What phenomenon causes "lunar waves"? In multiple video clips of the moon but also one of Jupiter, some kind of waves can be observed. Is this just the effect of the object moving behind layers of different refractive indexes (similar to what we observe at sunset) or is there a wave propagating through the atmosphere?

https://m.youtube.com/watch?v=xUGxysKSGEM

https://m.youtube.com/watch?v=EMSkd4Xhp0g

There is an answer on Quora, but I would love to see a more detailed answer, why we can see exactly these two rather sharp lines moving.

Video astronomy requires much more equipment than traditional eyepiece viewing. It helps to understand what is going on between the camera lens and the video screen.

Most important is the conversion of the cameras analog signal to the computer digital format. This is usually done with a frame grabber and its associated drivers. The cameras typically have 700 ish lines of resolution which are usually translated into 640 by 480 digital signal. The camera analog signal is 60 cycle interlaced. The computer display frequency is whatever the PC is set to. I'll let the Math people tell us how the drivers fit all those numbers together and make a nice picture. I think the answer is PI or at least within a decimal place or two. The numbers get rounded and every once in a while the computer screen hiccups. National Enquirer sort of news.

The frame grabbers come in a wide range of cost and reliability. There's no rhyme or reason to their reliability. They depend on the computers operating system which is not identical on every computer. The frame grabber and driver will work well on one PC but not another similarly equipped PC.

Typically the astro video cameras two output connectors, a coax and an S-Video. The person making the video could have proven the "Waves" were and artifact of the PC by simply connecting one of the cameras outputs to an analog video screen, a television with a composite input for example and the other output to the computers frame grabber. Provided the camera and analog video are functioning properly he could have shown us a rock steady image on the analog screen and the waves on the Computer screen. With a little skill he could have shown us an alien or two surfing on the waves.

Smoke, mirrors and snake oil. Suckers are said to be born at the rate of one per minute. I have a feeling the con artist birth rate is up there as well.

It is a bit of a shame, Video or near live viewing as many of us call it, is gaining in popularity. Having someone use what is not unusual for a Video astronomer to see just for a bit of sensationalism serves no useful purpose.

Another point to edit in. The uTube is a video of a video. The image we see is taken by a second video cameras pointed at a video image being displayed on a computer screen. Crunch the computer screen frequency and resolution with the frequency and resolution of the second camera. You end up with images of airplane propellers that appear to stand still or move very slowly. I wonder how much adverting revenue that sort of video would bring into uTube.


How was Sugar Grove Station supposed to work? Sugar Grove Station was an outpost designed to listen in on Soviet radio signals reflected off the moon.  How would this work?  Wouldn't the radio signals be distorted by the imperfect surface of the moon?  And wouldn't they also be extremely weak since they wouldn't be beamed directly at the moon?

I can't comment in detail but Earth-Moon-Earth communication at radio wavelengths is well established.

At wavelengths longer than a few cm (frequencies below 10 GHz), the Moon appears smooth and acts like a reflective sphere as far as radio waves are concerned.


Is there a flaw with the newer purposes and correlations attributed to the HR diagram? (And would a third axis of mass correct the enclosed flaw?) When I was younger, I was looking at HR diagrams, and began to experiment with the HR diagram.

I was looking at plotting different groups of stars on the HR diagram when I found RV Tauri stars.

These are stars between 0.4 and 9 solar masses; they have reached the end of their "life" and the fusion shell of such a swollen star is advancing towards its surface (when it hits, the planetary nebula starts to form), thus its heats up and swells further. This phase occurs after the Asymptotic Giant Branch/Red Clump phases (AGB for high-metallicity stars, RC for low-metallicity stars).

Taking into account the above information, RV Tauri stars are BOTH more luminous and hotter at the surface than red giants (and AGB/RC stars), they should appear to the upper-left of the latter of the aforementioned groups (given the inversion of the temperature axis). All seemed well.

But then I saw this:

My knowledge of astrophysics tells me that due to stellar winds and the equation E=MC^2, a star's mass (after "birth") will usually decrease over time (unless receiving matter from another star). But if RV Tauri stars are above and to the left of red giants, it means that according to the graph, an increase in mass occurs every time a star migrates to the RV Tauri stage.

I know that all graphs have their limitations, but in my mind it was wrong to claim that these correlations were set in stone. Only axes could ever display data in a perfect way (they treat different units of data as separate simple measures, not "more unstable" compound measures). So I added a third axis of mass (as this is whole problem is to do with plotting the evolutionary "tracks" of stars); this is what is known to affect stellar evolution to the greatest extent. Here is what I came up with:

I did this in order to show that the HR diagram shows general trends of stars (not the evolutionary ones that scientists claim).

My question:

Was this a valid flaw with the HR diagram - and if so, is mass the best axis to add to it?

--EDIT--

The HR diagram is not flawed, I respect that. I also know that there will always be outliers. But the extra correlation of mass seems to be too flawed for that (as detailed above). My new question: is the attribution of these extra correlations wrong?

Yours is a very, very interesting work. If you publish it it may happen that 3D diagrams will be used in the future. Please publish it.

But this does not mean that there is a flaw in the H-R diagram. It is correct as it is: it displays Luminosity Vs. Color and is perfect at that. And then it happens that some extra relations appear: stars are not randomly scattered on the HR diagram, but they group in branches, and these branches are related to stages of their life. The position on each branch is related to each star's mass. This is not a general relation holding for all the diagram. Almost the same happens with size, but this is more tightly related to Luminosity, per definition.


Are moons geologically active? Are there natural satellites in the Solar System that are geologically active? This includes volcanism, existence and motion of tectonic plates, et cetera.

Is it a common or a rather rare feature among such bodies?

Yes.  Moons around Jupiter (Io, Europa and Ganymede), Saturn (Titan and Enceladus) and Neptune (Triton) all have some form of geological activity.  Charon also may have geological activity, being in a binary system with Pluto.  However, while Earth's geological activity is caused by internal heating and tectonic plates, the geological activity of the moons around Jovian planets comes in the form of tidal forces.  Io is the most iconic instance of tidal stress, because Io's plumes are frequent, volatile and make the world look extremely chaotic, with its surface frequently being altered and renewed by its non stop volcanic activity.  (Because it is chaotic)
As for tectonic plates, Europa is the closest you get to tectonic plates with moons in our star system.  Water replaces lava when it comes to ice worlds.  Ice worlds being worlds that have ice instead of rock for their crust.  This means that water mantles are a frequent occurrence, with the core of ice worlds being mineral rich stone.  This is the case for Triton as well, which has cyro-volcanism from the sheer tidal stress Neptune exerts on the captured dwarf planet.
Enceladus and Titan have water mantles, Enceladus being the world notable for its massive plumes, high albedo and tiger stripe surface fractures.  Titan may also have tectonic activity for similar reasons to Europa.


star atlas with absolute magnitude and spectral type Is there any star atlas someone recommends?

Then for some kind of star with a definite spectral type, we can know its absolute magnitude.

BSC5p may be a nice database to start with.

The parallax (check according box) and vmag will provide a basis for the calculation of the absolute visual magnitude. The absolute visual magnitude may be lower (star may be absolutely brighter), if the extinction isn't negligible.

1/parallax is a good estimate for the distance. Take this distance as an approximate for the luminosity distance, if you can assume negligible extinction. Now calculate the visual magnitude of the star at 10 parsec distance to get the absolute visual magnitude.

Example: Alp1Cen (HR 5459) has vmag -0.01, and parallax 0.751 arc seconds. Therefore the distance is about 1/0.751 = 1.33 parsec. We get absolute visual magnitude
$$ M=m-5\cdot (\mbox{log}_{10}D_L - 1)=-0.01-5\cdot (\mbox{log}_{10}1.33 - 1)=4.37.$$

An overview of absolute magnitude and spectral types.

More detailed discussion, and tables can be found in this paper.

More tables.

This book seems to contain a table with values as of 2009, which is cited here.


How accurate is Stellarium at depicting the Earth, from the Moon, approaching a solar eclipse (from Lunar perspective)? This is how Stellarium depicts the positions of the Earth and Sun 24 hours before the solar eclipse (from Lunar perspective) on Jan. 13, 2131

A close up of the Earth on that day (Jan 12) shows no indication of any crescent Earth visible.

On Jan. 11, there is the barest of indications of a crescent Earth visible.
On Jan. 10, more of a crescent Earth is depicted.

Is there anyway of telling the accuracies of these depictions? Is there reason to think the human eye could see something of the Earth or its atmosphere on January 12, or would it appear entirely black?

While a black disk might not be entirely accurate, it is not a too bad approximation. Better would be using orbital night-time images of Earth.
There are images in the NASA archive which show Earth at night, the programme is titled "The Black Marble" which depicts Earth at night. There's a video which covers 22 days. The actual image depends on atmospheric conditions and on which side Earth shows - you might see some lights of civilisation. Similar to new moon conditions where you can also see features on the moon, an observer on the Moon would see some features on the Earth's surface. Additionally, maybe some of the refracted light of the atmosphere or airglow or aurorae is visible - but with the atmosphere being less than 1% of Earth radius, that's not much in comparison to the disk of Earth in the observer's FOV; yet it might be enough to be detectable, depending on sensitivity of the observer.


Mathematical astrophysics subjects for math graduate students I'm looking for a cool and interesting subject in mathematical astrophysics to study for my master's project. What I really aim for is certain processes in the cosmos (multiple body-problem, black holes, asteroid belts, colliding stellar objects, etc...), but my background is not very much on the physics side, unfortunately. However, I read about special relativity, gravitational waves and how to measure in space, but not in a very mathematical way.

I would like to hear from someone whether they know similar subjects like the above that are reachable for a graduate math student, like me, to study for their master's project.

My background is mainly in algebra (Galois, Geometry, crypto), but I also have done statistical data analysis courses and (P)DE courses; thus I have seen a rich part of mathematics, but my specialty is really in abstract algebra. However, especially now, I would like to get to know subjects that are not mainly abstract algebra, but more PDE, for example.

I'm ready to dive into depths of mathematical physics if necessary. Thanks for any suggestions!

As a first step Newtonian Mechanics is very important. Both at an undergrad level and graduate level. So a calculas based first course is very important. Also very useful is a source on undergrad Atomic Physics and a course in Nuclear Physics. There are several others besides these. I would recommend the series of courses in a Halliday and Resnick type of text as a start. This will help set you up for many other courses in Physics. IMHO.


What triggers solar flares? The sun is a big ball of hot plasma which contains free electrons. However, how does the absence of metallic elements in the sun generate the magnetic field to orchestrate these free electrons to display such beautiful solar phenomenon?

Magnetic fields are generated by currents - i.e. by the motion of charged particles. As you say, the Sun is full of freely moving charged particles, and these generate currents which in turn generate magnetic fields. No metals required.

Most of the magnetic field generation is thought to occur at the interface between the radiative interior of the Sun and an outer convective envelope. This region, called the tachocline, is subject to large shearing motions which are able to take small magnetic fields and amplify them. The stronger magnetic fields are then buoyant, because magnetic fields in a plasma exert a pressure. They therefore emerge at the solar surface in the form of loops of magnetic field.

These loops are strongly coupled to the plasma in the Sun. As the plasma moves around turbulently, driven by convective motions and differential rotation on the Sun's surface, the footpoints of the loops are sheared and twisted. There comes a point where the loop will snap back into a configuration with lower magnetic potential energy through a process called reconnection. The reconnection process has a side effect of accelerating particles within the magnetic loops. These relativistic particles smash into the photosphere (actually, they are mainly stopped in the chromosphere which sits above the photosphere), where they release their energy, heating plasma to millions of degrees, which evaporates into the corona. This is a solar flare.


Are we made of stars we're seeing? a fresh astronomy enthusiast here.
Recently I've been reading upon how immensely far other stars are from our solar system and how is it possible that we may be seeing stars that are already dead. My question is - if there is a star that is a millions of light years away from us and we are seeing it shine tonight, but in reality that star died long long time ago (perhaps also millions of years ago), is it possible that matter from that star somehow travelled through space to our solar system and at some point in history it collided with the Earth and now we're "made" of this star (made as in that star stuff is present here on Earth)?
To me, I don't see reason why not, because even though matter cannot travel faster than light, my intuition tells me that the answer to my question is yes, it is possible that this could happen, (if only in theory) given enough distance. But maybe I'm not considering some important points which are obvious to more experienced folk.

Stars really are immensely far, however it's a common misconception that the stars that you can see are millions of light years away. Most of the visible stars are a few tens to a few hundreds of light years away.

However it is possible that there are stars that have exploded in a supernova: Eta Carinae looks to be approaching the end, and is 7500 light years away (so we see it as it was 7500 years ago). It's one of the most powerful stars in the milky way, but it is so distant that it looks like a faint star.

It is impossible for matter from an Eta Carinae supernova to reach the solar system before light from the supernova, because matter must be slower than light. No matter how far the star is, whether near or far, light beats matter in any race. In fact, Eta Carinae is too remote for any matter from its eventual supernova to ever reach the solar system.

The "starstuff" of which we are made was present in the molecular cloud that collapsed to form the solar system about 4.7 billion years ago, that molecular cloud was enriched with material from ancient stars that died during the 8 billion years that elapsed before the formation of the sun.


What was earth's mass before the collision with theia? Assume the "Big Splash" or "Giant Impact" (whichever name you prefer) theory is more or less correct.

EDIT: With so many variations of this theory, with so many names and qualifiers on them, such as "direct impact theory" and "glancing blow hypothesis", etc., let's assume that the impact was direct enough that nothing of Theia (other than Earth and the Moon) was left that was large enough to for its gravity to compress it into a hydrostatically equilibrious shape, and scatters too much to coalesce (on its own) in to anything large enough either.

Assume "Theia" was the size of Mars (some variations on the theory use other sizes, but for the sake of this question, let' stick with Mars)

How big was Earth before the impact?

It can't be as simple as "Earth+moon-Theia(mars)=pre-impact size", can it?  Because there must have been some debris ejected completely from the earth+moon system, right? or was it such a small amount that it can be considered negligible?

I'm not sure if there was a significant amount of debris, however the calculation you mentioned would at least give an upper bound on the value:

$
M_{piE}=\text{Greatest possible mass of pre-impact Earth}\\
M_E=\text{Mass of Earth today}=6.0\times10^{24}kg\\
M_M=\text{Mass of the Moon}=7.3\times10^{22}kg\\
M_T=\text{Mass of Theia}\approxeq6.4\times10^{23}kg\\
$
$$
\begin{eqnarray*}
M_{piE}&=&M_E+M_M-M_T\\
&=&(6.0\times10^{24})+(7.3\times10^{22})-(6.4\times10^{23})\\
&=&5.4\times10^{24}kg
\end{eqnarray*}
$$
So it wouldn't have been more than about $5.4\times10^{24}kg$.


What are the arguments against the Feng and Gallo thin disk explanation of galactic rotation curves? The well-known galaxy rotation problem is described here. Basically (as one moves outward from the galactic centre, $R$ increasing) the observed pattern of variation in orbital speed $V$ is very different from the pattern expected on the basis of the distribution of mass inferred from detectable radiation. This is illustrated by the two curves in the following figure.

Feng and Gallo in several papers such as this 2010 article have proposed a method for modelling mass distributions in discoidal galaxies.  The method can be applied to an individual galaxy to produce a "tailor-made" mass distribution which (by applying basic Newtonian physics) predicts a galactic rotation curve matching the curve observed for the galaxy. They explain the failure of other attempts, using "ordinary" physics, to predict observed galactic rotations on the use of crude luminosity:mass assumptions and on the inappropriate application of Keplerian models to galaxies.

"Mysterious" explanations of the galaxy rotation problem such as Dark Matter  and MOND are still being considered seriously. Presumably therefore Feng and Gallo's ideas are not widely accepted.  What are the reasons for the rejection of their explanations?

Feng & Gallo have published a series of extremely similar papers, all of which essentially claim that they have "discovered" a major flaw in the way (some) astrophysicists think about rotation curves. Instead of assuming spherical symmetry, they try to solve for the mass distribution, using a rotation curve, without assuming spherical symmetry, instead adopting a planar geometry with cylindrical symmetry.

Of course they do have a point; statements that the flat rotation curve can be compared with a Keplerian prediction (that assume spherical symmetry, or that all the mass is concentrated at the centre) are overly simplistic. So far so good, but they then go on to claim that their analysis is compatible with the total stellar mass of galaxies and that dark matter is not required.

So, in their planar model (and obviously this is open to criticism too) they invert rotation curves to obtain a radially dependent surface density distribution that drops pseudo-exponentially.

Problem 1: They concede (e.g. in Feng & Gallo 2011) that "the surface mass density decreases toward the galactic periphery at a slower rate than that of the luminosity density. In other words, the mass-to-light ratio in a disk galaxy is not a constant". This is an understatement! They find exponential scale lengths for the mass that are around twice (or more for some galaxies) the luminosity scalelengths, so this implies a huge, unexplained increase in the average mass to light ratio of the stellar population with radius. For the Milky way they give a luminosity scalelength of 2.5 kpc and a mass scale length of 4.5 kpc, so the $M/L$ ratio goes as $\exp[0.18r]$, with radius in kpc (e.g. increases by a factor 4 between 2 kpc and 10 kpc). They argue this may be due to the neglect in their model of the galactic bulge, but completely fail to explain how this could affect the mass-to-light ratio in such an extreme way.

Problem 2: In their model they derive a surface mass density of the disk in the solar vicinity as between 150-200 $M_{\odot}/pc^2$. Most ($\sim 90$%) of the stars in the solar neighbourhood are "thin disk" stars, with an exponential scale height of between $z_0= 100-200$pc. If we assume the density distribution is exponential with height above the plane and that the Sun is near the plane (it is actually about 20pc above the plane, but this makes little difference), a total surface mass density of $\sigma = 200M_{\odot}/pc^2$ implies a local volume mass density of $\rho \simeq \sigma/2z_0$, which is of order $0.5-1 M_{\odot}/pc^3$ for the considered range of possible scale heights.  The total mass density in the Galactic disk near the Sun, derived from the dynamics of stars observed by Hipparcos, is actually only $0.076 \pm 0.015 M_{\odot}/pc^3$  (Creze et al. 1998), which falls short of Feng & Gallo's requirements by an order of magnitude. (This does not bother the cold, non-baryonic dark matter model because the additional (dark) mass is not concentrated in the plane of the Galaxy).

Problem 3: For the most truncated discs that they consider, with an edge at $r=15$ kpc, the total Galaxy mass is $1.1\times10^{11}\ M_{\odot}$ (again from Feng & Gallo 2011 ). The claim is then that this "is in very good agreement with the Milky Way star counts of 100 billion (Sparke & Gallagher 2007)". I would not agree. Assuming "stars" covers the full stellar mass range, then I wouldn't dissent from the 100 billion number; but the average stellar mass is about $0.2\ M_{\odot}$ (e.g. Chabrier 2003), so this implies $\sim 5$ times as much mass as there is in stars (i.e. essentially the same objection as problem 2, but now integrated over the Galaxy). Gas might close this gap a little, white dwarfs/brown dwarfs make minor/negligible contributions, but we still end up requiring some "dark" component that dominates the mass, even if not as extreme as the pseudo-spherical dark matter halo models. Even if a factor of 5 additional baryonic dark matter (gas, molecular material, lost golf balls) were found this still leaves the problem of points 1 and 2 - why does this dark matter not follow the luminous matter and why does it not betray its existence in the kinematics of objects perpendicular to the disc.

Problem 4: Feng & Gallo do not include any discussion or consideration of the more extended populations of the Milky Way. In particular they do not consider the motions of distant globular clusters, halo stars or satellite galaxies of the Milky Way, which can be at 100-200 kpc from the Galactic centre (e.g. Bhattachargee et al. 2014). At these distances, any mass associated with the luminous matter in the disk at $r \leq 15$ kpc can be well approximated using the Keplerian assumption. Proper consideration of these seems to suggest a much larger minimum mass for the Milky way independently of any assumptions about its distribution, though perhaps not in the inner (luminous) regions where dark matter appears not to be dominant and which is where F&G's analysis takes place. i.e the factor of 5-10 "missing" mass referred to above may be quite consistent with what others say about the total disk mass and the required dark matter within 15kpc of the Galactic centre (e.g. Kafle et al. 2014). To put it another way, the dynamics of these very distant objects require a large amount of mass in a spherical Milky Way halo, way more than the luminous matter and way more even than derived by Feng & Gallo. For instance, Kafle et al. model the mass (properly, using the Jeans equation) as a spheroidal bulge, a disk and a spherical (dark) halo using the velocity dispersions of halo stars out to 150 kpc. They find the total Galaxy mass is $\sim 10^{12} M_{\odot}$ and about 80-90% is in the spherical dark halo. Yet this dark halo makes almost no contribution to the mass density in the disk near the Sun.

Problem 5: (And to be fair I do think this is beyond the scope of what Feng & Gallo are doing) Feng & Gallo treat this problem in isolation without considering how their rival ideas might impact on all the other observations that non-baryonic dark matter was brought in to solve. Namely, the dynamics of galaxies in clusters, lensing by clusters, the CMB ripples, structure formation and primordial nucleosynthesis abundances to state the obvious ones. A new paradigm needs to do at least as well as the old one in order to be considered competitive.


Explanation of Longitude of Periapsis I'm looking for a mathematical justification of the longitude of periapsis as it makes no mathematical sense to me as a notion. By definition, it is the sum of the argument of periapsis and the longitude of the ascending node, each of which makes sense on their own.  I understand these latter two notions geometrically. But I don't know what the longitude of periapsis is supposed to represent.  The longitude of the ascending node is an actual angle measured within the ecliptic, while the argument of periapsis is an actual angle measured within the given bodies orbital plane.  These two planes are skewed with respect to one another by an inclination angle.  Thus, you cannot mathematically just add the two angles together; it geometrically has no representation.  At least not without making certain unmentioned assumptions which cannot possibly be true for all bodies.  I cannot make sense of why it seems to be the preferred orbital parameter.

This question is not a duplicate of What is exactly the "longitude of the perigee". The two-sentence afterthought regarding this topic therein doesn't adequately respond to the spirit of my question. I'm looking for a mathematical justification for its use, including why its regarded as more accurate than splitting up the angles into their separate components.

I agree that the common explanation of the longitude of periapsis, as the question gave it, appears at first sight to make no sense -- because it constructs a sum of two angles in two different planes, and that seems at first sight to lack geometrical meaning.

In fact the fault, if any, is in the explanation rather than in the geometry. It is not so difficult to show a geometrically sensible construction for the longitude of periapsis, without adding any angles in different planes. But before showing this, it may be worth answering the question 'Why do it at all, what's the point?'.

At this point the present answer links up with the answer given by James K.  One of the uses of such a construction came to attention in the early days of astrodynamics. When programmed orbit calculations are to be done for artificial space objects, the orbits to be calculated can in principle have any values whatever of the inclination and eccentricity, in principle down to zero.  When either or both of these orbital quantities approaches zero, then the position of the node and/or the periapsis, or else computations involving them, can become in practice numerically ill-defined, or anyhow show some undesired numerical behavior. As a result of the difficulty, searches were made a long time ago now, for alternative systems of orbital elements that do not generate undesired numerical behavior at zero or near-zero values of inclination or eccentricity.

The resulting formulae for orbital equations, usable for low-inclination, low-eccentricity orbits, typically made use of devices that included the equivalent of replacing the anomaly of an orbiting object by its longitude from a defined initial point, and replacing the argument of periapsis by a corresponding longitude from the initial point.  The development of orbital equations in terms of such quantities can usefully be generated, or at least illustrated, by the following construction that also provides an in-plane account of the longitude of periapsis, the subject of the question.

Sources for the geometry and formulae connected with this kind of development include R M L Baker (1967) 'Astrodynamics', especially Appendix C, and applications are shown for example in A E Roy, 'Orbital Motion' (especially 4th ed., 2005) (or google for other sources of the same title), especially chapter 8, Special Perturbations, section 8.5, for perturbational equations and their derivation.

Baker's 'Astrodynamics' illustrates the definition for these purposes of an alternative ('F G W') coordinate system.  See the figure below.

One starts with ordinary rectangular coordinate axes defined by points X, Y, Z on a unit sphere with center O, where the xy plane is for example the ecliptic plane, and OX is in a chosen initial direction, e.g. towards the equinox of date.  Define an orbital plane through F N G, intersecting the xy-plane at node N with inclination angle $i$ .  Angle XON is then the longitude $\Omega$ of node N. Define axis OW perpendicular to orbital plane F N G. Let angle FON = XON, and let angle FOG = 90°. Then make F the initial point of coordinate system FGW. In this coordinate system, the longitude of the orbital periapsis starting from the initial point is FOP, which is the sum, as usual, of $\Omega$ the longitude of the node FON and $\omega$ the argument NOP of periapsis, but now they are measured in the same plane -- which was the thing to be illustrated.

This FGW system can be conveniently oriented by the coordinates of point W, the pole of the orbital plane,
which has coordinates (in terms of the x,y,z axes and the quantities $i$ and $\Omega$) of

$ W_x =  + \sin (\Omega) . \sin (i) $ ,
$ W_y =  - \cos (\Omega) . \sin (i) $ ,
$ W_z =  \cos (i) $ .

Then initial point F can be shown (with no difficulty but at a little length) to have coordinates relative to initial axes x, y, z, of

$ F_x = 1 - W_x^2 / (1 + W_z) $ ,
$ F_y =  - W_x W_y / (1 + W_z) $ ,
$ F_z =  - W_x $ .

Quantities Wx, Wy, Wz are sometimes identified as $h_x/h_m, h_y/h_m, h_z/h_m,$ and can be called direction cosines made by the orbital angular momentum vector (in direction OW) with axes x, y, z.

You might also find some of the formulae useful in Preliminary orbit-determination method having no co-planar singularity by R M L Baker and N H Jacoby, Celestial Mechanics 15 (1977) 137-160.


How did we first determine the Earth's departure from sphericity? I'm quite interested to know the history of the study of the Earth's departure from spherical symmetry. What were the first methods used to model the non-spherical geometry of the Earth? For example, there are geodesy satellite and missions used now to determine the gravity field of the Earth but that is "recent" technology. They obviously had other methods prior to this.

Isaac Newton was the first to put it together and realized the Earth had an oblate shape in 1687.    See 1672 - Wikipedia.

In 1666 Robert Hooke reasoned that pendulums could measure variation in gravity, but this remained unobserved until 1671, when Jean Richter observed that pendulums kept different time near the equator (French Guiana compared to Paris).

Around that time, 1673, Christian Huygens observed that the wide swing of a pendulum would move in a very slight oval, so to make pendulum clocks more accurate, the swings were kept to a low angle and the swing kept perpenducular   That, however, has to do with the Earth's rotation, but not your question specifically.

Newton was the first to put it all together that the observed gravitational fluctuation was due to the equatorial bulge and faster speed of rotation near the equator.    Article here also credits him with being the first.

Also, related:   https://en.wikipedia.org/wiki/History_of_geodesy


How to read an eclipse chart? NASA has a page dedicated to lunar eclipses and provides charts. How are these charts to be read? What do P1, P4, U1,... mean? What about the world map below?

Click for full size view

'P' is the penumbra, the zone where the Earth blocks some, but not all, of the Sun's light from reaching the Moon. 'U' is the umbra, the zone where the Earth blocks all of the light from the Sun (see this primer). As the Moon moves across the two zones then you will get various times as the Moon touches those zones. So P1 is where the Moon just starts to touch the penumbral shadow, U1 is where the Moon just touches the umbral shadow cone, U2 is where all the Moon is inside the umbral shadow and the total eclipse begins. Similarly U4 and P4 are where the Moon last touches the umbral and penumbral shadows. Note that the times in the chart are in Universal Time so you need to account for your timezones' difference from UTC.


Polar satellites for Global Navigation Systems Why do we need 7 polar satellites for a navigation system like the Indian Regional Navigation Satellite System (IRNSS)?

IRNSS
is intended to serve an area spanning 100 degrees in longitude by 80 degrees in latitude.
Anywhere in that service area, at any time, a receiver needs to compare distances to four of the satellites.
To determine latitude, the satellites can't all be above the equator, so some of the orbits are inclined 29$^\circ$. Those satellites oscillate north-south in pairs. Polar orbits aren't needed; global systems serve the poles with orbits inclined only 55$^\circ$.


Why do pre-main sequence stars show lithium in absorption? This paper and this paper state without discussion that the presence of lithium absorption in the stars they observe as strong evidence of these stars being pre-main sequence stars. Because they state this without any discussion and justification, I assume that it's a commonly known and accepted fact.  The second of the two papers also state without discussion or justification that some observed strong H$\alpha$ emission was also evidence of the stars being pre-main sequence stars.

Googling around I was able to get a partial answer for why this is so.  Pre-main sequence stars retain their primordial lithium as they collapse, but at some point around when they become main sequence stars, the lithium in their photospheres is destroyed by fusing with protons. I haven't been able to find anything describing why H$\alpha$ emission is associated with pre-main sequence stars, other than this has been known for a very long time (since before at least 1945).

I am wondering

What is it about becoming a main sequence star that causes the lithium to fuse with protons near the surface?
How fast is the lithium destroyed, and does this destruction occur right when the star enters the main sequence?  I'm wondering how definite the presence of lithium absorption is in saying whether a star has entered the main sequence or not.
Why is H$\alpha$ emission such a prominent feature of pre-main sequence stars?

As pre-main sequence (PMS) stars contract towards the main sequence, their cores become hotter.

Lithium is turned into helium by proton capture reactions. These are initiated in the core at temperatures of around 3 million K, so much lower than for hydrogen burning.

At the same time, PMS stars, or at least the type of low-mass pre-main sequence stars that are being referred to here, are fully convective and this mixes material inside the star rapidly and effectively.

Thus the sequence of events is that the PMS star contracts; the core reaches $3\times 10^{7}$ K at some point before the main sequence; Li is destroyed by proton capture; the Li-depleted is completely mixed with the rest of the star.

In this way Li can be rapidly and totally destroyed on a timescale that depends on the mass of the PMS star. It is as short as 10 Myr for a star like the Sun, increasing to about 100 Myr for a star of $0.1 M_{\odot}$.

That is the basic picture, but there is a wrinkle for stars with $M>0.4M_{\odot}$, where the core becomes radiative rather than convective before they reach the main sequence, but after Li burning has commenced. The radiative core pushes outwards and its  base then drops below $3\times 10^{6}$ K. This means that although Li destruction runs to completion in the core, at least some Li can be preserved in the outer layers of such stars.

Li is therefore an extremely complicated function of age and mass. But for the purposes of identifying low-mass PMS stars we can clearly say that anything that shows strong lithium signatures is probably younger than 100 million years if it is below about $0.5 M_{\odot}$ (or equivalently is a K- or M-type star).

If you want much more detail, see my review article on Pre-main sequence Lithium depletion.

The H$\alpha$ emission of PMS stars is connected with their youth. It can arise in two ways. The first is associated with accretion from a circumstellar disc. This is caused by gas falling from the disk onto the star and heating up. The H alpha emission can be very strong and very doppler broadened ($>300$ km/s). As pre-main sequence discs only survive for 10 million years or less, then this is a very clear signature of a pre main sequence star.

On the other hand, young stars that have lost their discs also show strong (though not as strong as accretion-related emission) H$\alpha$ emission that is caused by non-radiative, magnetic heating of their chromospheres. This magnetic activity is associated with convective, rapidly rotating stars. Pre main sequence stars possess both these properties. Thus PMS stars must exhibit H$\alpha$ emission of some sort.


Does the Moon have any oxygen in its atmosphere? Since the moon has gravity, it's almost impossible that there aren't some gasses trapped on the surface by the moon's gravity. Has any free-floating oxygen been found on the Moon? If so, in what concentration?

The Moon's atmosphere is very thin compared to the Earth, so thin that it is usually said to have no atmosphere.  The Moon's gravity is not strong enough to retain lighter elements, so they escape into space.

Apollo 17 carried an instrument called the Lunar Atmosphere Composition Experiment (LACE).  Oxygen is not listed as one of the elements it found on this NASA web page.  The principle gases found were neon, helium and hydrogen.  Others included methane, carbon dioxide, ammonia, and water.  Additionally, ground instruments have detected sodium and potassium in the lunar atmosphere.

The recently launched Lunar Atmosphere and Dust Environment Experiment (LADEE - pronounced laddie, not lady) should be able to tell us more soon.

Update:
According to this article at Spaceflight Now, LADEE did detect oxygen in the Moon's atmosphere.


Did comets 266P/Christensen or P/2008 Y2 (Gibbs) cause the Wow! signal? Continuing my fascination with the Wow! signal, I stumbled upon an article from 2016 titled Famous Wow! signal might have been from comets, not aliens.

It describes the hypothesis that the signal might have been generated by an (at the time) unknown comet. Quoting from the article:

  Antonio Paris […] thinks the signal might have come from one or more passing comets. He points the finger at two suspects, called 266P/Christensen and P/2008 Y2 (Gibbs).

…and:

  To test his idea, Paris proposes looking at the same region of space when the comets are back. Comet 266P/Christensen will transit the region first, on 25 January 2017, then P/2008 Y2 (Gibbs), on 7 January 2018. An analysis of the hydrogen signal of the comets should reveal if he is correct.

(emphasis mine)

It has now been two years since these comets came back, and I would be surprised if this hypothesis was not tested. Assuming it was tested, what were the results?

This hypothesis was put forth by Paris Antonio in the paper "Hydrogen Clouds from Comets 266/P Christensen and P/2008 Y2
(Gibbs) are Candidates for the Source of the 1977 “WOW” Signal".

As you correctly suspected, he tested his theory in 2017 leading to the paper "HYDROGEN LINE OBSERVATIONS OF COMETARY SPECTRA AT 1420 MHZ". In this paper he claimed to have detected a radio signal from the comets and concluded that they were the source of the WOW-signal.

It seems like this paper has mostly been ignored by the community as it is, lets say, not very convincing.
It appeared only on arXiv and the "Washington Academy of Sciences". I am not familiar with the latter one, but judging from the paper, it has not been peer-reviewed.

I will let the following sentence of the paper speak for itself:

  The data collected was saved using the spreadsheet output format option of the SpectraCyber software and
  imported into Microsoft Excel as a text file. The data were then replotted and interpreted using the Chart
  Wizard feature in Microsoft Excel and converted into JPEG format

There is also this response to the paper, which makes very clear why it did not get any more attention:

  This is a statement regarding the claim that the “WOW!” signal was caused by hydrogen emission from an unknown comet or comets. It points out inaccuracies which are fatal to the theory that the “WOW!” signal was caused by a slow-moving comet. It also points out missing details from the author’s paper.

  The staff of the OSU Radio Observatory has examined the paper by Paris regarding the “WOW!” signal (Paris, Antonio. HYDROGEN LINE OBSERVATIONS OF COMETARY SPECTRA AT 1420 MHZ) and comet 266/P Christensen.

  We conclude that comet 266/P Christensen is not the source of the “WOW!” signal for a number of reasons.

  Using the ephemeris at:
  http://ssd.jpl.nasa.gov/horizons.cgi?find_body=1&body_group=sb&sstr=266P%20
  we see that Comet 266/P Christensen, at the time the “WOW!” signal was observed in 1977, was nowhere near the position of “WOW!”. (all positions are J2000).
  “WOW!” was at:        RA 19h 25m 31s  or  19h 28m 22s        Dec -26 deg 57’
  266/P was at:        RA 18h 32m 15s                        Dec -27deg 22’.
  The declination is near but the right ascension is nearly an hour off, placing 266P in a different part of the sky when the WOW! signal was observed.
  Another comet, P/2008 Y2 was closer, at:  RA 18h 39m 39s.        Dec -29 deg 38’
  The declination was almost 3 degrees off and the right ascension 47 minutes off, placing P/2008 Y2 in a different part of the sky when the WOW! signal was observed.
  It is important to point out that the OSU telescope beamwidth in right ascension was only about 3 minutes (of time), but the comets were 47 and 55 minutes (of time) away. The comets would have passed thru the OSU telescope beam roughly 55 and 47 minutes (of time) earlier.
  The observations of the comet made by the author in 2017 near the position of the “WOW!” object are irrelevant, because that is not where the comet was in 1977 when the “WOW!” signal was observed.
  The author does not cite any references regarding observations of hydrogen emission from comets. We have contacted a comet expert and a hydrogen expert and they are both unaware of any hydrogen emission ever having been observed from a comet.
  The author does not cite any references of variable emissions from comets. Such variability would have to be incredibly unusual to match the “WOW!” signal. The signal would have to be exactly constant at 30 sigma for 2 minutes since it matched the OSU antenna beam exactly. It would also need to be less than 0.5 sigma for 2 minutes, at a time 3 minutes earlier or later, since it did not appear in the other OSU beam.
  The author does not show any specific frequencies in the spectrum plots so it is impossible to compare them with the “WOW!” frequency, or to demonstrate that the comet signal bandwidth is less than the 10kHz bandwidth of the WOW! signal.

  Dr. Robert S. Dixon
  Director, Ohio State University SETI Program

So it seems that this hypothesis was already excluded before it was tested. This is already briefly mentioned in the article you linked to.
And while it is not clear (to me) what exactly he measured during his observation, it was most likely not the same thing that caused the WOW! signal.


Gravitational tidal force problem if we have spherical mass held by its self-gravity, there will be a limit to distance - let's say it is $r$ - that the center of this body may approach a much more massive body (lets we call $M$ body).

Our spherical mass here would be held - as I understand - by gravitational tidal force. But the question is what is the distance $r$ between to masses his effect will hold?

$$r=\left(\frac{2M}{m} \right)^{1/3} \times R$$

$m$ - Spherical body mass

$R$ - Spherical body radius

$M$ - Massive body

I guess this is the equation for this limit, but I don't understand the conditions of this limitation.

That equation is the Roche limit. It pertains to objects that are held together by self-gravitation only. No chemical bonds allowed! For example, an artificial satellite in low Earth orbit is almost inevitably going to be well within the Roche limit for that satellite. For example, the Roche limit for the ISS is almost halfway to the Moon. The ISS isn't being torn apart by tidal forces.

The kinds of bodies that this limit does apply to include rubble pile asteroids and comets. For example, comet 67P/Churyumov-Gerasimenko, currently being investigated by the Rosetta spacecraft, has some rubble pile characteristics to it. An even better example is comet Shoemaker–Levy 9, which was torn apart into more than 20 pieces before it collided into Jupiter.


Is the Ordovician meteor event detectable in the lunar cratering record? Approximately 468 million years ago there were a large number of L-chondrite meteorites falling to Earth. This is called the Ordovician meteor event and was probably the result of a large collision in the asteroid belt.

Does the lunar cratering record also show evidence of this event?

The very, very short answer to your question is: "Not that's detectable by any current methods or data that we have."
The longer answer has to do with how we know how old anything is on the Moon or other planetary surfaces.  What we do is we use craters themselves to date a surface: The more craters, the older the surface because it's been around longer to accumulate those craters.  We can tie to those to an absolute age by saying that X rock sample collected by Apollo or Luna or Chang'e is Y years old (dated via radiometric methods) and it is from a surface that has Z craters.  Do this a lot and you can build up a function that relates the number of craters to an age.
The problem comes in using this to date any specific craters to try to find a non-uniform function (e.g., an age spike):  You have already assumed a crater chronology function that does NOT have that spike, so using it to find a spike becomes a circular argument that is very difficult to get out of.  There are some proposals on how to do that, but they're based on models and not actual data (such as, the large objects that form large craters would show those spikes, but the small objects that form small craters are a steady "clock" of impacts).
Right now, the lunar crater chronology has roughly a dozen points on it, so we don't have the resolution to say anything about a spike ≈468 million years ago.  It is certainly possible (likely, even) that the lunar crater record would show that spike if we had the resolution to measure it by dating many more craters through methods other than superposed crater measurements, and, indeed, it is generally assumed that the lunar crater chronology really should have lots of little spikes in it when asteroids break up / asteroid families form, but again we just don't have the data to really measure that ... yet.


Moon Images from Earth Is there a resource online of images of the moon (taken from the Earth) suitable for processing with a computer: I.e. taken with the same camera, optics, location, etc, over months/years?

Purpose: This paper looks at reconstructing the image of the Earth by looking at earthshine on the moon, but only considers a simulation. I was wondering whether it would actually work. Also I feel that there is a lot of info that the paper didn't use (and also I wonder what some machine learning techniques might achieve). One would also need historic images of the Earth (for training the system, re cloud cover).

If such a dataset doesn't exist, would it be something that could be collected? (the telescope clearly doesn't need to be very powerful, the photo exposure wouldn't take long, etc).

I occasionally view the Earth illuminated side of the new and old moons with my Mallincam electronic eyepieces. Unlike the sun illuminated side there are no shadows in the view but the features do stand out quite clearly.

There is little if any contrast across the view that the eye can perceive. Other than looking with the eye I have never attempted any processing of an image so anything is possible.

I think I understand the concept. The earthshine should be different based on what part of the earth is facing the moon.

Unfortunately the Earth's cloud cover will probably have more effect on the earthshine than the surface itself.

There are thousands of astro images on the Mallincam.io forum. Ask the group if there are any earthshines in the files. If not someone might provide you with a few.

https://groups.io/g/MallinCam


Generating random galaxy catalogs for correlation functions The galaxy correlation function, when computed directly from a galaxy catalog, relies on computing a randomly generated counterpart catalog.

When dealing with a simulated galaxy mock-catalog, where the sample of galaxies is roughly uniform over a large box (e.g. the galaxy mocks created from Millennium/Millennium II), the random catalog can be just be a uniform distribution of points in the same volume as the real data.

However, real-world galaxy catalogs are not homogenous boxes, and have very irregular shapes and observationally induced redshift and angular distributions. Even some mock-catalogs are endowed with these properties to better represent real data. In these cases, how is a random catalog best produced? With some sort of probability distribution in coordinates which attempts to mimic the "non-physical" (i.e. not due to observational constraints) part of the distribution? Or a simple binary mask which filters out empty regions, but otherwise leaves the random catalog uniform.

If the answer is that some nonuniform distribution should be used, is there a usual method for doing so? The literature I have found (e.g. for the SDSS published data, and for galaxy mocks mimicking SDSS's constraints) does not discuss this in any way. Note, if this is a highly involved process beyond a brief summary and a source or two, I do not expect a full answer here. Rather, I am trying to determine if there is an existing set of standard methods which are documented but have eluded me thus far.

Generating random galaxy catalogs for correlation functions
... the random catalog can be just be a uniform distribution of points in the same volume as the real data.
However, real-world galaxy catalogs are not homogenous boxes, and have very irregular shapes and observationally induced redshift and angular distributions. Even some mock-catalogs are endowed with these properties to better represent real data. In these cases, how is a random catalog best produced? ...
If the answer is that some nonuniform distribution should be used, is there a usual method for doing so? The literature I have found (e.g. for the SDSS published data, and for galaxy mocks mimicking SDSS's constraints) does not discuss this in any way. Note, if this is a highly involved process beyond a brief summary and a source or two, I do not expect a full answer here. Rather, I am trying to determine if there is an existing set of standard methods which are documented but have eluded me thus far.

For SDSS see:

"Large scale correlations in galaxy clustering from the two degree field galaxy redshift survey" (2006), by N. L. Vasilyev, Yu. V. Baryshev and F. Sylos Labini.

"The SDSS Galaxy Angular Two-Point Correlation Function" (12 Mar 2013), by Y. Wang, R. J. Brunner, J. C. Dolence. The include their SQL query to the SDSS catalog archive server:

1 INTRODUCTION
One of the most powerful and simplest probes of the galaxy distribution is the two-point angular correlation function, which quantifies the excess probability above a random distribution of finding one galaxy within a specified angle of another galaxy. For the case of a Gaussian random field, the two-point angular correlation function and its Legendre transform pair provide a complete statistical characterization of the galaxy clustering (see, e.g., Peebles 1980). Even for the case of non-Gaussianity, the two-point angular correlation function provides a simple and important statistical test of galaxy formation models (Tegmark et al. 2004). The two-point angular correlation function has been studied at bright magnitudes from the data releases from the Sloan Digital Sky Survey (SDSS) such as the Early Data Release (EDR; Connolly et al. 2002).
...
To accurately calculate the galaxy two-point angular correlation function, we must first minimize potential systematic effects in the galaxy catalog used to measure the correlation function. The systematics of the SDSS EDR were thoroughly studied by Scranton et al. (2002). To minimize the systematic effects of seeing and Galactic extinction, they determined that the SDSS EDR galaxy sample had to be masked to exclude regions with seeing greater than 1."75 and reddening > 0.2 magnitudes. Given the importance of minimizing the impact of systematic effects on the galaxy two-point angular correlation function and the significant changes that were made in the SDSS data processing pipeline between the SDSS EDR and the SDSS DR7, we have repeated many of the tests presented in Scranton et al. (2002) by using the SDSS DR7 data. In this paper we present the methods used to contain these systematic effects, the results of these systematic tests, the actual galaxy two-point angular correlation function for the SDSS DR7, and our massively parallel implementation that rapidly calculates correlation functions for large data sets.

Also: "The galaxy correlation function and power spectrum" (.PDF).
Wikipedia's "Correlation function (astronomy)".
CalTech: "Measurements of Clustering" (Use [Next] or [Contents] buttons to view all the pages).
There are fixups applied to the raw data to correct for redshift and angular diameter distance.

For example catalogs and a description of the procedures see Shaun Cole's website: "Mock Galaxy Redshift Catalogues" where software and full details of the N-body simulations and the contruction and properties of the mock catalogues is provided for both 2dF Galaxy Redshift Survey (2dFGRS)  and SDSS galaxy redshift surveys.
Halo bias relation to dark matter and N-body simulations are discussed in "BAM: Bias Assignment Method to generate mock catalogs" (15 June 2018), by A. Balaguera-Antolínez, Francisco-Shu Kitaura, Marcos Pellerejo-Ibañez, Cheng Zhao, and Tom Abel.
Also check out the (under construction, and too busy working and writing papers) website: "The Carnegie-Irvine Galaxy Survey (CGS)" - with missing papers available on arXix:
"The Carnegie-Irvine Galaxy Survey. I. Overview and Atlas of Optical Images"
"The Carnegie-Irvine Galaxy Survey. II. Isophotal Analysis"
"The Carnegie-Irvine Galaxy Survey. III. The Three-Component Structure of Nearby Elliptical Galaxies"
"The Carnegie-Irvine Galaxy Survey. IV. A Method to Determine the Average Mass Ratio of Mergers That Built Massive Elliptical Galaxies"
"The Carnegie-Irvine Galaxy Survey. V. Statistical study of bars and buckled bars"
"The Carnegie-Irvine Galaxy Survey. VI. Quantifying Spiral Structure"
"The Carnegie-Irvine Galaxy Survey. VII. Constraints on the Origin of S0 Galaxies from Their Photometric Structure"


How did Ole Christensen Romer measure the speed of light? How did Ole Christensen Rømer, who in 1676, shortly after Galileo's death, was said to have measured the speed of light as 220,000 km/s by timing the orbits of Io around Jupiter?

My only guess is the moon Io orbiting Jupiter is simply a clock. It pulses away with an orbital period of 42 hours and provides to the earth, 21 hours of light each orbit; this does not change. Now, as viewed from "above" we go counterclockwise around the sun, and as we move towards Jupiter, the duration of light from Io would be less than 21 hours, whereas if we are moving away from Jupiter, the duration of light from Io would be more than 21 hours. Suppose we measure the time from Io's first appearance from behind Jupiter to its reappearance and call that its observed orbital frequency $f$ as opposed to its actual orbital frequency ${f_o}$ which is 1/42 hours.

He must have figured out the Doppler effect and this equation...
$$f = \left( {1 + \frac{{\Delta V}}{C}} \right){f_o}
% MathType!MTEF!2!1!+-
% faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbItLDhis9
% wBH5garmWu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8sr
% ps0lbbf9q8WrFfeuY-ribbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-
% yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dc9Gqpi0d
% meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbGaeyypa0Zaae
% WaaeaacaaIXaGaey4kaSYaaSaaaeaacqqHuoarcaWGwbaabaGaam4q
% aaaaaiaawIcacaGLPaaacaWGMbWaaSbaaSqaaiaad+gaaeqaaaaa!3BBB!
$$

I hashed through the numbers myself and I got an answer of about 10 minutes more or less from 42 hours depending on which way the earth is heading with reference to Jupiter.

Ole Rømer did not measure a change in the frequency of light. He measured an apparent change in the orbital period of Io, one of Jupiter's moons.

The orbit of Io can be measured very accurately by observing when it enters or leaves the shadow of Jupiter. When the Earth is moving away from Jupiter, Rømer noted that the orbit of Io appeared to be very slightly longer than when the Earth was moving parallel to Jupiter.

Suppose the orbital period of Io is $p$ seconds. If you are not moving and you observe an eclipse at time $t$, the next eclipse will be at time $t+p$. However, if you are moving away from Io, the next eclipse will be seen at $t+p+x$, where $x$ is the time that light takes to travel from your position at time $t$ to your position $p$ seconds later.

The delay over a single orbit was too small for him to measure (about 30 seconds). But the delay was cumulative, and over about 30 orbits of Io, the orbit was delayed by about a quarter of an hour. He noted:

  [This] appears to be due to light taking some time to reach us from the satellite; light seems to take about ten to eleven minutes [to cross] a distance equal to the half-diameter of the terrestrial orbit.

Of course, Rømer didn't know the actual size of the half-diameter of the terrestrial orbit (the astronomical unit) However putting the modern value of about 150 million km this gives a value of the speed of light at about 220000km/s, which is not so far from the modern value of about 300000km/s


Why doesn't smashing larger and larger bodies incrementally into a rocky planet create a star? Let's start with a stationary Earth. If we smash a few Mercury-sized objects into the Earth, the Earth begins to accrete mass. Repeat this step with larger and larger objects, until we start impacting Jupiters into the growing Earth. If we cause an even larger planet to crash into the Earth (say, a 3-Jupiter mass object), we will eventually reach the boundary between planets and brown dwarfs. If we continue accreting more Jupiter-sized objects to the Earth, we will pass the brown-dwarf limit of 90 Jupiter masses, we will reach stellar masses. But instead of turning into a star, this object either stays molten as a "planet", blows itself apart, or even collapses into a black hole. I tested this in Universe Sandbox 2 about 20 times, and none of them coalesced into a star. Why does this happen, and would this be realistic?

Who can say for sure? I guess the physics in Universe Sandbox is not good enough.
What I would say though is that if you have a "protostar" that contains a higher proportion of heavy elements than a usual star, then the threshold for ignition of hydrogen will be lower than 75 Jupiter masses (e.g. How large can a ball of water be without fusion starting? ). If on the other hand it contains very little hydrogen (not enough to sustain a significant main sequence reaction rate), then it will be forced to rely on He, C or even O burning that require significantly higher temperatures and a much more massive object - probably in the region of 1000 Jupiter masses.
However, if you are telling us that some of your simulations collapse into a black hole at 90 Jupiter masses, that suggests that a more simple explanation is that the simulation physics is incorrect. I also think it would take a very peculiar composition indeed to avoid a nuclear burning phase prior to collapse to a black hole, even if you give the object several stellar masses of material.


Why haven't detected life in the universe? It would seem that if life were relatively common in the universe that there would be a cacophony of noise somewhere in the electromagnetic spectrum. Is life so rare and distant that the waves haven't reached us yet, or have they attenuate out, or are they unintelligible, or are we the first, or are we alone?

To quote a favourite movie of mine

  Pardon me sir, but it's a big-ass sky.

Our current method of detecting life (electromagnetic signals) is by targeting and scanning stars indivdually using radio telescopes.

This method is pretty costly because we don't have a huge amount of them and they can be better used for other (proper) research purposes.  Basically, it costs a lot to monopolise a telescope's resources by repeatedly pointing it at stars without a reasonable hope of a result.  Understandably, astronomers want to keep their funding by producing results rather than nothing.

The current estimates is that we can stumble upon signals by about 2040

Source

  By 2040 or so, astronomers will have scanned enough star systems to give themselves a great shot of discovering alien-produced electromagnetic signals, said Seth Shostak of the SETI (Search for Extraterrestrial Intelligence) Institute in Mountain View, Calif.

But again, this is pure guesswork.

A related question here on SE asks this same question from another direction

how far away could we detect that Earth has life?

One of the answers, quoted in part:

  A "blind" search could look for radio signatures and of course this is what SETI has been doing. If we are talking about detecting "Earth", then we must assume that we are not talking about deliberate beamed attempts at communication, and so must rely on detecting random radio "chatter" and accidental signals generated by our civilisation. The SETI Phoenix project was the most advanced search for radio signals from other intelligent life. Quoting from Cullers et al. (2000): "Typical signals, as opposed to our strongest signals, fall below the detection threshold of most surveys, even if the signal were to originate from the nearest star". Quoting from Tarter (2001): "At current levels of sensitivity, targeted microwave searches could detect the equivalent power of strong TV transmitters at a distance of 1 light year (within which there are no other stars)...". The equivocation in these statements is due to the fact that we do emit stronger beamed signals in certain well-defined directions, for example to conduct metrology in the solar system using radar. Such signals have been calculated to be observable over a thousand light years or more. But these signals are brief, beamed into an extremely narrow angle and unlikely to be repeated. You would have to be very lucky to be observing in the right direction at the right time if you were performing targeted searches

I'd really recommend reading the rest of this answer, and other answers for this question.

So, our "noise" isn't really strong enough to be detected over long distances above the greater (and stronger) chatter of the natural universe.

While we could engineer a stronger broadcast message and hope for a reply, it's a long, long project and unlikely to be funded.


Do primary mirrors in large observatories undergo regular removal and re-coating of the aluminum? Why? Performance of astronomical mirrors that are exposed to the environment for long periods of time can experience a slow degradation of performance. They usually need to receive some kind of regular maintenance, which may involve cleaning and/or re-coating.

While I'm told that the aluminum degrades and must be replaced from time to time, this is not consistent with my understanding of the behavior of aluminum in air. I'm pretty sure that a freshly evaporated layer of pure aluminum will quickly develop a native oxide layer of perhaps 20Å of aluminum oxide as amorphous $\text{Al}_2 \text{O}_3$ (alumina) which is then pretty much impermeable to diffusion of anything else the atmosphere might expose it to, including various pollutants.

I can understand that it might in some cases ultimately be simpler to strip and replace the aluminum after a number of cleanings due to accumulated damage from the cleaning, but is there any evidence that the aluminum must be replaced due to chemical degradation of the aluminum itself?

I found this article, Reflectivity Degradation Rates of Aluminum Coatings at the CFHT, Magrath, B. 1997, Pub. Ast. Soc. Pac. 109, 303 that seems to show that - at least at one observatory location - a representative test mirror exposed to the observing environment (in the dome) that was washed once a month showed no significant degradation in reflectivity over 32 months, similarly to a mirror that remained protected but not cleaned.

However, the test mirror that was exposed and not washed showed a continuous loss in reflectivity, dropping by about 10% over the same period. A fourth test mirror undergoing regular $\text{CO}_2$ cleaning lost about 5% reflectivity.

This is a small, limited test of course, less than three years, only one location, one wavelength, and only one parameter (reflectivity). But it gives a bit of support to the idea that while mirrors get dirty and require regular cleaning, the aluminum itself may not actually deteriorate.

So I'm asking: Do primary mirrors in large observatories undergo regular removal and re-coating of the aluminum? Why?, where "why" addresses the specific need for the removal and replacement. If these primaries actually do receive regular re-coatings of aluminum, is it because the aluminum actually degrades?

I'm looking for an answer that carries some backup references. If just for example, your answer is of the form You silly goose, everybody knows aluminum tarnishes like the Dickens!, please back it up with a reference to measurements of aluminum tarnishing. Thanks!

From Magrath 1997:

GIF ("blink comparator")

From http://global.kyocera.com/fcworld/charact/chemistry/chemiresist.html - alumina can potentially be remarkably resistant to chemical attack compared to other materials - note logarithmic scale.

The individual figures:

This might not be the type of telescopes your are thinking about, but as IACTs (Imaging Atmospheric Cherencov Telescopes) in the end also measure light in (or near) the optical range, their mirrors are of similar build.

The important arrays (H.E.S.S., VERITAS and MAGIC) have, at least partially, mirrors made of glass or with a glass surfaces, coated on
the front surface with aluminium (Al) and an additional single protective layer (e.g. SiO$_2$ , Al$_2$O$_3$ ). But as they are exposed to the environment the whole time without any luxury such as protecting domes or similar, the coating degenerates pretty fast.

In the case of H.E.S.S., which is located in the Khomas Highland of Namibia, the mirrors have to endure all kinds of environmental factors, beginning with the sand from the dessert, extreme temperature changes between day and night to curious birds picking at their reflected images. So after five years the optical efficiency of the mirrors was so bad, that one could actually see ones hand through from the mirror. To prolong the lifespan of the instrument, the mirrors were refurbished with a slightly different aluminium coating. In the following image the time of the mirror recoating is marked with the blue shaded area.

Image source: https://www.mpi-hd.mpg.de/hd2012/pages/presentations/Stegmann.pdf

The degeneration for the mirrors of the other observatories mentioned above where of similar timescales and they also did some recoating campaigns.

For further information see for example the following papers, which contain some overview about the different possible techniques:

http://www.brera.inaf.it/~canestrari/pubblicazioni/pubbl44.pdf
https://arxiv.org/pdf/1406.0622

If you ever happen to be in Namibia, go visit the World's largest optical telescope:

Image source: https://www.lsw.uni-heidelberg.de/projects/hess/HESS/hessmultnu.phtml


Why isn't the moon's surface made of mini craters? I thought that the millions of mini rocks that hit the moon would cause it to be entirely cratered and not flat.
Why is the moon not like this:

why aren't craters visible in the footprint photo?

Nice question, unfortunately your analoguous experiment is not as analoguous as you might hope.
In your comparison image you are using both, not enough impactors, and a too tiny size distribution. Impactors on the Moon (or any other objects) follow a reasonably well-known size distribution where the smaller an impactor is, the more frequent collisions with those do occur.
The visible and measured / counted size distribution of craters on the Moon follows this probability law quite well (e.g. this paper (Cross, 1966), but many others get about identical results). The main difference is that in your comparison you miss all the very tiny impactors which smooth-out the surface again.
Further, the Moon is covered with loose regolith of about 45µm diameter. In the sunlight it is subject to charging and thus the Moon surface is covered by a tiny sheet of statically elevated particles. This leads to a re-distribution of the surface regolith particles, smoothing out the tiniest craters even more.
Even further, the landing sites of Apollo were carefully chosen to be the most level and crater-free places to ensure a safe landing. The amount of cratering in a particular place is also random, even when all the surface is covered by several layers of craters (this is a study for asteroids, but applies to other bodies, too).
And further more, your comparison experiment is conducted in air. That affects the formation of craters and in particular the distribution of ejecta due to friction with air, more so, the smaller the impactors get and the slower the ejecta are.


How can I calculate the right ascension of an observer on Earth's surface in the TEME frame with python.skyfield? I would like to calculate the right ascension of a point on earth as specified above with the Skyfield Python library, and I can not figure out how to do this.
I know that calculating the geocentric position of the respective Topos object at a specific time  results in a Geocentric object that has an attribute .radec; however I am not confident that this delivers the right ascension in the TEME (Earth centered inertial frame.

An Earth-centered observer looking at that point on Earth’s surface would also be looking toward the point that is the zenith for that location on Earth.
Thus, you just need to find the local sidereal time (LST) for that Earth location.  That gives you the right ascension on the meridian for that place and time.  The meridian passes through the zenith, so that would give the R.A. of the desired point.
It looks like Skyfield has a GMST (Greenwich Mean Sidereal Time) attribute for any time object you create.  To go from that to LST, convert your longitude to hours (15 degrees per hour) and subtract if it’s west, add if it’s east.
So something like this:

from skyfield.api import load
ts = load.timescale()     # Timescale object
t = ts.now()   # Time object

RA_hours = t.gmst - west_longitude_degrees/15.

where you could change to a different time if you want, and you’d have to define that longitude variable.
You’d also want to check for negative values and make sure your answer falls into the 0-24 range, adding 24 if needed.


Could there be dark matter black holes? Could dark matter compress and form black holes? Since dark matter is even more abundant than normal matter, a dark matter black hole should not be rare...right?

The problem with trying to form a black hole with dark matter is that dark matter can only weakly interact (if at all) with normal matter and itself, other than by gravity.

This poses a problem. To get dark matter concentrated enough to form a black hole requires it to increase its (negative) gravitational binding energy without at the same time increasing its internal kinetic energy by the same amount. This requires some sort of dissipative interaction between dark matter and normal matter (or itself).

The following scenario should make this clear. Suppose we have a lump of dark matter that gravitationally attracts another lump of dark matter. As the two approach each other, they accelerate and gain kinetic energy. The kinetic energy gained will be exactly enough to then separate them to a similar degree to which they started, unless some dissipative process takes place.

An example is to suppose that dark matter is weakly interacting massive particles (WIMPs). WIMPs are gravitationally drawn towards the centres of stars. If the weak interactions happen sufficiently frequently then it might be possible for them to accumulate in stars, rather than shoot through and out the other side.

It has been hypothesised that black holes could be made like this near the centre of a Galaxy, seeded by dense neutron stars. The density of neutron star matter, combined with the enhanced density of dark matter near galaxy centres could result in dark matter accumulation in the neutron stars, leading to the formation of black holes.

Once a black hole is formed then any dark matter that enters the event horizon cannot emerge regardless of what kinetic energy it gains in the process. However, there is still a problem. Material in orbit around a black hole has less angular momentum the closer it orbits. To pass inside the event horizon requires the dark matter to lose angular momentum. Normal matter does this via an accretion disc that can transport angular momentum outwards by viscous torques, allowing matter to accrete. Dark matter has almost zero viscosity so this can't happen.

So building a supermassive black hole from a smaller seed would be difficult, but forming small black holes out of neutron stars might be easier. It has been proposed that a relative lack of pulsars observed towards our own Galactic centre could be due to this process.


How can comets have tails if there's no air resistance in space? I understand that solar radiation causes material to vaporize out of a comet into dust but why does the dust then trail behind the comet like a "tail"?

Assuming gravity is the only applied force acting on the comet, shouldn't all of the material, including the dust, be travelling at the same speed due to conservation of momentum? What causes the dust to travel slower than the comet's nucleus? In other words, why does the dust form a "tail" and not a "cloud"?

There are two forces that can cause the formation of a tail: the solar wind and radiation pressure.

The first misconception in your question is "the dust [travels] slower than the nucleus".  The tail is not left trailing behind the comet, it is pushed away from the comet by the sun. When the comet is moving away from the sun, the tail is in front of the comet.

Now radiation pressure is small but real. When light shines on something there is a small force. This pushes dust back from the comet in the direction opposite to the sun. The dust is still affected by gravity and a curved dust tail results.

The ultraviolet light from the Sun ionises the gas and gives it an electric charge. The solar wind carries magnetic fields and the gas (or more properly plasma) follows these fields in a straight line back from the sun.

So space around the Sun is not empty. There is powerful light and magnetic fields that are strong enough to push the dust and gas released by the comet away from the coma, and form the tail.


Why isn't interstellar medium pulled in towards nearest massive object? How does the ISM resist gravity? That's the only force acting on it, and all other particles seem to collect together to form stars. What makes the ISM so special among other particles?

It is not true that the particles in the interstellar medium (ISM) are only acted upon by gravity. For instance,

In many cases a significant part of the ISM is ionized, in which case it interacts with magnetic field which permeates the gas and may in some cases be quite strong.
In the vicinity of massive and hence luminous stars, radiation pressure may exert a strong force on the ISM. They also emit copious amounts of cosmic rays (i.e. relativistic particles) that transfer momentum to the surrounding gas.
Supernova explosions create hot bubbles that expand and sweep through the ISM, resulting in shock waves and galactic outflows.

In most cases, however, what may prevent a gas cloud from collapsing is simply its temperature.
Despite all the above processes, and despite gravity being the weakest force, gas clouds do sometimes collapse to form stars. The criterion for doing so is that the gas is dense enough, and that its internal pressure (or thermal energy) is weak enough. This is described by Jeans instability, which formulates the criterion for a cloud of gas to collapse through equating pressure forces, or thermal energy, to gravity. One way to express this is the Jeans mass $M_J$ (Jeans 1902) which is the critical mass of a cloud where thermal energy is exactly balanced by gravitational forces:
$$
M_J = \rho \left( \frac{\pi k_B T}{4 \mu m_\mathrm{u} G \rho} \right)^{3/2} \\
\propto \frac{T^{3/2}}{\rho^{1/2}}.
$$
Here, $k_B$, $G$, and $m_u$ are Boltzmannn's constant, the gravitational constant, and the atomic mass unit, while $T$, $\mu$, and $\rho$ are the temperature, the mean molecular mass, and the density of the gas.

In the second line of the equation it is emphasized that $M_J$ increases with temperature, and decreases with density. In other words, if the gas is too hot, or too dilute, the total mass needed to collapse must be higher.

In general, gas will not collapse to form stars if the temperature is above some $10^4\,\mathrm{K}$. If the temperature is higher, the particles simply move too fast. Since various processes may easily heat the ISM to millions of degrees, the gas has to cool before it can collapse. On way to do this is by cooling radiation: Fast-moving atoms collide (either with each other or, more often, with electrons). Some of the kinetic energy of the atoms is spent exciting their electrons to higher levels. When the atoms de-excite, photons are emitted which can leave the system. The net result is that thermal energy is removed from the cloud, until at some point it has cooled enough to collapse.


Is cosmology an accurate field? I'm new here this is my first question. I'm an engineering student and I really like mathematics, I've recently watched a movie about Stephen Hawking (The Theory of Everything) In which he makes various discoveries about black holes. This made me curious about cosmology and the only thing I know about this subject is

Cosmology is a branch of astronomy concerned with the studies of the origin and evolution of the universe, from the Big Bang to today and on into the future

This made me question how accurate it is, since there is no way to see

Your question is based on a false premise:

there is no way to see

On the contrary, the distant universe is being observed to infer information about cosmology and observational cosmology is a field of active research. Like all scientists, cosmologists make hypotheses and test them by making observations. Luckily for cosmologists, light travels at a finite speed, so by looking at objects very far away, you see how they were a long time ago.
A better question might be "How do cosmologists know what they do?".
Here are a couple examples of things that have been observed to gain insight on cosmology.

Measuring the redshift of galaxies shows that the universe is expanding. Observations of type Ia supernova even indicate that this expansion is accelerating.
Observing the cosmic microwave background disproved some hypotheses about the early universe.
Comparing the amount of stars and gas in galaxies to the speed at which they spin shows that something is amiss, so more observations are being made to try to figure out what is going on.

Now, of course, we have to make some assumptions to make this all work. For instance, cosmologists generally assume that the universe is homogeneous and isotropic at large scales.


Why does Mars appear to retreat across the sky? If you plot the movement of Mars across the Earth's sky it appears to move back on itself during its orbit.

Why does it appear to have a loop shape from Earth?

The effect is called apparent retrograde motion.

What happens is that Mars has a 'direction opposite to that of other bodies within its system as observed from a particular vantage point' when this loop occurs.

That's a bunch of words that don't mean a lot to me. A picture is worth a thousand clearer words:

(Imagine this turned sideways and you get the effect in your image)

Basically, because Earth and Mars are orbiting the sun at different rates, our vantage point of Mars changes for each combination of points in the orbit of each planet.

On this scale, the background of stars is pretty much stationary - any apparent movement of the stars due to this effect is going to be negligible. Thus, the stars are our point of reference.

As our vantage point of Mars changes, it appears to shift directions on the stellar background, creating the effect you describe.


How is the magnitude of a star measured? How does one measure the brightness of a star?, I did not find anything on the internet.

A device called a photomultiplier is attached to a telescope.

The telescope is pointed at the target star and an aperture is
closed down to avoid as much spurious light as possible, and a
reading is taken. The photomultiplier literally count the photons
hitting it.
Next the telescope is pointed at a well-known reference star in the
same part of the sky, the aperture is closed, and a reading is
taken.
Finally, the telescope is pointed at a dark part of the sky, the
aperture is again closed, and a reading taken.

Computer software compares the data from the target star, the reference star, and the dark sky to remove as much noise from light scattered by the atmosphere as possible. It's important to know how much of the measured light is coming from the sky and subtract it from the light measured from the target.

Often, this same procedure is repeated with a series of filters to get the luminosity of the target star at many wavelengths. Searching for a variable star's period requires switching from target star to reference star to dark sky time after time, hour after hour, night after night.

I paid my way through college doing this.


What of the following moon-situations would be better? Okay, so imagine that there is an Earth-like planet, with the following conditions:

It's further from it's sun than the Earth is from the Sun (not much, but enough for weather to be a little colder than the Earth).
It's more or less the same size as the Earth (same proportion of land and water, too).
Since it's further from it's sun, it takes more time to complete an orbit that the Earth (for instance, 400 Earth-days, instead of 365).

Given those conditions, I would like to know which of the following would be more stable for this Earth-like planet to have a similar day/night and moon cycle to the Earth:

A moon that's the same size as the Earth's moon, only closer.

OR

A moon that's as far away as the Moon is to Earth, only that the moon of this planet is bigger (let's say, twice as big as our moon).

Sorry if it's kind of complicated. Please tell me if it's not understandable and I'll try to edit it so it's as clearly as possible!
Thanks in advance :)

Both would be stable.   A single moon orbiting a planet is generally stable provided it's comfortably inside the true region of stability, in the Hill Sphere and provided that it's not so large that tidal forces become a stability issue or not so close that it dips inside the roche limit and might break apart.

The only way you might run into instability in your scenarios, is if you have the smaller moon very close, inside the Geosynchronous orbital distance, where the Moon would move ahead of the tidal bulge it creates and that would cause the Moon to be drawn towards the planet and in time, crash into it, similar to how Phobos is expected to crash into/break into a ring system around Mars.

As the planet moves away from the sun it's stable region expands.  The geosynchronous orbit is unrelated to the sun, that's between the masses of the planet and moon only, but as long as your moon is orbiting between geosynchronous orbit and inside the stable region of the hill sphere, it should be fine.   (unless you give the planet or moons a retrograde rotation, then you need to re-examine the long term tidal effects).    For most orbits, the planet rotates ahead of the Moon so the tidal bulge pushes the Moon slowly outwards, but this effect gets weaker as the Moon gets further, so it's generally long term stable over billions of years, unless the planet is very close to the sun and it has a tiny hill-sphere.

Only two well known moons in our solar-system orbit ahead of their tidal bulges that leads to orbital decay (a handful of tiny captured moons do too, but those are so small and their tidal forces are largely irrelevant).   Only Phobos and Neptune's wrong way moon Triton orbit ahead of their tidal bulges, resulting in them being pulled towards their planets, not pushed away.   Triton is sufficiently distant that it's timing to crash into/break into a ring system around Neptune is billions of years off.   All the other moons, for tidal reasons, should be moving away from their planets, mostly very very gradually.

The 4 Jovian moons, however, are more complicated as Jupiter has a gonzo magnetic field, a magnetosphere that's almost wind like and it's moons are tidally locked to each other and it's innermost moon is losing mass to Jupiter's magnetosphere - so . . . all bets are off when it comes to Jupiter's 4 inner moons.

2 or more large moons can sometimes interact with each other, creating some instability.  One moon systems are, more often than not, long term stable.

(too long?)


What exactly is space-time fabric? I have heard about space-time fabric but I can't understand its definition. Is space-time fabric a physical thing or did Einstein imagine it to assist him with general relativity?

'spacetime' is real, however the word 'fabric' is made so that anyone can 'visualise' the meaning of space-time
You cant touch or feel the fabric, but you can perceive it through the bending of light over it. When someone says that the spacetime is curved around a planet, the following statement holds true:

the time is slower near the surface of the planet relative to far away from the planet

the space is 'curved' towards the planet, so if you send a space ship to the planet, the ship will curve towards the planet, even of it is travelling on a straight path. So the straight path is not so very straight to an external observer even if it is straight for a observer going through the path

The word 'fabric' is used so that anyone can easily 'visualise' the spacetime
Our Universe has a large fabric of spacetime, with several heavy objects bending and curving it here and there.
The word 'spacetime' has also a non-gravity related meaning. Einstein stated that as the speed of an object increases in space, the time experienced by it decreases
that means that if an object travels at the speed of light through space, it will not travel through time at all. And if an is stationary in space, it will travell the fastest through time


Solar Pressure and Gravity I recently read some articles and pages on Solar Sails, and the possibility of using lasers to propel spacecraft, and I had a relatively outlandish idea.

Would it be possible for a star to be outputting enough light that planet-sized (or smaller) objects caught in it's gravitational pull would not cross a certain threshold?

A sort of 'reverse blackhole' if you will, where the event horizon is an area that the matter(not light) can not proceed further into the star.

I would assume this to look like a star with a large ring around it, equidistant from any point of the star's center, where matter would coalesce.

Furthermore, would it be possible that an object could remain 'stationary' (ie. not in orbit and no acceleration in any direction beyond the pull of gravity) around this star without fear of gravity pulling it into the star?

While I'm lacking the formulae, the applicable surface area of a body would have to be great enough, and it's density low enough that it's gravity remains below that threshold. So a smaller body is much more likely. If you think about it, most dust from near the sun gets pushed out by the pressure.

There wouldn't be a specific point where you would get the matter buildup, it'd be more like the Roche limit where the gravity and density are the factors of the distance from the larger body.

Without running calculations I'm also unsure as to whether it would in fact be a stable arrangement but more like an L1 style Lagrange point, where it requires some energy every now and then otherwise it drifts.

Edits are welcome, I feel that I haven't used the best language available here and may have rambled.


How long does it take to produce a star? Why does it take that long? I wonder, why stars take a really long time to become stars? Is it because it needs to gain mass? Or heat up? Something like that? And could it be sped up at all?

The time to "produce" a star actually depends on the mass of the star. Let's start with a solar type star.
For a typical solar type star, the formation time is about 10 million years (you can see this image on Wikimedia that gives an overview of the star formation process, adapted from Philippe André's figure in Observations of protostars and protostellar stages in The cold Universe, 1994). You can distinguish different epochs in the star formation process, that are the signature of different dominant physical processes. The very first stage of star formation is a gravitational collapse that leads to the formation of the protostar itself. The timescale for this collapse is the so-called free-fall time which depends only on the density of the object. When you get a central object in a hydrostatic equilibrium, things become more subtle: the core will contract adiabatically (without heat transfer) and when a temperature of about 2000 K is reached, dihydrogen dissociates (which is a highly endothermic reaction) which leads to a second phase of collapse, leading to the formation of the protostar itself. It takes about 1000 years to get to this stage, from the hydrostatic core.
The next stage, the protostellar phase, is mostly an accretion phase. It means that the timescale for this epoch is given by an accretion time, that varies with the accreted mass (which is quite low for a solar type star). It takes about 200 000 years to accrete 90% of the final mass of the star.
Then, since the star is still contracting, the temperature at its center is increasing; when a temperature of 1 million Kelvin is reached, the protostar starts to burn its deuterium. At this stage, the Kelvin-Helmholtz mechanism allows the protostar to contract and to radiate away its gravitational energy. The meaningful timescale is then the Kelvin-Helmholtz time (which varies as the square of the mass and the inverse of the radius and the luminosity), that is much longer than the previous timescales. Temperature continues to rise, up to 10 million Kelvin, when hydrogen eventually starts to burn, which is the birth certificate of a star. It takes around 10 million years to get to this point.
But, as I said, this scenario depends on the mass of the star. It is valid for Sun-like stars, but not quite for massive stars. It is much faster for massive stars, and the star formation process is quite different. In particular, the accretion rate is much higher, the radiation pressure of the protostar is insanely higher, and their interplay is not completely understood. However, there are some theroretical works that gives an estimate of about 100 000 years to form a massive stars (see for example works from McKee and Tan).


What parameters determine whether galaxies colliding will result in a merger or a hit and run? Colliding galaxies sometimes merge and sometimes pass through each other. Either way, there are huge changes as a result. What are the parameters that matter in determining whether a collision will result in a merger or a hit and run, or something in between? What will be the result of the Milky Way-Andromeda collision?

Thinking about this some more, I suppose the most clearcut distinctions for the result would be whether the two supermassive black holes end up unbound, bound, or merged. Would it be possible for the bulk of the two galaxies to merge, but one or two of the SMBH's go on their merry way?

The main factor is the velocity of the encounter. The higher the relative velocity between the two galaxies, the easier it is for them to pass through each other without being slowed down enough for a proper merger to take place, and without being strongly distorted by the encounter. (In a very high speed encounter, the two galaxies will spend almost no time close enough for tidal forces to be effective.)

In clusters of galaxies, where the typical velocities are around 1000 km/s, mergers are rare; in small groups, where the velocities are around 100 km/s, mergers are more common. So the Milky Way and Andromeda are pretty much destined to merge.

During a merger it's possible for stars in the outer parts of the galaxies to be ejected by tidal forces, but the central regions of both galaxies should definitely merge. Thus, the supermassive black holes (one in each central region of the original galaxies) will end up in the center, too. (Unless you have something exotic like a merger where one of the galaxies already has an unmarked binary SMBH; then you might get one of the three SMBHs ejected via a 3-body interaction. But I suspect that's pretty unlikely.)


Are Barlow lenses stackable for bright objects? I'm back to the refractor that I own, and I want to maximize the zoom capacity. I realized today that I own more than one barlow lens, and I was wondering if I could stack them together for looking at bright objects, like Jupiter. I'm aware that looking at anything else would probably be disastrous due to the stacked barlow lenses taking up more light. Is this an effective, or desirable way to approach the situation? What will happen if I do stack more than one barlow lens? Will it have the effect of an enhanced image, or will it do nothing but remove light?

Yes, stacking Barlow lenses is a common practice to effectively increase focal length by multiplying their individual focal lengths. When I say common, most advanced eyepieces actually have many glass elements and are a type of a Barlow lens themselves, so just by using a single Barlow lens in front of your eyepiece you'd already be, technically, stacking Barlows. It is a technique that is particularly useful for bright object like our Solar system's planets, with Jupiter that you mention perhaps even the best example.

Your image quality might vary substantially tho with the Barlow and eyepiece quality of glass elements and the manufacturing precision. You might also want to play with the order at which you stack them and find an optimal arrangement of all of the glass elements they add to the system. The more precisely they're made, the less the order will matter though. And you'd technically want the less precise ones at the end of the stack, so their deficiencies don't magnify with each added element. And yes, with any additional glass element you'll be losing a bit of the illumination so this is, like mentioned, most suitable for bright objects.

Do not however, under any circumstances, do this when observing the Sun! You shouldn't need additional glass elements anyway, but should you try, you'll most certainly cause them to overheat, expand and permanently deform quite fast, regardless what material their tube and thread are made of, metal, alloy or plastic.