cosmology - At what rate are stars accelerating?

As has already been mentioned, stars within a galaxy do not generally expand. The stars in a galaxy are gravitationally bound together.

But as you observe more and more distant galaxies, you see a general trend that distant galaxies are moving away from us at a speed that's proportional to their distance. (There are some small variations due to the random motion of individual galaxies; for example, the Andromeda galaxy is approaching us, and will collide with the Milky Way in about 4 billion years.)

This does not indicate that everything is expanding from some central point. An observer in a galaxy a billion light-years away would see the same thing, all other galaxies receding at a speed proportional to the distance from the observer. This can be interpreted as space itself expanding. Going into more detail would require General Relativity, which I'm not competent to explain.

Your question is about the rate of expansion. The answer to that is what's called the Hubble Constant, which describes the ratio between a galaxy's speed of recession and its distance from us. The current best estimate of this ratio is 67 kilometers per second per megaparsec. A parsec is about 3.26 light-years; a galaxy one million parsecs away will be moving away from us at about 67 kilometers per second.

Source: https://en.wikipedia.org/wiki/Hubble%27s_law#Determining_the_Hubble_constant

software - I can't find Rigel on Tycho 2 catalogue

I'm trying to develop a planetarium using Tycho 2 catalogue.

To read it I use the WCSTools. But I have a problem.

On Wikipedia I have found that Rigel star has RA: 05h 14min 32,3s and Dec: -08º 12’ 06’’. I have translate them to decimal degrees (78.6375, -8.2017). I've used that to find it on Tycho 2 catalogue (file catalog.dat) but I can't find it.

To search into the catalogue I have used the function TY2READ from ty2read.c file.

And this is how I search the star:

void ReadTy2Catalog()
{
    double raCenter = 84.5;
    double decCenter = -1.2;
    double raDistance = 10.;
    double decDistance = 10.;

    int nMaxStars = 20000;

    char* filePath = "D:\Fuentes\Repos\Planetarium\StarsCataloguesLib\Resources\";
    Ty2Read read;

    read.Read(
        filePath,
        TYCHO2,         /* Catalog code from wcscat.h */
        raCenter,       /* Search center J2000 right ascension in degrees */
        decCenter,      /* Search center J2000 declination in degrees */
        raDistance,     /* Search half width in right ascension in degrees */
        decDistance,    /* Search half-width in declination in degrees */
        0,              /* Limiting separation in degrees (ignore if 0) */
        0,              /* Inner edge of annulus in degrees (ignore if 0) */
        1,              /* 1 to sort stars by distance from center */
        WCS_J2000,      /* Search coordinate system */
        2000.0,         /* Search coordinate equinox */
        0.0,            /* Proper motion epoch (0.0 for no proper motion) */
        -20.0,          /* Limiting magnitudes (none if equal) */
        30.0,           /* Limiting magnitudes (none if equal) */
        1,              /* Magnitude by which to sort (1 or 2) */
        nMaxStars,      /* Maximum number of stars to be returned */
        1);             /* Verbose*/
}

I have checked all the stars returned and none has Rigel's RA and DEC.

What am I doing wrong?

How does an accreting black hole acquire magnetic fields?

There is actually a similar question on this site: Can magnetism escape a black hole?, however the answers do not focus on accretion, which is my main concern, so I start a new one.

In Kip Thorne's book Black Holes and Time Warps: Einstein's Outrageous Legacy, there is a paragraph in Chapter 9, describing how the central black hole of a quasar (or radio galaxy) acquires a magnetic field through accretion:

Where do these magnetic field lines come from? From the disk itself.
All gas in the Universe is magnetized, at least a little bit, and the [accretion] disk's gas is no exception. As, bit by bit, the disk's gas accretes into the hole,
it carries its magnetic field lines with it. Upon nearing the hole, each
bit of gas slides down its magnetic field lines and through the horizon,
leaving the field lines behind, sticking out of the horizon and threading
it [...]. These threading field lines, firmly
confined by the surrounding disk, should then extract the hole's
rotational energy by the Blandford—Znajek process.

Unfortunately this description does not seem clear to me (although Thorne generally is excellent in explaining things throughout the book). To be specific, I cannot get a picture of the gas "sliding down" its magnetic field lines through the event horizon, while making the magnetic field "stick out" of the horizon at the same time. And here Thorne did not seem to point to any original research papers for further study.

So, my questions are:

(1) Do today's astronomers still believe that disk accretion is the main process by which supermassive black holes acquire a magnetic field?

(2) If the answer to (1) is "yes", then how can I build the picture (if there is such a picture) that Thorne is trying to convey in his paragraph?

(3) Is there any research paper that addresses this problem to some detail?

Any help is appreciated!

Is starquake unique to neutron star?

I'm not sure what the current status of neutron starquake theory is, but last time I looked there were a couple of ideas.

The outer parts of a neutron star consist of a solid crust of neutron-rich nuclei (plus electrons, and a little deeper, free neutrons). Neutron stars are born rotating extremely fast, but they spin down due to the loss of rotational kinetic energy through magnetic dipole radiation. As a result, they are born oblate, but as the spin rate decreases this is not the lowest energy configuration. It used to be thought that starquakes (pulsar glitches) were caused by cracking of the crust and rearrangement towards a more spherical configuration.

The second idea is that it could be due to changes in the very intense magnetic field of the neutron star. The magnetic field is tied very tightly to the crustal material, so if the magnetic field shifts, possibly associated with the neutron star spin down, then it will put the crust under stress, which can be relieved by a starquake.

White dwarf stars also contain solid, crystalline material, however they do not spin so fast and do not gave similar ultra-strong magnetic fields. I have not heard that they experience starquakes.

"Normal stars" do not have a crust or any other solid layer, so there can be no similar starquake phenomenon.

orbit - Why doesn't Jupiter increase the chances of an asteroid to strike the Earth?

Polyphant is correct, it can operate either way. It's hypothesized that Jupiter in 2:1 resonance with Saturn was the cause of the late heavy bombardment. Source

The 2 largest objects in the solar system operating in resonance tended to stir everything up. Many small objects including Neptune and Uranus were thrown around, some into the sun, some in towards the inner solar-system where some crashed into other planets and some out of the solar system or into the Kuiper belt, but all that ended 3.8 billion years ago.

The dummies answer is that most of the stuff in the solar system that had orbits that were likely to crash into a planet have already done so, and Jupiter sped that process up.

The slightly longer answer follows:

For the time being, the asteroid belt is mostly stable, as are Jupiter's two Trojan regions, L4 and L5 and Jupiter's hildas are also stable. So that's basically why we're in a low bombardment period now. The inner solar-system objects are mostly in stable orbits where they aren't in position to crash into planets. To collide, orbits need to cross and mostly the inner solar system objects don't cross orbits with planets.

See here:

Computer simulations suggest that the original asteroid belt may have
contained mass equivalent to the Earth. Primarily because of
gravitational perturbations, most of the material was ejected from the
belt a million years after its formation, leaving behind less than
0.1% of the original mass. Since then, the size distribution of the asteroid belt is believed to have remained relatively stable.

Similarly, Jupiter Trojan objects, L4 and L5 and Jupiter Hildas are in mostly stable orbits due to the high mass of Jupiter, so it's a two fold answer. First is that late heavy bombardment removed most of the inner solar system objects that were bombardment candidates, and 2nd, the huge mass of Jupiter compared to the inner planets and the significant relative distance between Jupiter and Mars and the small mass of Mars), together creates a healthy amount of relatively stable orbital regions where asteroids can stay in stable orbit and not be in position to crash into the 4 inner planets or be subject to n-body instability of multiple body orbital systems. (I can add various articles on the stability of Jupiter's L4 and L5 and Hildas, but they're not hard to google).

For Kuiper belt objects, I don't believe Jupiter has much of an effect pro or con, for earth impacts, though it blocks a few of those, but it should only be a small percentage, but I suspect Kuiper belt object collisions with inner planets are less frequent. For inner solar system objects (asteroid belt, L4, L5 & Hildas), that's where Jupiter significantly reduces impacts with inner planets, for most of the last 3.8 billion years.

A curious sidebar is that Jupiter may, at some point in the future, stir things up in the solar-system again and create another much smaller heavy bombardment period. This would depend on the Jupiter-Mercury resonance and if Jupiter was able to pull Mercury away from the sun, as some models suggest it might.

This is low probability and if it happens it won't happen for billions of years, but if Jupiter does cause Mercury to migrate away from the sun, Mercury passing through the asteroid belt, hildas and L4 or L5 would likely cause a significant increase in bombardment.

This article doesn't mention the asteroid factor, but Mercury passing through any of the asteroid rich regions of the inner solar-system would stir things up quite a bit and significantly increase the chance of bombardment.

exoplanet - How does gradual crossing over of the Roche limit transform a planet or moon?

Bodies typically progress outward rather than inward. (See Why is the Moon receding from the Earth due to tides? Is this typical for other moons? .) The only orbiting bodies that might approach are ones that orbit faster than the main object spins, IOW, closer than synchronous orbit. Even then they could recede if locked into resonance w/ other bodies, eg, moons, further out. (See Does anyone know why three of Jupiter's largest moons orbit in 1:2:4 resonance? .) Deimos and Phobos are approaching Mars though.

Supposing you do have an approaching body, eccentricity and inclination will be damped into a slowly degenerating circular orbit. As the body approaches, the acceleration of the body, through the main body's two tides' net pull, increases roughly as the 6th power of distance. (See Tidal Evolution of a Planet and its Moon.) And tidal heating will soften the body, allowing even more deformation.

It is a runaway process at some point, and that point may be quite far into the Roche limit. How far would depend on body size, material tensile strength, structure of the body, thermal conductivity, changes with temperature, etc. It would take detailed modelling to describe the process. The catastrophe could start in the most vulnerable locality of the body and spread from there (Ka-Boom!), or involve the whole body concurrently (Squish!). It may not go "boom", but at the end you might be able to observe it in real time.

Another possibility is that the body will start disintegrating at the near end, where the forces are strongest. By conservation of momentum (or would it be energy?), every time a piece leaves, the rest of the body is pushed slightly the other way, sending the remainder slightly higher, delaying the process. This could take quite a while, but there is always a chance that things will destabilize at some point and go into catastrophe.

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.

earth - What is the distance between 2 cities?

This is hardly an astronomy question, but I like drawing, so here you are:

Longitudes are measured from the Greenwich meridian, so the angle between Kampala and Quito is
$$theta_mathrm{Q} + theta_mathrm{K} = 82.5^circ + 37.5^circ = 110^circ.$$
(remember that $0^circ30' = 0.5^circ$).
The shortest surface path is along Equator. Since $110^circ$ is $frac{110^circ}{360^circ} simeq 0.3$ times the circumference of Earth at Equator, the length of path A (the dashed line) is
$$mathrm{A}:,,d = 0.3 times 40,075,mathrm{km} = 12,245,mathrm{km}$$

For path B (the solid line), you need a bit more trigonometry. The radius of Earth is $R = 40,075,mathrm{km},/,2pi = 6,378,mathrm{km}$. The rest will be left as an exercise.

planet - Resources on planetary stability

I am a fifth (and last) year undergraduate student in Physics with good level of Mathematics formation and basic Astrophysics formation. I recently read some theories about Solar System formation and evolution and became interested in planetary stability, but I couldn't manage to get a good introduction to the topic.

I was wondering if there is a standard book or resource that approach this topic with precision that you could recommend. Any advice will be welcome.

the moon - Total solar eclipse, supermoon, and spring equinox all happening at the same time: anything special about this?

Today (March 20, 2015) is seeing a rare combination of the spring equinox, a total solar eclipse, and a supermoon. I am wondering if there is anything special astronomically about all three of these happening at the same time, like is the equinox a particularly more or less likely time for solar eclipses to happen (my guess is that it has no impact eclipses).

The supermoon/total solar eclipse combination doesn't seem surprising to me, since if the opposite were to happen (moon far away and solar eclipse) we would end up with an annular eclipse instead of a total eclipse.

exoplanet - Do any known exoplanetary/solar bodies have "annular" eclipses similar to Earth's?

This will depend the position of the observer and (obviously) the relative sizes of the star and the eclipsing body.

For an intelligent observer standing on the surface of a planet the most obvious and likely candidate for an eclipsing body would be a moon of that planet. The nearer the planet is to the sun the larger that moon has to be, and the further the planet is away from the star the smaller the moon can be.

Finding planets around stars is hard enough, finding moons that will be orbiting quite closely around those planets across interstellar distances is even harder (I'm not going to say impossible, but it's pretty close) with current technology, so at the moment the answer is "None, that we know of".

Also don't forget that, according to current theories, the moon was formed when a large Mars sized body collided with the nascent Earth, the chances of another Earth/Moon type system is probably remote. This means that most natural satellites are likely to be Phobos sized bodies. Therefore to get an eclipse the planet would have to be further out from the star (so the star looks smaller) and that would tend to put it on the edge of the "Goldilocks" zone, making the likelihood of there being an intelligent observer somewhat rare.

solar system - How did Meeus calculate equinox and solstice dates?

In Astronomical Algorithms (2nd ed, ch. 27, 2009 corrected printing) Jean Meeus gives expressions to calculate the date and time (dynamical time, equivalent to Terrestrial Time) of equinoxes and solstices from the year -1000 to the year +3000. The expressions are accurate to 51 seconds or better for the years 1951-2050. First what Meeus calls the "instant of the 'mean" equinox or solstice" is calculated using a fourth degree polynomial; there are 8 expressions. There are different expressions for each solstice or equinox, and different expressions for the year ranges -1000 to 1000 vs. 1000 to 3000. Then two corrections are applied; the corrections are calculated the same way no mater which time period or equinox or solstice is being corrected. The first step is to calculate:

$$T = frac{(text{mean JD of event} - 2451545.0)}{36525}$$

$$W = 35999.373°T - 2.47°$$

$$Delta lambda = 1 + 0.334 cos W + 0.007 cos 2 W$$

Next, an additional correction is computed involving 24 periodic terms with various periods.

Can anyone explain, in general terms, how Meeus derived these expressions? I'm especially interested in understanding what the "mean" value represents?

optics - Why does a mirror bent 'like a potato chip' allow space telescopes to be smaller and have a wider field of view?

Freeform optics are a response to the specific challenge of cramming a telescope in a very limited space. A traditional instrument would have all optics symmetrical and aligned on the same axis. It would waste a lot of space within the cubesat. Also, traditional designs tend to be much longer than they are wider; they don't fit well in a cube; it is very hard to make classic instruments that are as short as they are wide.

But with freeform optics you could bounce light in a few directions within the cube. You'd still achieve a decent focal length, and you would use all the volume available to you.

Since light is reflected from mirrors at angles different from normal, you cannot use the traditional symmetric shapes such as parabolic, spherical, etc. You need to basically take a paraboloid and squish it in one direction so that it works about the same like a parabolic mirror (I'm simplifying), but at an angle of reflection of, say, 45 degrees.

In such an instrument you could have multiple "potato chip" mirrors, as in the diagram above. You have to design the instrument as a whole; computer simulations will adjust the shape of each mirror until the performance of the whole instrument is close to a classic straight design.

As far as I can tell, the manufacturing precision is such that freeform optics are only usable at long wavelengths such as infrared, where less precise optics can be used. But technology improves all the time. It also depends on how much aberration you can tolerate in your image.

For usage from ground level this is less useful, unless you absolutely need a telescope in a very small form factor for some reason. Classic optics are still preferred when space and shape are not restricted.

observation - How big will Apophis appear?

Current estimates put Apophis's diameter around 325 m and its 2029-04-13 approach about 38000 km from the center of the Earth. I figure an angular size <= 2 arcsec, almost starlike even if you manage to track it in a telescope.
Ephemerides show it at apparent magnitude 3.5 or so just before closest approach - visible but not outstanding to the unaided eye at night - and spending about 36 hours within 1 lunar distance of the Earth.

extra terrestrial - Can a tidally locked planet have their own habitable zone?

As you suggest, it might be possible for a habitable corridor to exist along the stationary terminator. But there are ideas around for more than that. The planet might be exposed to tidal forces the volcanism of which warms the far side. It might have a thick stormy ocean or atmosphere which evens out the surface temperature (All but the smallest planets have atmospheres). It might have habitable moons which when tidally locked to the planet rotate regularly versus the star. And if it, like Mercury, has an eccentric enough orbit it might rotate relative to its star although it is tidally locked. Planetary diversity is huge.

orbital elements - Name for 1-e and 1+e terms?

As the commenter states, $e$ is indeed called the orbital eccentricity. If you add a radial scale length (e.g., semi-major axis) to both of those values the $1-e$ describes the periapsis (closest approach of orbit) and the $1+e$ apoapsis (furthest) of an elliptical orbit. They don't have a specific special name, as they are dimensionless measures, but can be quite useful in determining the orbit of planets and other Keplerian systems.

Periapsis:
$$
r_{p}=a(1-e)
$$
Apoapsis:
$$
r_{a}=a(1+e)
$$

Perhaps the could be named the maximum radial eccentricity and minimum radial eccentricity, if you needed to describe these parameters in a report or class homework etc.

Birthday of the Universe - Astronomy

With every improvement of measurement we are able to determine the age of the Universe more exactly. I just wondered how much and what means it would need to narrow the range of age so that it would be possible to determine the exact date of the Big Bang.

I know that this would take a lot of assumptions for the sake of simplicity - I am just curious; this being said: let us assume that all current theories hold and no new side effects or new theories would evolve.

I read this post and some physics articles about the matter, but my question focuses on the accuracy gap between our current best telescopes and the accuracy that would be needed to narrow down the age to "24 earth hours".

The black hole binary that was detected by advanced LIGO - how do such hypergiant binaries form?

With today's announcement of the historic detection of gravitational waves from the merger of 36 solar mass and 29 solar mass black holes 1.3 billion light years away, one can not help but wonder how such a black hole binary system was formed.

Has there ever been any observation of a hypergiant (class 0 or Ia star) binary system in the optical or other EM radiation? I would expect that these observations would be rare give the short lifespan of these stars.

If a black hole binary formed from a binary of population 3 stars with masses over 600 solar mass, how long would one expect that they would remain in orbit around one another before they merge?

observation - Planet-timer "device" from 1970s or 1980s possibly by Edmund Scientific

I ended up finding this on page 14 of the Edmund Scientific Holiday Sale catalog, with sale ending on December 31, 1983:

except that it's "Planetimer" (and not "Planet-timer"), catalog number H9454.

A 1200dpi image somewhat shows how it's supposed to work:

My original question was going to be: could this device have worked?

I would also appreciate any other information on this product (including a better scan, ideally of the product itself, if anyone still has one).

For reference, here is the page on which the ad appears and the cover of the catalog in which I found it:

solar system - Alignments of planets

The orbits of the planets are coplanar (in the same plane) because supposedly during the Solar System's formation, the planets formed out of a disk of dust (ha, ha) which surrounded the Sun. Because it was a disk, all in one plane, all of the planets formed in that one lousy plane as well.

Single rings and disks are common in astronomy. Jupiter's moons are coplanar too.

The common explanation is that orbits are unstable and they all eventually tend to get into the same plane and stay there. Wouldn't it be fun to have a planet orbiting the Sun at a right angle to the other planet's orbits? You'd never know when the damn thing's going to hit what.

universe - Second Big Bang

As such the answer 'I don't know' is more appropriate than anything else.
But for an answer to give---
Fate of universe depends upon many aspects - but mainly the density of the universe. There is a critical density of the universe which is not enough to produce gravitational effect to stop expansion and nor that weak to keep the universe to expand at an increasing rate. This can be more clearly understood with help of 4-d diagrammatic representation of the expansion(or contraction). When it is critical, the diagram is flat with no net curvature. When the density is less CD(Critical Density), there is a saddle shaped diagram which represents vigorously increasing rate of expansion. When density is greater than CD, there is a contraction.

Now, apart from baryonic matter, mysterious dark matter and dark energy come into effect. All these, at this moment, is making the universe accelerating, as we all know. Till now, expectations are towards forming a 'rip', or violent expansion of universe where even atoms will be torn away in distant future.

Concept of second Big Bang is still far from our views, but quoting Stephen Hawking --- "God not only plays dice but also casts it where no one can see" --- Let nature do what she wants.

orbit - Directly calculating lat/lon of a satellite directly from RA/declination

I have RA/declination values of a satellite and the observer's location in terms of lat/lon. I want to convert the values for satellite into lat/lon. I have tried to use the method which uses Greenwich mean sidereal time and local sidereal time but i am not getting the expected results. Following are the available values:

Right Ascension:14.664624,
Declination:77.531587,
Observer lat 21.732398,
Observer lon 70.290948

gravity - How was the hypothetical ninth planet kicked so far out of the Solar System?

It's hard to say much about this planet, given that most of its properties are unknown. It hasn't been directly observed; instead, its effects on Trans-Neptunian Objects (TNOs) have been simulated and match observations. That said, its mass can be estimated, which is why it is conjectured to be the core of a giant planet.

One of the papers that Batygin & Brown cite is Morbidelli et al. (2012). Morbidelli has done prior work on the evolution of the Solar System if a 5th gas giant formed early in its history, which led to the Jumping Jupiter scenario. This is all described in a modification of the Nice Model.

Jumping Jupiter models with the four gas giants lead to one getting ejected from its stable orbit via interactions with the others (see
Nesvorný (2011)). This is one of the ice giants - Uranus or Neptune. However, if we postulate the existence of a 5th planet - a third ice giant - then it can be ejected from its orbit, leaving the other four in a stable arrangement.

Batygin & Brown are implying that the object perturbing the TNOs may be the core of this 5th gas giant.

Since writing the first draft of this answer, I've found out that Batygin has made some estimates that this planet would have been ejected long before the Late Heavy Bombardment - thought to be the result of a Jumping Jupiter scenario - occurred, meaning that it could not be that ejected ice giant, unless we accept a different cause of the LHB. This makes things more interesting, as different initial setups are possible.

If a white dwarf collides with a giant star, could it create a TZO?

Thorne and Żytkow's original paper on TŻOs actually opens with a comparison of TŻOs and the type of object you mention, with a white dwarf degenerate core instead of a neutron star degenerate core. They note that the equilibrium states - essentially, stable configurations - of such combinations lie near the Hayashi track (actually acting a bit like AGB stars, in some cases), indicating high metallicity, as is the case with TŻOs.

These objects generate energy the same way TŻOs do: matter is accreted by the core, releasing gravitational potential energy, and the red giant envelope continues some fusion, although, of course, core fusion has been substantially disrupted by the arrival of the new degenerate core. The main difference in energy production are the ratios between nuclear contributions to luminosity and gravitational contributions to luminosity:
$$L_{text{nuc}}/Lapprox0.99,quad L_{text{grav}}/Lapprox0.01quadtext{for white dwarf core}$$
$$L_{text{nuc}}/Lapprox0.04,quad L_{text{grav}}/Lapprox0.96quadtext{for neutron core}$$
Why the difference? $L_{text{grav}}$ is proportional to
$$frac{GM_c}{R_cc^2}$$
where $_c$ refers to values for the core. The masses and radii of neutron stars differ drastically from those of white dwarfs. This becomes less important in the case of supergiant TŻOs (i.e. $M>10 M_{odot}$), because convection cycles "burned" nuclear fuel back outwards into the envelope, and so energy ratios become more like those found in the case of a white dwarf core.

This difference in energy production ratios also means that the objects will remain in roughly stable states for different amounts of time; red giants with white dwarf cores can survive in equilibrium for at least an order of magnitude or more as long as TŻOs.

One interesting thing to note is that TŻOs and red giants with white cores may share some of the same problems when it comes to stability. The envelopes are expected to be composed similarly and act similarly, with the potential difference in nuclear fusion rates, and so the same dynamical instabilities are possible in both cases. However, Thorne and Żytkow state that they find this possibility unlikely.

gravity - What did LIGO Actually See? (Gravitational waves discovery)

LIGO didn't "see" anything. It monitors the relative lengths of the paths taken by two laser beams in vacuum pipes about 4km long (although the laser path consists of about 75 trips up and down the arms) and at right angles to each other.

A gravitational wave, travelling at the speed of light, changes the ratio of these lengths (one gets shorter, one gets larger, then they swap) by about plus or minus 1 part in $10^{21}$ (a billion trillion) about 30-200 times per second as it passes through the instrument.

The whole event lasted about 0.3 seconds and the trace (which has been all over the news) simply records the fraction by which the length of the arms changes as a function of time.

The event was (nearly) simultaneously recorded by two almost identical setups in different parts of the USA. The detection of the same signal in both detectors rules out a local cause of the disturbance, and the small time delay between the detections allows a rough location of the gravitational wave source on the sky.

light - Why doesn't the moon twinkle?

The first handful of hits on Google actually return incomplete and even wrong answers (e.g. "Because the Moon is much brighter" which is plain wrong, and "Because the Moon is closer" which is incomplete [see below]). So here's the answer:

As you mention, when light enters our atmosphere, it goes through several parcels of gas with varying density, temperature, pressure, and humidity. These differences make the refractive index of the parcels different, and since they move around (the scientific term for air moving around is "wind"), the light rays take slightly different paths through the atmosphere.

Stars are point sources

Stars are immensely far away, effectively making them point sources. When you look at a point source through the atmosphere, the different paths taken from one moment to another makes it "jump around" — i.e. it twinkles (or scintillates).

The region in which the point source jumps around spans an angle of the order of an arcsecond. If you take a picture of a star, then during the exposure time, the star has jumped around everywhere inside this region, and thus it's no longer a point, but a "disk".

…the Moon is not

The same is true for the Moon, but since the Moon (as seen from Earth) is much larger (roughly 2000 times larger, to be specific) than this "seeing disk" as it's called, you simply don't notice it. However, if you are observing details on the Moon through a telescope, then the seeing puts a limit on how fine details you can see.

The same is even true for planets. The planets you can see with the naked eye span from several arcsec up to almost an arcmin. Although they look like point sources (because the resolution of the human eye is roughly 1 arcmin), they aren't, and you will notice that they don't twinkle (unless they're near the horizon where their light goes through a thicker layer of atmosphere).

The image below may help understanding why you see the twinkling of a star, but not of the Moon (greatly exaggerated):

---

EDIT: Due to the comments below, I added the following paragraph:

Neither absolute size, nor distance is important in itself. Only the ratio is.

As described above, what makes a light source twinkle depends on its apparent size compared to the seeing $s$, i.e. its angular diameter $delta$ defined by the ratio between its absolute diameter $d$ and its distance $D$ from Earth:
$$
delta = 2 arctan left( frac{d}{2D} right)
simeq frac{d}{D},,,mathrm{for,small,angles}
$$

If $delta lesssim s$, the object twinkles. If it's larger, it doesn't.

Hence, saying that the Moon doesn't twinkle because it's close is an incomplete answer, since for instance a powerful laser 400 km from Earth — i.e. 1000 times closer than the Moon — would still twinkle because it's small. Or vice versa, the Moon would twinkle even at the distance it is, if it were just 2000 times smaller.

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Finally, to achieve good images with a telescope you not only want to put it at a remote site (to avoid light pollution), but also — to minimize the seeing — at high altitudes (to have less air) and at particularly dry regions (to have less humidity). Alternatively you can just put it in space.

Topography / elevation data of Mars

For a design project I'm looking for elevation data for Mars' surface - the idea is to replicate a surface area of Mars as a physical model, using the elevation data to create a very rough 3d model of that particular area's topography.

Where can I find such data?