Is Earth's orbital eccentricity enough to cause even minor seasons, without axial tilt? I was reading the answers to this question about an exoplanet having seasons without axial tilt, and several responders mention that orbital eccentricity could cause a similar effect, but that the orbit would need to be "very eccentric," as opposed to Earth's, which is "very close to circular."

If the Earth had no axial tilt at all, would its eccentricity be high enough to have any discernible effect for the inhabitants?  Even if it didn't cause major shifts in temperature, would it be enough for pre-scientific people to track the passing of years?

Very cool question. I want to get into a little bit of detail here because otherwise there would be a one-paragraph answer, and I don't think that would cut it. So here goes.

The planets in the solar systems have orbits with pretty low eccentricities (see this for more eccentricity values). At the upper end is Mercury, with an eccentricity of 0.2056. At the lower end is Venus, at 0.00677. Earth is in between but moderately low, at 0.0167. The distance between perihelion and aphelion is 5 million kilometers - in an orbit with an average radius of about 150 million kilometers. Note, though, that eccentricities are always changing.

We would certainly have "seasons" if there was no axial tilt, but they most likely would not be dramatic. As Wikipedia says

  Because of the increased distance at aphelion, only 93.55% of the solar radiation from the Sun falls on a given area of land as does at perihelion.

But on this page, it says

  Orbital eccentricity can influence temperatures, but on Earth, this effect is small and is more than counteracted by other factors; research shows that the Earth as a whole is actually slightly warmer when farther from the sun. This is because the northern hemisphere has more land than the southern, and land warms more readily than sea.

So more land means that the planet can absorb heat better, which counteracts the change in distance.

But I think that's pretty boring. Don't you? So let's calculate how eccentric Earth's orbit would have to be for it to have seasons without axial tilt. From the chart here we can see that the highest average hemispherical temperature is 22 degrees Celsius, while the lowest is 8 degrees Celsius.

What about other planets?

There's a steady downward trend as we get further away from the Sun (Venus is an exception because of its runaway greenhouse effect). For Earth, the average surface temperature is 287 K (15 degrees C). So our maximum would be 295 K and our minimum would be about 281 K (Kelvin = Celsius + 273). Compare that to the other planets.

I made a graph, which unfortunately I cannot paste here, that shows that to have a surface temperature of 295 K, the planet would have to be - well, not much closer than we are. Relatively, that is. Roughly 0.975 AU from the star. To have a surface temperature of 281 K, it would have to be at 1.05 AU from the star. This neglects, by the way, the different levels of land/sea absorption.

So, actually, if the Earth's orbit had an eccentricity of about 0.35, it could have some moderate seasons.

I hope this helps.

Note: I used this eccentricity calculator for the sake of accuracy and time. I would still be obliged if anyone could check my overall calculations for this answer.


What's an order-of-magnitude main sequence star look like? I'm looking for a very rough, order-of-magnitude approach to the main sequence.

What I mean is, I have a spherically-symmetric hydrogen distribution. I'm looking to get a rough approximation for density $\rho(r)$, temperature $T(r)$, and pressure $P(r)$ given the total mass $M$.

To do this, I need an equation of state. Then I need an approximation for the rate of fusion, which I can balance against the heat lost due to radiation (for which I can use Stefan-Boltzmann).

So, how can I throw this into a back-of-the-envelope calculation that tells me that, e.g. solar mass stars should live ~10^10 years, without crunching on some differential equations?

To get an order of magnitude estimate you can just use the total mass $M$ and luminosity $L$ of the star and an assumption of your fusion process. Main sequence stars fuse Hydrogen in to Helium through the proton-proton chain, which converts 0.7% of mass into energy. So the estimated lifetime of the star would just be: $0.007\frac{Mc^2}{L}$ ($c$ is the speed of light). For example, the sun would have a lifetime ~$10^{11}$ years, but that's assuming that all Hydrogen is being converted to Helium via the proton-proton chain.

Given the scaling from observations of the Sun, you can use the mass-luminosity relation to estimate lifetimes for other main sequence stars.


Could light be dark matter? Is it possible that light itself is dark matter?  I am speaking of photons (e.g. visible light, infrared, ultraviolet, etc...).  I realize light is understood to be massless, but it is obvious it at least contains energy because we can see with it (e.g. it energizes the cells in our retinas).  I wonder if light has a very tiny "net mass" (e.g. 0 mass * relativistically infinite speed).  I would think that light at least has a little mass, in proportion to its energy.  For example, take E=mc^2, then m = E/c^2 would describe how much mass it has.  If this is true, light should have a very little gravity too.  Although the effect would seem minimal, light is practically everywhere. Gravity from light would be more concentrated inside galaxies, and even more concentrated in the center of galaxies where there are many stars (like dark matter is).  It would be interesting to run the calculations, assuming light does have gravity, and see if this matches the gravitational observations of dark matter in the universe.  It would be funny and ironic if dark matter really is light.

Edit: Note that it appears light does have gravity as per the discussions here: How does light affect the universe?  If that much is true, I wonder if this is significant enough to account for dark matter?

Dark matter, is just a name for something we know nothing of. It was named to account for an extra gravity source for which there have been indirect observations, but yet we cannot explain.

The force of gravity exerted by light is negligibly small yet we have measured the gravitational pull of Dark Matter to be big enough to affect whole galaxies; it is what binds galaxies together.

Furthermore, we have included everything we can observe (all ordinary matter including photons) when we do the calculations for the amount of gravity there should be. So light is already there. 'Dark matter' is that extra gravity which we cannot account for.


Do celestial bodies actually appear larger along the horizon? Whether it be the moon (especially when full) or tonight, as Mars is closer than it has been in decades, it appears that these bodies are larger when close to the horizon than overhead.

Is this an optical illusion (i.e. the actual appearance is no larger), or is there some refraction or other effect that actually makes the appearance larger?

No, it's an illusion. Probably the ancient one. Simple experiment you can do is, set grid on telescope, measure the angle subtended when moon is at horizon and when moon is atop. You will see angle subtended by moon is same, hence the size are same. It's merely an illusion.

For more details:
https://en.m.wikipedia.org/wiki/Moon_illusion


What does the milky way look like from earth to the human eye without light pollution? Cameras are great, they allow us to compress several seconds of light exposure into a single instant. This allows us to take amazing pictures of the night sky, like this one.

Of course you can see we also have a great view of the landscape, we know that this is a trick from a camera and we're collecting a timed sample of light. This isn't something a human eye can see because we can't compress time into a single vision.

I'm curious though -- people knew about the milky way long before we could do this cool trick with camera. That means they must have seen at least something of the concentration of stars and gases from earth -- So it makes sense that without light pollution this could be seen with the naked eye to some extent -- What does the milky way look like from earth to the human eye without light pollution?

It is pretty obvious from a dark sky.

Sky and Telescope have a simulation (using stellarium) of the sky with a limiting magnitude of 6.5 (about the limit with excellent eyesight and a very dark sky). The Milky Way is very clear. Light and dark tracks are visible. It is clearly something that every person would know about and be able to see nightly. It is no surprise that it is mentioned in the myths of many ancient peoples.


Can the martian dichotomy (SIH) and the moon's formation (GIH) be related? If we assume that the Single Impact Hypothesis regarding the martian dichotomy (wikipedia) and the Giant Impact Hypothesis regarding the Moon's formation (wikipedia) are true, then is it possible that these two events were related?

Here, by related I mean that they were not independent from one another.

Early in the solar system's history, the Sun was surrounded by a protoplanetary disk, full of gas, dust and rock. Eventually, protoplanets began to form. These were small, rocky bodies - smaller than the rocky planets today, but bigger than asteroids. Think of them as dwarf-planet-sized objects. All the terrestrial planets formed from them.

Anyway, as you might know, the object that slammed into the Earth (according to the GIH) was one such protoplanet, lovingly named Theia. The resulting debris coalesced into the Moon. The SIH tells of a similar story: Once again, a protoplanet headed on a collision course, this time towards Mars. It slammed into Mars, creating a large basin. Simple but effective.

There's one thing that can relate these two disaster tales together, and that is the protoplanetary disk. Remember, the protoplanets formed from the same disk. The differences in them stemmed from the materials they formed from. So we could relate the two suicidal protoplanets to each other via that connection. Also, most collisions in the inner solar system were due to the erratic orbits of these protoplanets, so it is likely that the fault for the collisions lies solely on the protoplanets.

I think you want something a bit different from random collisions, though; the previous reason is a bit of a cop-out. Well, there is something more interesting: the rocky planets weren't alone in the early solar system. There were still their big siblings: the gas giants. The gas giants hadn't yet grown to their full sizes, but their cores and early atmospheres were still pretty massive, and commanded a strong presence in the outer solar system. It is possible that the two objects that hit the Earth and Mars formed together farther away from the inner planets, and were gravitationally perturbed by the gas giants, swinging in from an outer orbit towards the inner solar system.

You might have heard of the Nice Model. Basically, this says that the gas giants formed closed to the inner solar system than they are now. They encountered some of these early protoplanets and flung them into the inner solar system, moving outwards in the process. thus, collisions increased in the inner solar system.

It's a "nice" explanation. Trouble is, the majority of this "flinging" happened later on in the solar system's history; it has been suggested that the gas giants did this and thus caused the Late Heavy Bombardment. Still this idea shows that there could have been interaction between the protoplanets and the gas giants.

So how does this relate the two suicidal protoplanets? Well, it means that they could have formed together, further out in the solar system, and have been brought in by a gas giant. They could even have been part of a larger object, which broke apart after various collisions. But if the two objects had formed together (even somewhere in the inner solar system), or been part of a larger object, they should be made of the same materials, right? So if we were to travel to Mars we should be able to find similar materials as we did on the Moon. So far there hasn't been much luck along that avenue, but the search will continue.

To summarize: The early solar system was chaotic. It is likely that the impacts were unrelated, and that the two suicidal protoplanets formed apart in the inner solar system, but they could have formed together further our and been perturbed by one of the gas giants. They may or may not have been formed neary each other, or even been fragments of the same object. Detailed analysis in the future could give us some clues as to their formation.


Could spy satellites use laser guide stars (for adaptive optics)? Are sodium lasers useful for Earth observing space telescopes/spy satellites?

The guide star laser is used to adapt the optics at a specific time and location, for specific atmospheric conditions. It is not, as your question implies, used to calibrate the optics for long-term use.

Therefor, if order to calibrate the satellite with a laser fired from Earth, the reconnaissance target would have to provide the laser. This is useless for non-cooperative targets, which I would imagine make up the bulk of the reconnaissance targets.

I suppose that one could fire a laser from the satellite itself, but this would have the obvious disadvantage of making it even more obvious when a spy satellite was overhead.

In any case, the guide star image does not penetrate the entire atmosphere, I believe that it produces an image just a few tens of kilometers up. This is useful because it is the thicker, denser and more turbulent lower air of which is the most concern to optics. Firing the laser from above would thus see the laser energy absorbed in the thinner, stiller, more predictable upper atmosphere, thus it would have must less advantage.

One final reason not to use a guide star laser on a reconnaissance satellite would be power budget. These satellites are as small as possible, with as small a heat and reflectivity index as possible. The added power source, be it RTG, conventional batteries, or solar, would likely increase the reflectivity of the satellite.


Does Tobler's First Law of Geography Apply to Star Composition? There is a principle in Geography called Tobler's First Law of Geography which states that "Everything is related to everything else, but near things are more related than distant things."

Does this principle apply to star composition?  Do stars that are closer together have similar compositions than those that are far apart?  I'm guessing that stars that are formed in the same stellar nursery would have similar compositions.  Have studies been done to compare the compositions and proximity of stars?

As you say stars composition depend on the composition of the molecular cloud where they were created. You have a molecular cloud where many stars are being created at the same time, all with the same composition and age, but some are bigger than others. As time goes the bigger stars will die earlier, adding new heavier materials to the cloud which will lead to a new generation of stars with a bigger metalicity.

So the star's composition not only depends on where it was created but also on how old it is.

The best way this can be checked is by studying the stars within a star cluster. You may find this site interesting.


"Periapsis" or "Periastron"? I was taught from Bate Mueller and White, that the proper terms for the closest and furthest points and distances from a body in orbit around another unspecified body are "periapsis" and "apoapsis" as depicted here.

However, in comments to this question, it is strongly suggested that the usage of these terms is incorrect.

“Apses” are the points closest to and furthest from a primary body—see
en.wikipedia.org/wiki/Apsis, among many other sources. These points
are called “peri-” and “apo-” with the suffix pertaining to the body
(e.g. “-gee” for Earth, thus “perigee”). The generic word for a
celestial body is ἄστρον

“Periapsis” would mean “the point closest to the point closest to the
body.” Nonsense. The proper word is “periastron”: “periapse” is a
misconstruction.

Is the usage of "periapsis" really incorrect or perhaps just a misnomer?
Should we replace "periapsis" with "periastron"?

No. These words are English, not Greek.  "Periapsis" means the point on the orbit when the two bodies are at their closest.  It doesn't matter if this good Greek or bad Greek, it is correct English.
Apsis actually derives from "arch" and indicates the two points where the orbital curve is most "arched": ie the points of greatest curvature.  There is the "periapsis": The close point of greatest curvature and the "apoapsis" "the distant point of great curvature".
There is no such thing as a "misconstruction".  The idea that a word does not mean what it means is obviously nonsensical


The furthest horizon in the Solar system Where can I observe the furthest horizon in the Solar system ? And what the length of it ?
The furthest horizon on Earth can be observed from mount Everest ~ 336 km, On Mars - from mount Olympus ~ 386 km.

Edit: If the walls of the Rheasilvia crater can be seen from the opposite sides (it appears so) you can see the surface as far as 505 km.

The distance depends on the diameter of the planet and of your height above the surface (such as on a mountain). The greater the diameter, the farther away the horizon will be.

You can see this in the figure below. $d_3 > d_1 > d_2$. On a large planet your horizon (at distance $d_1$) will be farther away than on a smaller planet with horizon distance $d_2$. But if you stand on a mountain on the same planet then the distance will be even larger ($d_3$).

You can calculate the height from Pythagoras' rule because we have a triangle with one unknown edge. The distance from the planet's centre to the point where you see the horizon is the radius of the planet and the distance of the eye of the observer is the radius of the planet plus the height of the observer above the surface.
$$(r+h)^2 = r^2+d^2$$
where $r$ is the radius of the planet, $h$ the height above the surface, and $d$ is the horizon distance. If we rewrite this equation we get:
$$d^2 = (r+h)^2 - r^2 $$
$$d^2 = r^2+h^2+2rh-r^2$$
$$d^2 = h^2 + 2rh$$

For Venus we have $r=6052\textrm{km}$ and $h=11\textrm{km}$ (Maxwell Montes), we therefore get a horizon distance of 365km. This is still smaller than the horizon distance from Olympus Mons. Olympus Mons is the highest mountain and all other rocky planets are smaller, the horizon distance from Olympus Mons is, therefore, the greatest horizon distance.

Whether the horizon distance in the Rheasilvia crater is greater depends on whether you would be able to see the crater edge from the middle of the crater. Vesta's radius is 262km. If you stand on the crater edge, which is 13km above the crater surface, you would only have a horizon distance of 83km. This means that from the centre of the crater you would not be able to see the crater's edge.

EDIT Above I assume that the 13km is the height of the crater edge above the centre of the crater as measured from the geodesic. If the height is the height above a flat (not spherical flat) surface than the horizon is indeed 505km (see comments below).


Would planet explode without gravity? A planet (as well as a dwarf planet) must, according to the IAU definition, have sufficient mass to assume hydrostatic equilibrium (a nearly round shape). Does it mean they would break apart or explode if gravity vanishes, unlike small bodies like comets or minor planets, whose integrity doesn't depend on gravity?

Even rocky planets would explode. I think there are two ways to see this.

From the perspective of forces, the earth is in equilibrium between the compressive force of gravity and the elastic resistance to compression of the materials that make it up. By Newton's third law, the mantle is pressing upwards on the crust with a force equal to the weight of the crust. If gravity disappears, you will still have that upward force with no downward force to balance it, so you will get upward acceleration.

You may think that the tensile strength of the crust will hold the planet together. But the upward force is the same as the weight of the crust. We know that very large stone structures cannot support their weight under tension.

You may also think that iron and rock aren't very compressible, so the mantle wouldn't expand very far. But the pressures are very great. The core has a density at least 25% greater than iron does under normal pressures. Plus, the temperature is around 6000K, equal to the surface of the sun and much higher than the boiling point of iron at atmospheric pressure. So the expansion won't just be a matter of some cracks forming.

From an energetic point of view, the potential energy of all the parts of the earth spread out across the protoplanetary disk was converted to heat and elastic potential energy when the earth formed. At least one study suggests that about half that heat remains, and in any case heat from radioactive decay has been added over time. If all the energy remained, it would be enough to disperse the earth with the same velocity that parts came together on average when it formed. Given that the energy is at least on the same scale, I think it's reasonable to expect an explosive breakup.


What is the meaning tiny bundle of energy smaller than an atom At the beginning of a video on youtube titled "history of the world in 2 hours", it is said that "every thing begins with this tiny bundle of energy smaller than an atom". I want to know what it means.  atom is matter.  energy is different from matter and is measured in joules where as size is measured in volume units. How can one say energy smaller than an atom?

What the video is clumsily alluding to is that the universe was very much smaller than it is today. However, if the universe is infinite, then it was still infinite at all times in the past. All one can say is that the density was much higher.

Sometimes commentators are more precise. One can define a size scale for the currently observable universe and ask how that volume of space evolved with time. This of course assumes an accurate knowledge of cosmology and the relevant cosmological parameters.

A ball park number (see here) is that the universe has got bigger by a factor of $10^{30}$ since the end of the inflationary epoch (at $t \sim 10^{-32}$ s; which is not fully understood yet). Thus the current observable universe, of size $10^{27}$ m, was contained within a diameter of 1 mm at the end of the inflationary epoch. Prior to the inflationary epoch it must have been compacted into a much smaller volume than this - and I think this is the origin of the statement in your question.

The reason that your source talks about energy is because that is in what form the density of the universe was at that epoch. It was only later that this energy started to "freeze out" into various forms of matter. It is now commonly supposed that the Higgs mechanism or some form of it, is what gives elementary particles the property of a rest mass that might serve as a definition of "matter". The Higgs mechanism kicks in at the epoch of electroweak symmetry breaking (at temperatures of about $10^{15}$ K), giving paticles mass. Prior to this the density of the universe was in the form of massless entities that you might refer to as "energy". This symmetry breaking occurs after the end of the inflationary epoch at $t \sim 10^{-12}$s, and therefore when the currently observable universe was larger than 1 mm. So prior to this, and certainly when the currently observable universe was "smaller than an atom", the contents of the universe could be described in term of energy (without rest mass).


what degree in the sky does the sun change color? I would like to know at what angle in the sky the sun changes from a white yellow to orange and red. I know that after sunset it's considered twilight until 18° beneath the horizon. So how many degrees above the horizon generally before the sun changes color?

Here's a partial answer:
As mentioned in the comments, the transmission of the atmosphere depends quite a lot on local factors. But given a transmission $T_0(\lambda)$ at zenith, the transmission at an angle $\theta$ from zenith can be written
$$
T(\lambda,\theta) = T_0(\lambda)\times X(\theta),
$$
where $X$ is the air mass.
The air mass can be approximated as $X=\sec\theta$ up to $\theta\simeq70^\circ$, but as you approach the horizon, the calculation becomes increasingly model-dependent. A relatively simple expression is given by Pickering (2002):
$$
X(\theta) = \csc\left(90^\circ-\theta + \frac{244}{165+(90^\circ\!\!-\!\theta)^{1.1}} \right),
$$
where $\theta$ is measured in degrees, and $\csc x\equiv 1/\!\sin x$. This model doesn't take into account refraction (which requires ray-tracing), so may be off by half a degree or so when the Sun is at the horizon.
If $S_0(\lambda)$ is the un-transmitted Solar spectrum, the observed spectrum is then
$$
S_\mathrm{obs}(\lambda,\theta) = S_0(\lambda)\times T_0(\lambda)\times X(\theta).
$$
Calculating the color that the human eye perceives, given a spectrum, is not trivial, but I recently outlined an approch in this answer.


What is the most extreme weather found on another planet? On Venus, there is really inhospitable weather, as well as within the gas giants in our solar system. Are there examples of even more extreme weather on planets found in other solar systems than ours?

I'd say that HD 189733b is a good candidate for the most extreme known weather on another planet (outside our Solar System).

According to some recent news accounts, the atmospheric temperature is believed to be over 1000° C, with 7000 kph winds. (For comparison to the data in Rory Alsop's answer, that's about 1900 meters per second.)

And it rains molten glass. Sideways.

UPDATE : As Guillochon points out in a comment, HD 80606 b likely has even higher winds, though they're not continuous. It's a Jovian with an extremely eccentric orbit. Quoting the Wikipedia article:

  Computer models predict the planet heats up 555 °C (1,000 °F) in just
  a matter of hours triggering "shock wave storms" with winds that move
  faster than the speed of sound, at 3 miles per second.

which, in civilized units, is about 4800 meters/second. Probably no molten glass rain, though, so it's not clear that it's more "extreme".


In km/h, what actually is the "speed" of Andromeda away from us: cosmologically? Andromeda is about 2.5 million ly away.

Actually, in this universe, at what "speed" (in km/h) are two objects separating cosmologically - I mean strictly due to the "expansion of the universe" - if they are 2.5 million ly apart?

I do understand that local "ordinary" or "peculiar" motion completely swamps this effect.  If I'm not mistaken, the "local" "ordinary" motion of Andromeda per our galaxy happens to be about 400,000 km/h towards us.

Is the "speed" due to the "expansion of the universe" drastically smaller than this?

I assumed that the expansion of the universe (or "of the spacetime metric") is even everywhere: it's well known that it only affects "the largest structures" but I still assumed that the expansion is the same in my room, my galaxy, my cosmological region.  Perhaps this assumption is totally wrong?

The rate of expansion, measured in the customary units of (km/s)/Megaparsec
is not known with great accuracy. Recent measurements include 67.6 (SDSS-III), 73(HST) 67.8 (Plank) 69.3 (WMAP) [wikipedia]

The Andromeda galaxy is 0.78 Mpc from us, so taking the Hubble constant to be about 70, gives a recession of about 55 km/s. This is not a very great speed: compare with the orbital velocity of the sun around the galaxy at over 200 km/s, or the escape velocity of the galaxy (over 500km/s)

As you note, this is pretty much swamped by the proper relative motion of our galaxies. Its blueshift indicates that Andromeda is approaching us at over 100 km/s. For galaxies outside of the the Local group, the Hubble flow dominates.

Now the value of 55km/s assumes that space is smooth and homogeneous. This is approximately true on a universal scale, but it is not true on the scale of a galaxy cluster, where local gravitational effects dominate the curvature of spacetime. The general expansion of spacetime has very little effect on the motion of galaxies in the local group, as discussed by Iorio's paper on the motion of a gravitationally bound binary system


Would a naked eye supernova become a disc in a matter of days? Stars are points of light even in telescopes- if they go supernova, their diameter does expand, but given the distance of even nearby stars, they would still be points of light, I suppose?
I am asking because this video suggests that a very large disc would be seen in the sky after a few days if Betelgeuse were to go supernova. How long would it take for us to see a disc instead of a bright spot?

The human eye has a resolution of roughly 2 arc minutes, or about 0.5 milliradians (15 pixels across a full moon). The distance to Betelgeuse is a bit uncertain, but lets say 600 light years, which is near enough. So to show a disk simply because of the size of the source, it would need to be about 0.3 light years across.
The source can't grow faster than the speed of light, and it reasonably might grow that fast as the radiation from the supernova heats the dust and gas already shed by Betelgeuse. If so it would take about 0.15 years or about 8 weeks to grow large enough to (just) show a visible disk. The actual material ejected in the supernova explosion would move at a fraction of that velocity.
One thing that might happen is that scattering in the Earth's atmosphere might make a very intense point source look larger. Light would arrive at your eye from a number of directions close to the point source, having scattered on its way through the atmosphere. Effects in the eye might also make a very bright point source look larger.


Do all orbiting objects have barycenters? From the simple perspective of someone like myself, it appears that our sun is "fixed in place" (from the perspective of the solar system itself) and that everything else of lower mass orbits around it.  I suspect that the sun wobbles due to the other objects (that the barycenter is either near it or within its radius).

It appears from reading about binary stars of more-or-less equal mass that they cannot have one "fixed in place" and the other orbiting it.  The barycenter is basically between them.

Is that perspective correct?  Is it ever possible for a low mass star to be the "fixed in place" center with a large mass star orbiting it?  Or does the barycenter always shift toward the more massive object?

The barycenter of a system consisting of two objects of mass m1 and m2 with their centers separated by a distance d is always along the line connecting the two centers and m1/(m1+m2) of the way along the line from the center of m1 to the center of m2.

So for the Sun and the Earth, where the Sun weighs in at about 333,000 Earth masses, the barycenter will be about 1/333001 of the way from the center of the Sun to the center of the Earth, or about 280 miles from the center of the Sun in the direction of Earth.

(So it might as well be fixed in place for all you or I could tell without high-quality instruments, but it does wobble in a 270-mile orbit once each year.)

The presence of the rest of the planets makes this all a lot more complicated, of course and the Sun actually traverses a much more complicated path than it would if the Solar System was a simple two-body system. In this case, the barycenter is possibly better thought of as the center of mass.

OTOH, since Jupiter is so much heavier than everything else, to a decent first approximation the Solar System is a binary system. The barycenter for the Sun-Jupiter pair is actually outside the Sun, at about 1.09 Solar radii.

See my answer at What point does Earth actually orbit? for more.


Is the argument of perihelion random? I am currently designing star and planet systems in the RPG framework GURPS. This game system has a very elaborate set of rules to set up a star system, complete with planets and the like. However, one (for me at least) critical issue is not addressed in the book: The argument of perihelion.

Now, since I am writing a program to generate these systems for me, I would like to know what steps I can take to make a planet system as realistic as possible. Looking at data from our own planet system, the argument of perihelion looks to be pretty evenly distributed over all angles $[0, 2\pi)$.

Is there scientific evidence that this is actually the case, or are there any good suggestions on how I could proceed with my program?

(The related question on RPG.SE can be found here.)

Argument of perihelion or most planets/bodies changes very slowly over time due to higher order perturbations from other planets' motions (mostly Jupiter and Saturn for the solar system). General relativistic effects also cause the perihelion to advance over time, though this effect is smaller than the others for most purposes.

So given enough time, the arguments of the planets' perihelia would likely end up being fairly randomly distributed at any given time. Also, the planets' orbits are often dynamic on such timescales due to the effects of higher order perturbations showing up, which can cause eccentricity changes, which also affect the positions of perihelia.

So, my guess would be that it is okay to have the arguments of perihelia randomly distributed, since it is inconceivable (at least for me) that any sort of resonances would be visible at this level in order for the distributions to be non-random.


Will Earth at some point stop rotating anti-clockwise, stay still, and then rotate clockwise? Will Earth at some point stop rotating anti-clockwise, stay still, and then rotate clockwise?

No. This would require some force imposed externally. Momentum is a wonderful thing.


Dust mass-loss rate from a massive star given a set of parameters? I've been looking for examples at how mass-loss rates are determined.

I'm studying a circumstellar dust shell ejected from a Wolf-Rayet star. I have some parameters like, expansion velocity of the shell (60km/s), the dust mass of the shell (0.1 M_sun), the radii of the shell (R_in=10000 AU and R_out=60000) and its age (T=26000 yrs).

I was wondering if there's a formula relating those parameters and if they are sufficient to determine the dust mass-loss rate or its dependent on other factors.

Could anyone help?

Roughly: the mass loss rate for a spherically symmetric wind is given by
$$\dot{M} = 4\pi r^2 \rho v_w,$$
where $\rho$ is the density in the wind, $r$ is the radius at which that density is measured and $v_w$ is the wind velocity.

Here you have $v_w$ and have the mass of material within two concentric radii - so you can work out the average density at some average radius in the shell.

The age of the shell is not relevant to the mass-loss rate, but assuming the wind parameters are unchanged over that time, they do tell you ho much mass has been lost in total $\simeq \dot{M} \tau$.


How much more life could the Sun acquire via star lifting? It has been proposed before that we could use this technique to remove hydrogen from the Sun to lower it's rate of fusion and extend it's life, so it doesn't fry our planet.

I am wondering how much more life could we possibly get out of the Sun doing this? I am thinking we will want to keep the Suns luminosity constant, perhaps lower than it is now even, it used to be only 70% but perhaps that is too low without us having to have too much carbon dioxide in the atmosphere for comfort (1000 ppm is the limit before we start getting affected iirc).

Anyway, in order to to that I believe the star lifting would have to be done regularly over the future lifespan of the sun so a very long term project. It has to be regularly tuned so to speak as the core depletes it's fuel supply and collapses a little, we will have to remove a little more material to restore balance to keep the same power output.

Does anyone know how to figure out how long we could keep doing this?

There will then of course, come a time when we can't remove more fuel from the sun because the core will have exhausted all accessible hydrogen by then and will have to resort to helium fusion.

Or can we keep the suns output constant even with helium fusion? Or do we by then have to consider radically different methods, like somehow removing the spent fuel from the core and replacing it with the hydrogen we removed the previous billion(s?) of years prior?

TL;DR: the main sequence lifespan of the sun can be increased by a factor of 12.2.

Perhaps the most complete astrophysical analysis of stellar engineering for extending Earth habitability is Martin Beech's book Rejuvenating the Sun and Avoiding Other Global Catastrophes (2008).

In order to maintain the biosphere the sun's interior need to be mixed (in order to avoid the red giant phase) and material needs to be removed (in order to avoid a too great luminosity).

Material removal

Removing material is tricky because the potential energy at the Sun's surface is $U_\odot = GM_\odot/R_\odot=$ 1.9e11 J/kg. While just 2e-6 of the mass-energy embodied in the matter and 0.3% of the potential fusion energy it is still cumbersome. If a Dyson sphere was used at perfect efficiency the maximal mass extraction rate would be \begin{equation}
\dot{m}=\frac{L_\odot}{U_\odot} = \frac{L_\odot R_\odot}{GM_\odot} \approx 2.0061\cdot 10^{15} \text{kg/s},
\end{equation}
a typical mass for a minor asteroid. The timescale to disassemble the sun using just solar luminosity is \begin{equation}\tau_{disassemble}=\frac{3GM_\odot^2}{5R_\odot L_\odot} = 18.852\text{Myr}.\end{equation} Long before this time changes in pressure would reduce luminosity, making this estimate an underestimate by about an order of magnitude. I get 556.93 Myr, a bit more than Criswell's 300 Myr.

Another idealized model is that the lifting process fuses hydrogen (using the $p-p$ process) to power further lifting. In this case each kilogram of lifted mass produces $6.45\cdot 10^{14}$ J, allowing lifting of 3380 kg more fuel. This could of course speed up arbitrarily if there was technology for it.

I am leaving out how to do it. Beside Criswell's classical proposals (speeding up rotation, sucking off plasma using magnetic fields etc.) Beech suggests a stream of ramscoops or a stellar wrap could do it. This is not really key to the question.

Luminosity decrease

Luminosity can also be decreased by increasing non-thermal core pressure, perhaps through strong magnetic fields or rapid internal rotation. This would extend the main sequence lifetime as \begin{equation}\tau_{NTPS}\sim \tau_{MS} \left(1-\frac{p_{NT}}{p_T}\right )^{-7.5}.\end{equation} A 10% increase over current pressure would double the sun's main sequence lifetime and about halve the luminosity at hydrogen exhaustion. Achieving this is nontrivial given the current solar structure (the magnetic fields are generated in the convective outer envelope), but Beech notes that were the mass reduced below about half the current mass the modified sun would be full convective and magnetic fields would also produce a higher $p_{NT}$ in the core.

Another way of reducing luminosity is increasing the stellar opacity $\kappa$. In order to reduce the luminosity by a factor of 100 (and the surface temperature by a factor of 10) the opacity needs to be increased by a factor of 100. However, Beech notes that merely adding heavy elements will not help since they increase mass and hence luminosity. While one can envision "dialysis" where helium is removed and replaced by larger $Z$ elements this appears complex, and there are no local readily available sources of enough high $Z$ material in the solar system.

Mixing

Engineering enhanced mixing before the mass is removed is nontrivial. Impactors and lasers simply do not penetrate deep enough to matter. Beech suggests employing a sub-stellar mass black hole oscillating through the sun to mix it. If the hole is small, the time until absorption is long.

Result

With mass-loss and complete mixing Beech finds the main sequence lifetime increased up to a factor of 12.2, with reasonable factors between 4 and 6.

Beech's scenario has the problem that the late stage sun while having an acceptable luminosity at Earth's orbit will be far hotter, releasing significant UV radiation. The end result is in many ways similar to a blue straggler star.


Does conservation of energy make black holes impossible? I was musing today about black holes, and came across what seems to be a contradictory fact about black holes. If any matter were to actually fall into a black hole, it seems like it would need to gain infinite energy.

This is seen by considering an object close to the event horizon of a black hole. If we consider escape velocity for a particle at the event horizon, it has an escape velocity of the speed of light. The energy required to achieve this escape velocity would therefore be infinite. As we approach the event horizon, it seems like we should be able, then, to define an arbitrarily small distance across which the particle gains an arbitrary amount of energy.

As the object approaches arbitrarily close to the event horizon, it seems like its relativistic mass would therefore grow arbitrarily high, resulting in a corresponding increase in the gravity of the black hole, which seems impossible.

If we extrapolate back to the formation of the black hole, it then seems like it should be impossible for any particles to fall into the black hole, even as it forms. Instead, mass should be distributed in a probability cloud whose density asymptotically approaches zero at the event horizon of the black hole. New particles could then enter this cloud of incredibly dense (but not black hole dense) matter, where they would be captured rather than falling past the event horizon, within which there would be a vacuum.

If this were true, there would be no black holes, only hollow spheres of radiation and matter which externally look like black holes, since their gravity would be great enough that particles entering the sphere would exit at an incredibly slow rate. Interestingly, such spheres wouldn't suffer from the apparent information paradox that black holes do.

That or I'm missing an obvious explanation for why that's all wrong, which seems more likely because I'm neither a physicist nor an astronomer. What's the critical flaw in this argument?

For simplicity, let's consider a Schwarzschild black hole, so that the spacetime is spherically symmetric and static. In particular, the Schwarzschild time $t$ coordinate gives a direction in which the geometry 'stays the same' (a Killing vector field), and its inner product with the orbital four-velocity $u$ is conserved:
$$\epsilon = -g(u,\partial_t) = \left(1-\frac{2M}{r}\right)\frac{\mathrm{d}t}{\mathrm{d}\tau}\text{,}$$
where $\tau$ is the proper time of the orbiting particle. One can think of this as the specific (per-mass) energy, including mass-energy: a particle escaping to infinity that becomes asymptotically at rest with respect to stationary observers would have $\epsilon = 1$.

  If we consider escape velocity for a particle at the event horizon, it has an escape velocity of the speed of light. The energy required to achieve this escape velocity would therefore be infinite.

The energy as measured by whom? Imagine a family of stationary observers everywhere surrounding the black hole, or at least along an infalling particle's trajectory. Those observers measure the speed and energy of the particle as it falls past them. As the particle nears the horizon, they will report speeds arbitrarily close to the speed of light and arbitrarily high energies.

But to a far-away stationary observer, those observers near the horizon are experiencing increasingly divergent gravitational time dilation, and the orbital energy of the particle stays constant. Flinging a particle of mass $m$ into the black hole will increase the mass of the black hole by $m\epsilon$.

  What's the critical flaw in this argument?

All energy gravitates, so I would say the main flaw is forgetting to add the gravitational potential energy of the particle to the mass of the black hole as well. Or better put, you should be concerned with the orbital energy, not just its mass+kinetic parts ('relativistic mass').

In this situation, you have a well-defined conserved orbital energy. If you insist on measuring the Lorentz factor according to close-by stationary observers, then yes, it diverges to $+\infty$, but then you would have to admit a gravitational potential energy term that diverges to $-\infty$, because their sum must resolve to be the orbital energy.


When will the Milky Way "arrive" at the Great Attractor, and what all happen then? The Great Attractor is described as a location to towards which the Milky Way, along with all other galaxies in the Laniakea Supercluster are moving. How long will it take for the Milky Way to "arrive" there, and what will happen when it does — what, in fact does "arrive" mean in this context?

I don't want to make any assumptions here regarding the Milky Way's presence in the Laniakea Supercluster simply because of how recent the discovery is. The findings could very well be accurate, but I don't want to base this answer off of them. Fortunately, I've found a few papers that get us around that little issue, as well as the University of Hawaii's site, that led me to them . Coincidentally, one paper bears the name of one of the researchers who recently announced the Laniakea findings, R. Brent Tully, who was also involved with the other.

The two papers (here and here) suggest that, no matter whether the Virgo Supercluster is or is not part of the Laniakea Supercluster, the Local Group (and by extension the Milky Way) is not being pulled toward the Great Attractor. Instead, it is headed for other galaxy superclusters beyond the Great Attractor, including the Shapely Supercluster.

The idea that the Milky Way is not moving directly towards the Great Attractor could render the question moot, except that it simply shifts the destination: What will happen when the Local Group reaches the further superclusters?

Well, we don't [yet] know. As the papers say, there are a number of sources "pulling" on the Local Group, and so we can't say for sure just where the Local Group will wind up. This means that we also can't set a definitive timetable for the arrival. Finally, modeling galaxies with precision is not easy. Some theorists have used models in general relativity that treat many galaxies as grains of dust, so getting more specific is tough! We won't know just what will happen during after the "arrival" until we get a lot more data. Even the composition of the Great Attractor itself is rather mysterious.

I'll end with that odd term, "arrival". As the article you referenced (which, unfortunately, misses a lot of the better points of the findings, such as actually describing Laniakea) says,

  The giant structures making up the universe often have unclear boundaries.

That's true on a smaller scale, too (see Where does the Milky Way end? for an interesting discussion). We do know which galaxies are in the Local Group, but not where the Group's gravitational influence ends and other galaxy groups begin to dominate. We could define "arriving", though, at the instant that the destination supercluster beings to attract one of the galaxies in the Local group that are further out, instead of the now-probably-merged Milky Way and Andromeda galaxies. At that point, the Local Group could be distorted by the gravity of the galaxies in the supercluster, or could simply merge into the supercluster without any problems. But like I said earlier, it's too early to do anything but speculate.


Why can we see the Pillars of Creation, but not Proxima B? I was wondering how is it that we can see the Pillars of Creation (I know they're no longer there too) which are labeled as 6,500 light years away from earth and yet Proxima B is labeled at just 4.2 light years away and yet we cannot see it clearly and it was very difficult to find?

I understand that the Pillars of Creation are giant gas bubbles with different molecules that make it so visible and Proxima B is a relatively tiny planet that doesn't emit light but I cannot fathom how much greater the distance is from Proxima B and yet it is clearly much more visible. Shouldn't our current technology be able to view 'close up' images of Proxima B?

What am I missing here?

First, let's talk about size. The Pillars of Creation aren't just "giant gas bubbles"; they're clouds of gas and dust four light-years long. That's enormous, about 36,000,000,000,000 kilometers. Proxima Centauri b, on the other hand, has a diameter of 0.8-1.4 Earth diameters; one Earth diameter is approximately 12,700 kilometers. That's miniscule, in comparison.

Let's look at the angular diameters of the objects. The general formula is
$$\delta=2\arctan\left(\frac{\text{diameter}}{2\cdot\text{distance}}\right)$$
where the angular diameter is in radians. The Pillars of Creation are 6,500 light-years away, conservatively, giving just them an angular length of $3.52\times10^{-2}$ degrees. Proxima Centauri b is 4 light-years away, with an angular diameter of about $2.02\times10^{-8}$ degrees. 6 orders of magnitude is nothing to sneeze at.

Additionally, the Pillars of Creation are located in an emission nebula. Light from the young stars that have just been born ionizes gas in the Eagles Nebula, which in turn emits the light. The dark gas and dust in the Pillars of Creation stands out quite sharply in all of this, making it easy to see.


Celestial Coordinates What is the standard coordination system used to describe the location at a celestial object approximately due east and at an angle of 10 degrees above the horizon?

The coordinate system for an object in the sky measured relative to the horizon is known as altitude-azimuth. The altitude is the angle above the horizon (10 degrees in your case), and the azimuth is the angle around the horizon, usually measured from North. (Due east would be 90 degrees azimuth in your example.)

See Horizontal Coordinate System on Wikipedia


Is there any star recognition framework/library available? Being a daytime software engineer and a sparetime photographer, I was looking for a nice DIY project for the next weeks. I finally decided to build a star tracker with a camera mount, so that I can take deep sky pictures with my DSLR.

While planning and layouting the components for this, I had to decide whether I want to manually adjust the rotation axis of the device so that it aligns with the rotation axis of the earth - or go the nerd way and let the system auto-arrange itself by attaching a suitable fixed USB camera, evaluate the video/images and write some software to move the device with stepper motors and screw drives until the correct orientation is reached.

As I do not want to reinvent the wheel, is there any star recognition framework that you've heard of? Preferrably open source, the language is of marginal importance as long as I can get the relevant data in and out. I'm thinking of something that I can feed with an image file and get back an array with the recognized objects with their x/y locations within the image. I did some research on that but could not find anything promising. What I need is an automatic identification of the brightest stars, so that I can check the current orientation against a reference image and get some vectors for the stepper motors. I hope I got the idea across.

As I do not want to reinvent the wheel, is there any star recognition
  framework that you've heard of? Preferably open source, the language
  is of marginal importance as long as I can get the relevant data in
  and out. I'm thinking of something that I can feed with an image file
  and get back an array with the recognized objects with their x/y
  locations within the image.

I'd take a look at the astrometry service. You can upload a picture to their site and receive an astrometric labeled overlay. They do have an API. I'm not sure if an array output option is builtin, but I have a feeling it's doable within what they're offering.


How does the Moon's gravity affect Earth's oceans despite Earth's stronger gravitational pull? Given that Earth has a much stronger gravitational pull than the Moon, how does the Moon have any influence on Earth's oceans?

Everything in the universe has a gravitational influence on everything else in the universe. It isn't a question of the strongest gravitational pull winning out and all the others doing nothing.

The Earth is the strongest pull on the oceans, but the Moon and the Sun both have easily measurable effect in addition to the Earth's. Other bodies (Venus, Jupiter,  a small asteroid in another galaxy,....) all have much smaller effects which will be hard or impossible to detect amidst the noise due to waves and so on.


Where is all the antimatter? The universe supposedly started off with equal parts matter and antimatter and they are said to annihilate each other. Also, nature is famous for it's balance between everything. So all we see is matter and no antimatter (I guess that's a good thing, we would all have been annihilated otherwise), so where did all the antimatter go?

Also, does antimatter exist in the same space as matter? What are the leading theories about it?

To answer your second question first: Yes, antimatter does exist in the same space as matter. In fact, the universe creates antimatter (and an equal amount of matter) every day as a matter of course in events like lightning strikes and supernovae, and even in certain nuclear decays. Humans create it in particle accelerators for research and for commercial/medical applications such as Positron Emission Tomography. The thing is, when we create antimatter, we also create an equal amount of matter.

In the hot flash of energy after the Big Bang, particle-antiparticle pairs were popping into existence and annihilating each other constantly. There were almost exactly equal amounts. For some reason, though, for every 100 trillion (10^11) particles of antimatter, there were 100 trillion and one particles of matter. In the ensuing few minutes, all the antimatter and all but that tiny fraction of matter annihilated each other and turned back into energy. Everything we can see today, all the galaxies, stars, and planets, are made up of that tiny amount of matter that was left over. Particle physicists still aren't sure why there was this tiny imbalance in the amount of matter and antimatter, because all interactions we've seen so far produce equal amounts of both. This is one question particle colliders like the Large Hadron Collider are attempting to answer.


How are the world's biggest telescopes cleaned? How are the world's biggest telescopes, (such as the Very Large Telescope for example) cleaned?

My research includes what I have read about CO2 cleaning here. Are there any other ways to cleaning the mirrors? What if we were talking about the (cancelled) Overwhelmingly Large Telescope?

One of the ways they clean telescopes is to replace the metal coating on their surface. See, for telescopes, unlike bathroom mirrors, the metal is on the front of the glass. The reason for this difference is that having glass on the front makes the mirror more durable, but it also reduces the mirror's efficiency at creating an image. Because of this every few years the mirror needs to be taken off of the telescope, the old metal removed from the glass by an acid or some other chemical means, and then a new coating of metal is applied. On the tour of the Palomar Observatory they'll tell you that the 5.1 meter Hale telescope uses about the same amount of aluminum to cover it as is in a quarter (not sure if they meant volume or mass - also not completely sure it wasn't a nickle, or 2 quarters).

In the case of telescopes with segmented mirrors, like Keck, they can do this one segment at a time, which makes the process more convenient and spreads it out over time. It's also possible, though I don't know if they do this, to keep segments in backup to put in place of removed segments, because the telescope is made from a relatively small number of segments that have the same curvature and are, therefore, interchangeable.


Ephemeris data mismatch between Nasa Horizonz and Astro.com I have tried to compare the Ephemeris data from Nasa's Horizons with ephemeris
tables from astro.com. And they do not match. Example:

Date: 22th of July 2018. Body: Mars. Time 00:00 UT
Horizons: 309 degrees (Ephemeris type=Observer)
Astro.com: 305 degrees (http://www.astro.com/swisseph/ae/2000/ae_2018.pdf)

But some bodies are matching. Like Mercury and Saturn.

Am I doing something wrong?

Sources:
Nasa Horizons: https://ssd.jpl.nasa.gov/horizons.cgi#top

Astro.com: http://www.astro.com/swisseph/swepha_e.htm

You might be comparing an ecliptic longitude to a right ascension.
These are measured around different circles, the ecliptic and the equator respectively.
Their values coincide at the solstices ($\lambda$ 90$^\circ$ or 270$^\circ$, RA 6h or 18h) but generally not elsewhere.

With target body Mars, a geocentric observer location, and output quantities 2 (apparent RA & Dec) and 31 (observer ecliptic lon & lat) selected, JPL HORIZONS gives:

Date__(UT)__HR:MN     R.A.__(a-apparent)__DEC    ObsEcLon    ObsEcLat
2018-Jul-22 00:00     20 38 23.96 -24 58 44.6 305.5424192  -6.2964464

RA 20h 38m 24s is 309.60$^\circ$, but the quantity to compare is the ecliptic longitude, 305.54$^\circ$.

The Astrodienst ephemeris table, based on JPL DE431, gives ♒ 5$^\circ$ 33', i.e. ecliptic longitude 300$^\circ$ + 5.55$^\circ$ = 305.55$^\circ$, for Mars on 2018-07-22.


Are quasars simply AGNs that are viewed from a particular angle? I found the picture below in an answer to the post "Was the Milky Way ever a quasar". The picture is published on a website belonging to "NASA/IPAC Extragalactic Database". In the answer that has 16 "thumbs up" it says:

  A quasar is simply an active galactic nucleus (AGN) that is viewed
  from a particular angle; see the picture below, in which quasars are
  labeled "QSO". This is really a remarkable figure because historically
  all of the names in the figure were thought to correspond to different
  types of objects, when really they all refer to the same thing!

There is another answer to the question "Difference between quasar and Active Galactic Nuclei?" where someone states that a quasars:

  main property is that it's galaxy axis points towards the earth and
  this way we receive its light and radio signals. That's why they are
  one of the most energetic AGN.

This answer has gotten six thumbs up. However, there is no reference to any source backing up that claim so it seems like private opinion.

Does the picture above represent the mainstream view among astronomers today or is it more like a private opinion of someone?
According to Wikipedia, ten percent of all observed galaxies are classified as Seyfert galaxies. Would we perceive all of those as "quasars" if we happend to observe them from the right angle? (Maybe there is also a luminosity requirement)
According to Wikipedia Markarian 231 is the closest quasar at a distance of 581 million light years. Also according to Wikipedia, the Circinus Galaxy is the closest Seyfert galaxy, only 13 million light years away. Would we perceive there to be many quasars closer than 581 million light years away, if we just happend to view the active galaxy from the right angle?
Could someone please show me the scientific investigations proving that the galactical planes of galaxies perceived to host quasars always lies within a certain range of observational angles as viewed from the Earth? These kind of investigations should be available if the claim that whether or not an active galaxy is perceived to be a quasar is almost totally depending on observation angle has a real backing and is not just speculation.

There is total confusion in the answers you refer to.
Quasars were first defined because of their star-like appearance - quasi-stellar objects or QSOs.
The fact that they are Galaxy-sized objects with point-like appearances means they are very luminous, dominated by central nuclear emission and far away (as confirmd by their high redshifts).
It was later recognised that quasars are just the high-luminosity end of the AGN zoo.
Quasars can also be viewed at a variety of angles and have distinct properties as a result. So there are radio-quiet and radio-loud quasars, broad absorption line (BAL) quasars and optically violently variable (OVV) quasars. The distinction between these types is thought to be dominated by viewing angle, mass of the central black hole and the accretion rate. The nomenclature can also vary depending on what wavelength region you are talking about (radio, optical, X-ray etc.).
These objects have lower luminosity counterparts amongst AGNs - FR I and FR II AGNs, Seyfert I and IIs and blazars (or BL Lac objects) - again, whose differences are largely explained by viewing angle.
I don't think these days it is helpful to think of quasars and AGNs as different objects. They are actually similar and it is just a question of the scale of the accretion process going on at their centres that is different and covers a continuum rather than a bimodal distribution.


Function for current distance between in light-seconds between Mars and Earth I'm looking for a function that given a time (for example Unix time) gives back the current distance between Mars and Earth in light-seconds.

It can be a mathematical function or programming function (preferably in Python or pseudocode), but must not rely on an Internet connection.

This question is similar to a question I asked erlier, but again I need to get the distance without an Internet connection.

Thanks in advance!

Sidenote: I'm planning on learning orbital mechanics, but I need this function earlier. :)

There is no simple function that is accurate. Both Earth and Mars are orbiting in ellipses (Kepler's first law). They are travelling at varying speeds (Kepler's second). To find the current distance between them you have to calculate their positions in three dimensions.

In other words you have to do orbital kinematics. How do I calculate the positions of objects in orbit?

If accuracy is not important. You can approximate the orbits with circles in the same plane. The Earths position is then
$$(\cos(2\pi t + \alpha), \sin(2\pi t +\alpha))$$
and Mars is
$$(1.5\cos(2\pi t/1.882 +\beta), 1.5\sin(2\pi t/1.882 + \beta))$$

The distance between them is calculated by pythagoras

The distances are in AU and the time is in years (converting to lightseconds is then easy). $\alpha$ and $\beta$ are constants chosen to fit the positions of the planets at time 0. The values 1.5 and 1.882 are chosen because Mars's orbit is about 1.5 times bigger than Earth, and a Mars year is 1.882 times longer than Earth.

The circular approximation however is poor for Mars, and this ignores the fact that Mars isn't in exactly the same orbital plane as the earth, so the values will only be rather approximate.


Could there be another planet between Mercury and the Sun? Could there be another planet between Mercury and the Sun?
Kepler found a lot of planets orbiting its star even 20 times closer than Mercury.
If there were such planets in our system - would it be possible to discover them?

It is very unlikely. While the hypothetical planet Vulcan between Mercury and the Sun was ruled out many decades ago searches for Vulcanoid asteroids would very likely have detected anything that might qualify as a intra-Mercurial planet.


Does a set moon sky equal a new moon sky? I am planning some astrophotography. And comparing two times.

On one night I plan a midnight shoot when a waning crescent moon rises at 1am. This is 1 week ahead of the new moon.

The other night would be on a new moon.

Would the darkness of the sky be expected to be any different? I ask because a lot of articles I read about stargazing and astrophotography say the phases of the moon are important, but never mention the setting and rising of the moon as an important factor.

After the moon has set, the sky is dark. There is a little "lunar twilight", but this is pretty insignificant. Once the moon has set you don't need to worry about the moon. The sky will be dark at midnight.


Why does Titan have an atmosphere while similar moons such as the Galilean moons don't? The Galilean moons of Jupiter are similar in size to Titan and are also protected by their parent planet's magnetic field. How come only Titan is able to maintain an atmosphere?

As in real estate, so in astronomy:
Location, Location, Location
Where an object forms in a system will significantly impact its makeup.  For example, during the stage of planet(esimal) formation, due to the radiation of the (proto-)star, various chemicals and atoms will be expelled from the innermost areas, but may stay around long enough to be part of planet(esimal) formation further out.  This is the basic reason that the inner (rocky) planets, gas giants, and ice giants (and beyond that, Kuiper belt and Oort cloud objects) show significant compositional variations between each other and even within their own categories.
Galilean moons
Let's consider the impact of location on the Galilean moons of Jupiter.  The first one to consider is where in the solar system did the moon(s) in question form?  We're not 100% sure of the answer to this for any moon (even our own). But the current predominant theories hold that the Galilean moons formed from a disc of gas bound to Jupiter early during its formation.
Now when any astronomical body undergoes gravitational collapse, be it planet or star or whatever else, there must be a corresponding release of energy and heat.  This means that planets are pretty hot in their early lives, and the bigger they are the hotter they are and the longer it takes them to radiate it away (a volume versus surface area scaling consequence).  Jupiter, being the biggest and heaviest of the planets, also emitted the most radiation as a result of this process.  So much so that nearby moons would be scoured of various chemicals and gases, depending on how far away they were.  I bring this up in discussing the compositional variations among the Galilean moons in another answer.  Io, being the closest of the Galilean moons, was scoured of most of its ices, while the more distant Galilean moons have abundant and spectacular ices.  The magnetic field of Jupiter is even strong enough to strip Io of charged particles in its limited atmosphere, which are added via its vulcanism, and that ultimately results in sizeable radiation belts that substantially enhance Jupiter's magnetic field.
Titan
Titan is singularly unique, being the only (known) moon in the solar system to have a meaningful atmosphere.  Titan also has an unusually large orbital eccentricity, and is the only large moon around Saturn (in contrast with the Galilean moons of Jupiter, all large and of roughly similar sizes).  Moreover, the observations of the Cassini-Huygens probe suggest that Titan contains significant amounts of Oort cloud materials (its nitrogen in particular) that would not have been found in sufficient quantities in the Saturnian system at the time of Titan's expected formation.
The main theory for Titan's origins posits a similar disc accretion method as for the Galilean moons, and even that Saturn may have had a system of moons similar to the Galilean moons early on. Titan in this case is expected to have formed relatively further out. But then a series of large impacts disrupted the system in novel ways.  Impacts and viscous torques of the accretion disc caused any (large) inner moons to fall into Saturn, while Titan survives thanks to its more distant starting point and accretes some of the material of the impactors (some of which may have formed other moons, like Iapetus).  Some, perhaps all, of these impactors would be expected to have been Oort cloud objects, thus helping to explain the Cassini-Huygens data.  As long as these impacts occur after Saturn has lost its capacity to scour away atmospheres, Titan's accretion of their material then grants it its atmosphere and curious composition.


Examples of absorption lines for main sequence stars Where might I find a detailed table or figure containing the absorption lines and their corresponding wavelengths for each type of main sequence star?

I'm trying to get the chemical abundance of some elements on a G0V spectrum but I don't know which lines I'm looking at.

There are several online sources of spectra (eg SDSS), but they usually just provide a FITS file with data, or a plot vs wavelength without any annotation. Of course, you could use the  NIST atomic spectra database to identify lines, but that quickly becomes tedious.

There are many figures containing spectra for various classes of stars in the book by Gray and Corbally, Stellar Spectral Classification. Many of these figures were previously available on Gray's web site, but the links no longer work. I scanned one that may be of use, Figure 7.1 containing spectra of G through K stars. In particular, one of these spectra is for a reference standard G0V star, $\beta$ CVn, with the stronger Ca, Fe and H-Balmer lines identified.

Another good resource for annotated spectra of many star classes is Richard Walker's, Spectroscopic Atlas for Amateur Astronomers. I have the printed version, but pdf files of older versions are available online. This atlas contains spectra of a G0IV star, and the Sun, G2V, that have similar absorption lines.

There are also collections of standard spectra, such as the Miles library. These are often included in software used for processing spectra, along with tables of common lines for various elements that can be shown on the plot. Programs I have used for amateur spectroscopy that display these include Rspec (commercial), Vspec and ISIS (Christian Buil).


Is Polar Lights observation possible at the latitude of 56° N? Back in 2002, me and my friends observed a green glow in the sky at night in the form of giant slow moving spurts of flame, looking more dense near the horizon and more blurred at height. It was surrounding the area, not just on one side, as I see on most of the imagery available. It was bright enough to see for several people sitting around a bonfire.

Is it possible for the natural phenomena, 'Aurora Borealis' take place as far south as 56° N, 37° E; in a Moscow suburb, Russia?

Yes. The Aurora form in a ring, roughly centred on the Magnetic pole. The pole does wander slowly, but it has been located in the Canadian Arctic for some time.

As the pole is on the American side of the Arctic ocean, aurora are seen at lower latitudes in America than in Russia, nevertheless, when a powerful solar storm occurs, aurora can be seen at surprisingly low latitudes, even into the subtropics, as Wayfaring stranger notes in her comment.

Aurora in Moscow is a notable, but not exceptional occurrence, as this news report indicates http://www.themoscowtimes.com/article/507096.html


Origin as binaries and multiple system The majority of hot stars originate as binaries or multiple systems. How is it with the cooler spectral types? Are they usually born as single stars?

Many hot stars are born in multiple star systems because the cores of these stars tend to split (see Jeans instability). With lower mass stars this still can happen. However, there are other ways. For example, in a young star cluster, close encounters with other stars can cause a star to be captured by another one.


Do boulders erode differently on asteroids than on the Moon? If I understand it correctly, boulders on the Moon are only found near fresh craters, because micrometeorites erode them over time. Asteroids are believed to have formed sometimes even earlier than the Moon, but some images show asteroids covered by boulders. And NASA is planning the ARM mission to go pick up a boulder from an asteroid.

Are boulders more frequent on asteroids than on the Moon, and if so, by what kind of mechanism? For example, it is not primarily micrometeorites, but temperature changes that erodes them on the Moon. Or don't microgravity objects attract as many micrometeorites as the Moon does?

Intact boulders on asteroid 25143 Itokawa:

Eroded boulders on the Moon:

The moon does attract more particles.  But more importantly, those particles hit the moon with velocities of the order of the Moon's escape velocity, 2.4 km/s.  That's a very powerful sandblaster...


Can a gas moon exist? Could a gaseous moon exist in the same way as a giant gas planet? All the moons in the solar system are rocky, or icy. Why shouldn't gas planets  have gas moons?

LocalFluff's comment is spot-on. You need mass to have gas, and moons just don't have enough.

It is thought that gas giants gathered the gas they have today by accreting large amounts of it from the protoplanetary disk in the early days of the Solar System. At first, they were only gas-less cores (not rocky, exactly, but not gaseous), but they quickly became the most massive objects in their immediate vicinities, and thus gobbled up all the gas nearby them.

Now, less massive bodies, like Earth, can still accrete gas. However, they have difficulty retaining it. Lammer et al. (2014) calculated that under conditions like those experienced in the young Solar System, planets of one Earth mass or less could retain captured hydrogen envelopes for no more than ~100 million years - a long time for us humans, but shorter for astronomical objects.

The hydrogen escapes via atmospheric escape, which happens when particles in the atmosphere have velocities higher than escape velocity. This phenomenon is known as Jeans escape. Atmospheric escape happens more often with lighter gases, such as hydrogen. It is also influenced by stellar winds, which can cause even gas giants (generally close to the star, such as hot Jupiters) to lose some or all of their atmospheres.

I wouldn't call gas moons impossible, but certainly very unlikely.


Elliptical galaxy morphology I understand what differentiates elliptical galaxies from spiral, lenticular, and irregular galaxies. What is the difference between a compact elliptical (cE) galaxy and a dwarf elliptical (dE) galaxy? Are there criteria which separate these two subtypes?

The basic criterion is that compact ellipticals live up to their name by being compact -- small in size but with a high density of stars -- while dwarf ellipticals arguably fail to live up to their name because they are more extended and diffuse. (Given that "dwarf" generally means "faint" or "low in stellar mass" when applied to galaxies, you could argue that a better set of terms would be "compact dwarf ellipticals" and "diffuse dwarf ellipticals", respectively.)

The figure below (from Janz et al. 2016) shows size (effective radius "$R_{e}$", which is the radius inside of which half the galaxy's light is found) versus stellar mass for a variety of objects. The relevant part for this discussion is the upper right, where you can find regular elliptical galaxies (green plus signs), dwarf ellipticals (green pentagons), and compact ellipticals (red open circles, plus the black open circle labeled "M32", plus the red plus signs in the same region of the plot). From this you can see the dwarf and compact ellipticals have similar stellar masses (compact ellipticals can sometimes be more massive), but the dwarfs are physically larger. This means that, since they have similar stellar masses and thus similar numbers of stars, they are more spread out and diffuse than compact ellipticals, which are small and dense. Compact ellipticals seem to be an extension of the size-mass correlation of normal (higher-mass) ellipticals, so some astronomers argue they are a continuation of the normal elliptical population, while dwarf ellipticals are a deviation.


What's the proper terminology for nebula clouds? I'm writing a research paper over outer space (yeah, yeah, broad topic) and I'm wondering what the proper terminology for nebula clouds is.  This is an excerpt from my paper showing how I'm going to use the term:  "Outer space is the host of all the types of stars and galaxies and a lot of other interesting phenomena, such as black holes, supernovas, and ________."  Long story short, would I use "nebula clouds" or "nebulae"?

"nebula clouds" sound a little bit redundant, because, is there any nebula that is not a cloud?

I would stick to "nebulae". (And if you want to be consistent, you should be writing "supernovae" too).

I am not an expert on this topic, but I have never seen any use of "nebula cloud" before.


why does pluto have a high orbital inclination Pluto has a high orbital inclination compared to the planets in our solar system.  What has caused Pluto to have such a different orbit -- was it always like this, or did something happen to make it so?

I think the best answer is that there is no particular reason.

In any planetary system, most orbits tend to stay close to a common plane - close, but not exactly there. Even the big planets are slightly out-of-plane with each other, but the differences are tiny.

As you move away from the bulk of the planetary system's mass, smaller bodies tend to be more random. They are more easily deviated from encounters and near misses. Their origins might be different from the rest. If they get close to the outskirts of the system, that's a more unruly place, and orbit-changing events are more likely - especially for small bodies. Finally, the whole distribution of orbital planes has a bit of a stochastic (random) component anyway, and there will always be outliers that are quite different from the bulk.

In theory, even some larger planets could be significantly "out of plane" (much more than they are right now), but that's unlikely and it tends to be smoothed out over large periods of time.

So, Pluto is different because it's smaller and it's not really a planet, but don't attach too much significance to it.

Try to install Universe Sandbox and play with some of the included scenarios. Big systems bound by gravity can be pretty complex, and completely orderly configurations are rare.


Can we compress any object to create black Holes? In general, when a star runs out of nuclear fuel, gravity gets the upper hand and the material in the core is compressed even further and creates black holes. I am clear till  here.
Now the question is: Does that depend on the mass of the star (or object)?
Naturally, the more massive the core of the star, the greater the force of gravity that compresses the material and easy to create Black Hole.
For smaller stars, when the nuclear fuel is exhausted and there are no more nuclear reactions to fight gravity, the repulsive forces among electrons within the star eventually create enough pressure to halt further gravitational collapse. The star then cools and dies peacefully.
In science videos and discussions is said that we can create black holes from any object. For example, if we are able to compress Earth to the size of the tennis ball, can we then create a black hole?
Isn't the nuclear fusion / reaction necessary to create a black hole? Of course, to fight against gravity we may require some kind of energy in this case, Nuclear reactions. But I am generally concerned like, does Nuclear Reaction is only to fight gravity, it does not play any other role in creating Black Hole.

Do you mean, "Can we in principle", or just, "Can we..." ?

The answer to the latter is no. We have no technology to create black holes. It was a remote possibility that was considered when creating the high energy densities in the LHC, but in practice the energies aren't high enough.

Can we in principle do it? The answer is yes. If you can squash enough mass (or energy) into a very small volume then the inevitable consequence is a black hole.

Most would say that the volume in question is governed by the Schwarzschild radius, $r_s$  which is roughly 3km multiplied by the mass in solar units. Thus for an Earth mass $r_s$ is about 1 cm.

Actually the radius within which collapse to a black hole is inevitable is a little bit larger because even the "hardest" equation of state, where the speed of sound equals the speed of light, cannot resist collapse at radii below about $1.5 r_s$.

The problem is that to compress materials this much would be incredibly difficult. For the example of an Earth mass, we are talking densities of order $10^{30}$ kg/m$^3$. But (long) before you got to that stage, yes you would have the problem of overcoming the nuclear fusion reactions would be initiated that would oppose your compression (ie you would end up making a mini-star before you could get to a black hole). Because the Schwarzschild radius depends linearly on mass, then less massive black holes need to be even denser. However, we are again talking about "in principle". So assuming compression could overcome the various opposing forces, then a black hole could be formed.

It really doesn't matter what the black hole is made of. In a star, the sequence of nuclear fusion events is a consequence of the physical conditions in the stellar interior. It is not anything that is required for black hole formation.


Is it possible to observe if there is traces of life on an exoplanet? We can observe exoplanets, but is it possible with today's technology to observe if there is life as we know it on an exoplanet? What do you look for when doing this kind of observation?

Direct observation of exoplanets (and then of traces of life on them) is still a big challenge.

Up to now, there are several  indirect methods (effects on the parent star or on other stars), and direct detection is performed by using devices such as coronagraphs on faint stars, where very bright planets are imaged.

A way to image things such as as "forests" is very far in the future, and could be achieved by using extreme coronagraphy in space interferometers .

Another way is to use spectroscopy to find traces of biological activity in the athmosphere. This solution is very tricky due to the faint light reflected by extrasolar planets.

It is anyway a field where progresses are very quick, so stay tuned!


Moons within a Gas Giant Assuming a gas giant is primarily gaseous past our visibility, is it possible that a moon traveling at a sufficient velocity would be able to exist within the atmosphere, or would terminal velocity from the atmosphere prevent an object of that size from maintaining appropriate centripetal force? For example, Neptune has winds that are so fast they move beyond the speed of sound. Would a moon be able to exist in an environment like that?

No, this can never be stable over long periods of time.
First of all, drag from the air in from of the moon would cause it to quickly deorbit and plunge into the gas giant. No amount of wind will be able to keep the moon up in the air. A gas giant's orbital speed near the cloud tops will be over 30 km/s (See the orbital velocity of Metis, Jupiter's innermost moon). There will be astronomical amounts of drag if the object is large. If the object is smaller, then it will be irregular, causing the same amount of drag. Also, a gas giant's weather is never constant. There will never be a circle in the gas giant's atmosphere that has a constant wind speed. These fluctuations will probably cause the moon to deorbit over time, or, if it is high in the atmosphere, to be thrown out of the atmosphere into the vacuum of space. The latter is highly unlikely.


How does gravity affect spacetime Scientists say that gravity warps space and time. They also say that the more gravity there is the slower time moves. Why and/or how does gravity do this.

In fact time always "moves" at the same speed to any given observer. It appears to move at different speeds to an external observer, but you cannot experience slowed time as such - except in the sense that you might observe external clocks ran faster than the watch you had your wrist.

An attempt to explain: The supposition - very strongly supported by the experimental evidence (the latest discovery of gravity waves being the jewel in the crown) is that we live in a four dimensional spacetime. An individual always experiences time as "moving" at a constant speed, but as has been remarked by others, externally gravity appears to add curvature to the "straight line" we are moving along on the time dimension and so we "gain distance" in this direction more slowly when seen externally.


Power spectrum of matter in the Universe I have a picture of a power spectrum of matter in the Universe. What is the connection to Lyman alpha? Please describe it for me (horizontal and vertical and shape).

Power spectrum

The distribution of matter in the Universe is not uniform$^\dagger$. Rather, it has clumped together by gravity to form the structure we see, from planets and stars, to galaxies, to groups and clusters of galaxies. Exactly how much the Universe clumps on the various scales can be described statistically by the two-point correlation function $\xi(r)$, which gives the excess probability of finding a clump of matter at a certain distance $r$ from another clump, relative to a random, Poisson-distributed matter.

The Fourier transform of $\xi(\mathbf{r})$ is called the matter power spectrum $P(k)$, where $k = 2\pi/r$ is the wavenumber. The power spectrum thus shows readily how much structure there is on various physical scales, i.e. a high value means much structure. It evolves (increases in amplitude) with time or, correspondingly, redshift $z$, and so may be written $P(k,z)$.

The power spectrum can be written as the product of the primordial power spectrum $P_*(k) \propto k^{n_s-1}$ originating from cosmic inflation, and a transfer function $T(k,z)$ (squared) describing what happens at a later epoch. A good description is given by Peebles (1980).

The figure

The figure you show is taken from Tegmark & Zaldarriaga (2002). It shows the power spectrum as a function of wavenumber, but on the top $y$ axis you see the corresponding spatial scale. This scale is expressed in comoving megaparsecs (Mpc) (where 1 parsec equals 3.26 light-years). This factors out the size of the expanding Universe — or, equivalently, the epoch at which an observation is made — such that observations at different epochs in the history of the Universe can be readily compared. A distance $r$ at redshift $z$ will expand to $r(1+z)$ at redshift $z=0$. Using comoving coordinates, no matter at what value of $z$ we observe $P(k,z)$, we "extrapolate" to the current power spectrum $P(k)$.

Moreover, the distance is divided by the dimensionless Hubble constant, $h \equiv H_0\,/\,100\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1} \simeq 0.7$. The reason for this is that different observations may have made different assumptions about the exact value of $H_0$; in general inferred distances will scale as $H_0$, so measuring distances in $h^{-1}\mathrm{Mpc}$ allows for direct comparison.

In other words, $1 h^{-1}\mathrm{Mpc} \simeq 4.7\times10^6$ light-years at redshift $z=0$, but at redshift, say, $z=4$ — when the Universe was five times smaller in all directions — we had that $1 h^{-1}\mathrm{Mpc} \simeq 9.3\times10^5$ light-years.

Observational probes

The power spectrum depends on various cosmological parameters, mostly on the matter density parameter $\Omega_\mathrm{m}$ and the expension rate $H_0$, but also the baryons ($\Omega_\mathrm{b}$) and dark energy ($\Omega_\Lambda$).
Given these cosmological parameters, the transfer function and the resulting matter power spectrum can be calculated. In the plot, the red line shows $P(k)$ as calculated theoretically from linear perturbation theory. For details on the calculations, see Tegmark & Zaldarriaga (2002). It is compared to constraints from various observational probes of the cosmological parameters:

Black: Anisotropies in the CMB shows how matter clumped in the very early Universe, and its polarization pattern, caused by subsequent scattering, gives constraints on matter distribution in later epochs, on the largest scales.
Green: Clustering of galaxies (here from the 2dF survey) shows how matter has formed structure on (comoving) scales roughly from a few tens of Mpc (a bit larger than the typical distance between galaxies) to several hundred Mpc (above which the Universe is homogeneous).
Blue: Abundances of galaxy clusters. Here, the error bars reflect the spread in the literature.
Magenta: Weak lensing measures photons that have traveled through fluctuations in the metric caused by intervening matter; this technique probes the power spectrum on $\sim10\,\mathrm{Mpc}$ scales. These data are from Hoekstra et al. (2002).
Red: The smallest scales (largest wavenumbers) are probed by the Lyman $\alpha$ forest (LAF). Whereas all the previous techniques measure light, the LAF is the absence of light, namely absorption lines in a bright background source, caused by the neutral hydrogen in all the diffuse clouds and filaments of gas lying between the source and us. The background source is usually a quasar, but may also be, e.g., a gamma-ray burst. As light blueward of the quasar's own Ly$\alpha$ emission line travels through the Universe, it is gradually redshifted toward the rest wavelength of Ly$\alpha$ (1216 Å), so whenever a parcel of hydrogen gas is present along the line of sight, it will cause an absorption line at the corresponding wavelength, creating a "forest" of absorption lines in the blue part of the quasar's spectrum. These data are (primarily) from Croft et al. (2002).

$^\dagger$This is fortunate, since otherwise you wouldn't be here to ask the question.


Graph of apparent magnitude of Mars through time from around 2000 to present? I tried to search online but failed to find a graph of the apparent magnitude of Mars over time from 2000 to present.
From Wikipedia:

Mars made its closest approach to Earth and maximum apparent
brightness in nearly 60,000 years, 55,758,006 km (0.37271925 AU;
34,646,419 mi), magnitude −2.88, on 27 August 2003. ...
Every 15 to 17 years, Mars comes into opposition near its perihelion. These perihelic oppositions make a closer approach to
earth than other oppositions which occur every 2.1 years. Mars comes
into perihelic opposition in 2003, 2018 and 2035, with 2020 and 2033
being close to perihelic opposition.

So I am very curious how the present 2020 perihelic opposition apparent magnitude of Mars compare to the previous ones. It would be even more interesting if the graph also contains the distance to earth.
Could anyone point me to where I can find such a graph? Thanks.

TheSkyLive's Mars information page has graphs of its distance and apparent magnitude from Earth.
If you set the same year range for each, you can see how the quantities are related.
They provide similar pages for all the planets and selected comets and asteroids.


How did VLT's adaptive optics obtain this resolution for Neptune? Is it really working in visible wavelengths? This image of Neptune taken with the VLT is really impressive. The resolution is achieved by recent improvements in the adaptive optics.

Gizmodo: New Super-Crisp Images of Neptune Show How Far Our Telescopes Have Come
Space.com Telescope Upgrade Produces Stunningly Clear Views of Space

But I don't really understand, is this coming from just one 8 meter mirror, or is this using more than one of the four that make up the VLT? Also, is this really using adaptive optics that work in the visible, including blue wavelengths? Or is this a false-color image? See the excellent answer(s) to Why (actually) aren't ground-based observatories using adaptive optics for visible wavelengths?

It is an image taken with the new narrow field mode of the MUSE instrument using the GALACSI Adaptive optics module on a single (UT4) VLT telescope using laser guide stars.

I am having a great deal of difficulty (e.g. from this press release) in working out at what wavelength(s) this image was taken. I do not believe that the AO system is working at blue wavelengths and therefore the comparison with HST (which certainly does) is somewhat misleading. I think (from ESO's own instrumentation pages) that the MUSE narrow field mode has zero efficiency at blue wavelengths and the description of GALACSI only talks about AO correction approaching diffraction limited images at 650 nm (i.e. red wavelengths).

The captioning to the press release images found here suggest that the shortest wavelengths used in this false-colour image were 550nm and that most of the detail you see is coming from redder wavelengths (600-920nm).


What affects the evolution curve of a star's luminosity as a function of time? Take a star of a given mass (say $1.0\ \mathrm{M_{\odot}}$ or $1.1\ \mathrm{M_{\odot}}$), what affects the star's luminosity as a function of time and how much? (metallicity?, rotation?)

It seems to me that stellar evolution is basically set by the laws of physics; if we know certain parameters (e.g., mass). Of course, that's the trick since we can't directly measure the mass of a star with no companion(s).

I have run across a few issues with published values being in conflict. For example, this study gives the age of Zeta Tucanae as being about $2.1-3.8\ \mathrm{Gyr}$. However, mass/radius/luminosity is given as 0.99/1.08/1.26 relative to sun (Wikipedia sources). If you look at an evolutionary plot of the Sun something is wrong here. (I'm guessing mass.) By the way [Fe/H] is given as -0.18.

I think this question is too broad, but I'll take a stab at it.

The Russell-Vogt (or sometimes Vogt-Russell) theorem is that the position of a star in the HR diagram is determined by its mass and composition.

The luminosity is determined mostly by its central temperature and composition. In turn, the central temperature depends on mass and radius and the radius depends on the luninosity and effective temperature.

Thus the question you ask fills textbooks. But to first order.
The time dependence of luminosity is set by the time dependence of mass - ie mass loss (or gain) and the rate of change of composition, particularly in the nuclear burning regions of a star.

In a star like the Sun, mass loss is relatively unimportant, so it is the rate at which hydrogen is turned into helium in the core that sets the timescale for luminosity evolution. Other processes that alter the core composition like mixing (due to convection, rotational mixing or diffusion) are thought to be second order effects.

Restricting myself to the main sequence as an example. The luminosity of the Sun is set by the core temperature. The the nuclear reactions become faster as the mean particle weight increases and the core contracts and the temperature rises to maintain hydrostatic equilibrium. The rate at which this occurs is given by the luminosity of the star divided by the amount of H available (proportional to the mass of the star).

Overall chemical composition drives this as a second order effect. A lower metallicity star is less opaque to radiation. The radiation escapes more efficiently and the star is smaller and hotter at the surface for the same luminosity. Smaller stars are hotter in the middle for the same mass and thus more luminous. Thus the luminosity evolution of low metallicity stars is faster than those of higher metallicity. See for example Figs 1 and 2 of Bazan & Mathews (1990).


What would happen to a polished marble statue left in space for a million years? Consider it doesn't collide with any other objects. Would it be preserved perfectly in the vacuum or would its surface be damaged by anything like UV rays, radiation, gas, space dust, etc?

There are three main space weathering processes that will affect the surface of the marble.

Cosmic rays, high energy particle from the sun and beyond, will hit the surface. This can change the chemistry of the surface.
Solar wind particles, hydrogen and helium, can become implanted in the surface
Micrometeoroids will impact the surface, causing small craters, melting, and the inclusion of other elements such as iron.

These processes will tend to change the surface, developing a patina on a timescale of a hundred thousand years. The surface will darken (though as marble is not a typical rock in asteroids, there isn't any direct evidence of what happens with marble.

Marble is largely CaCO3, and this is in a equilibrium with CaO and CO2. At  standard temperatures and even the very low partial pressure of CO2 in the atmosphere, this equilibium favours CaCO3. In our atmosphere one needs a temperature of 550⁰C to decompose Calcite. However in space there is no CO2, and so the Calcite would very slowly decompose to CaO. Calcium in meteorites is mostly in the form of CaO.


Why do we observe spectral lines of specific energy? The basis of my confusion is that atomic orbitals, even when described accurately by quantum numbers, have definite energies, meaning they represent energy eigenstates of the wave function. They're stationary states, and thus separable solutions to the Schrödinger equation. The general wave function of an electron, however, is a linear combination of such states, so that general solution does not have a definite energy. Still, we observe discrete spectral lines at specific wavelengths (with some broadening).

Why do we observe spectral lines of specific energy when the wave function of the electrons in an atom are linear combinations of energy eigenstates?

It seems like the spectral lines that are observed are just the energy eigenstates, while, according to quantum mechanics, the wave representation of electrons is a linear combination of those states.

When an interaction occurs that results in the absorption or emission of a photon, we are not dealing with stationary states. Stationary states are solutions of the time-independent Schrödinger equation, but the absorption and emission of photons is a time-dependent phenomenon.

Spectral lines in fact do not have a definite energy. They have a natural width associated with the time taken for the transition to occur.

The probability that a transition might occur resulting in the absorption or emission of a photon of a given frequency can only be tackled by considering a time-dependent Hamiltonian. What one finds is that transition probabilities become large for frequencies close to the those corresponding to energy differences between stationary states.