic field and makes its final journey onto the neutron surface, probably passing through an accretion shock as it gets close to the magnetic pole, if the object is already accreting strongly. Roughly a few percent of the rest mass energy is converted into kinetic energy and then heat which is partly deposited in the neutron star crust along with matter (nuclei and electrons) and partly radiated away.

At the high densities in the outer crust the raw material (certainly if it contains many protons) will be burned in rapid nuclear reactions. If enough material is accreted in a short time this can lead to a runaway thermonuclear burst until all the light elements have been consumed. Subsequent electron captures make the material more and more neutron rich until it settles down to the equilibrium composition of the crust, which consists of neutron-rich nuclei and ultra-relativistically degenerate electrons (no free neutrons).