Why does the latitude of an observer affect the hour angle of a body in Stellarium? I am using Stellarium for astronomical data to help in studying celestial navigation.
While trying to track down a source of errors in my sextant reading or sight reductions I noticed that the local hour angle (shown HA on Stellarium's ephemera) of Venus varied if I changed the latitude of my location whilst keeping time constant.

Can anyone explain this. I thought the HA would only be a function of time, longitude, and the position of Venus (RA, Dec). Why would my moving north along my meridian affect the HA of a body? Aren't both my meridian and Venus' fixed (time is stopped), so the angle between them wouldn't change?

I noticed that it changed systematically. For the date and meridian in  question (16/5/2020; 21:30:00 0° Long.) it varied from 6h 47m 41.86s at both the N and S poles, to 6h 47m 43.78s at the Equator. delta=1.92s

I know it's only a tiny amount, but I would like to understand what the principle behind it is. Everything I found on Google seemed to suggest it shouldn't change. I wondered if it was something to do with parallax changing as I changed position.

Thanks for any help.

I do not have Stellarium, so I cannot confirm what is causing it with 100% certainty. But by using JPL's Horizons website, I can confirm that the position on the Earth's surface changes the apparent Right Ascension (R.A.) and Declination (DEC) of Venus. The following output is for an observer at 80 degrees W longitude and the latitude listed. The time was chosen so that Venus was approximately 7 hours east of the meridian; that is, the hour angle was approximately 7 hours.

Date__(UT)__HR:MN     R.A.__(a-apparent)__DEC
2020-May-17 01:00     05 22 07.26 +27 00 24.9 Equator
2020-May-17 01:00     05 22 09.23 +27 00 01.6 North Pole
2020-May-17 01:00     05 22 09.23 +27 00 48.4 South Pole

These results show exactly what you were noticing in Stellarium:

The R.A. of Venus changes by approximately 2 seconds from the equator to the poles.
The change is the same going to the North or South pole. I thought the values would not be the same because Venus is north of the equator, but the shift is identical in R.A. for those two locations. (Note that the shift in DEC is not the same.)

Observing from the Earth's surface (topocentric position) is important for the Moon if you are looking for occultations or close conjunctions or precise hour angle, but not as important for other objects which are much farther away. Stellarium probably has a setting to change the calculation from topocentric to geocentric, in which case the hour angle discrepancy will disappear.


Space objects visible from earth I recently saw the International Space Station without a telescope. Are there any other man-made space objects that can be seen using bare eyes?

Yes, there are quite a lot of them, but ISS is by far the brightest. The other satellites can be visible with magnitude fainter than 3. "Can be" means in dusk/dawn, when the satellite is in the sunlight.


Clarification on Greenwich Sidereal Time (GST) I know that LST = HA + RA.
And GST is LST + longitude(L).
If a star culminates, it's HA=0. Therefore, GST = RA + L.
Since RA and L are constants, GST must also be a constant. So, how can GST be different on different days of the year for the culmination of the same object for the same observer? Also if I'm given the L and RA, why am I given the GST in this question?

The flaw in your logic is that "RA and L are constants". The right ascension (RA) of the object on the meridian is not constant. It changes continuously, otherwise we would not say that the sky is rising in the east and setting in the west.

Also, the Sun moves about 1 degree per day along the ecliptic, so the RA of the Sun is constantly changing. If the Sun is on the meridian at 12:00:00 every day, and if the RA of the Sun is changing every day, then the same RA is not on the meridian at the same time on every day. (Note: Because of the equation of time, the sun does not cross the meridian at the same time each day. For purposes of this thought experiment, pretend that it is true.)

These two things taken together lead to the fact that 24 hours of right ascension cross the meridian every 23 hours 56 minutes 4 seconds. And this is why the question asks for a date when the LMC culminates (crosses the meridian) at a specific time (9 pm) and a specific location.


A black "superhole" possibility? When matter crosses the event horizon, it is easy to imagine that matter is torn apart into their individual components by tidal wave effects. Atoms would be ripped apart eventually.

At one time, the particles will fall so deep into the gravity well, that a single particle would be touching both sides of the gravity well at the same time. At that moment, I choose to assume that the particle particle core may be spaghettified, but externally it will appear to be shrinking.

Knowing that spaghettification is dependent on the size of the object, as well as the difference in gravity on both sides, a shrinking particle may eventually become so small that the steepness of the gravity well is no longer a problem.

The particle continues to shrink forever. Over time, gravity between all the particles that have shrunk, will again start to take effect - and I imagine that that is what happened in the big bang.

So the cosmic inflation, could just as well be particle shrinking, as a result of all particles in our universe being within the same black superhole.

Taking this idea, we could look at our own universe and I guess we would expect to see certain effects such as accelerating cosmic expansion, perhaps a cosmic background radiation and we would expect our universe to end as a cold, dead place.

Is this a known theory or idea, and where can I find papers on it?

Let's say you have a rocket near a Schwarzschild black hole. Near the horizon, the thrust required to keep stationary goes to infinity; in this specific sense, the gravitational force becomes infinite at the horizon. If the rocket is hovering above the horizon, then the difference in gravitational forces becomes arbitrarily large near the horizon. This can tear it apart. However, an object falling into the black hole will also gain a velocity arbitrarily close to the speed of light (as measured by a stationary observer as it passes) as it gets closer to the horizon, meaning it will be length-contracted. It shrinks to zero size. As a result, the difference in 'gravitational force' across it is more complicated, and in fact remains finite.

  Knowing that spaghettification is dependent on the size of the object, as well as the difference in gravity on both sides, a shrinking particle may eventually become so small that the steepness of the gravity well is no longer a problem.

A shrinking object tames the infinite 'gravitational force' and keeps the tidal forces finite. But the curvature is already defined in the limit of the size of the measurement probe tending to zero. (The static tidal forces correspond to six of the twenty independent curvature components, but let's not worry about that much.) So no, you can't 'get rid of curvature' by shrinking your particle/system/whatever. That's conceptually broken.

  Is this a known theory or idea, and where can I find papers on it?

You would have to have a much clearer idea before that can be answered reasonably. I've skipped all the way to the end of your question because I haven't understood anything more of what you're trying to say.


How can I determine if a typical low-end telescope is a refractor or reflector? Is there a way to distinguish (with no manual, product info etc)?

There is a wide variety of telescopes, so it's a bit difficult to give a general answer, but here are some pointers:

If there is an open-end, it likely is a reflector telescope (perhaps a Newton). In this case, you can see the secondary mirror attached inside.

When you look through the place where you set the eyepiece, are you facing the same direction as the telescope? If not, it is a reflector.

Look into the part that you would normally point towards what you are trying to observe. If you can see a mirror at the opposite end, it is a reflector.

On certain reflectors, there is a lens on the side that you point towards what you want to observe. In this case, there also is a smaller mirror attached to the inside of this lens. You can't see the reflective part of this smaller mirror, but there should be a couple of screws on the back, that can be used to align the mirror with the rest of the telescope.

On a refractor, the part that you point towards what you want to observe is a lens that should have a rather round surface (as opposed to flat). This lens usually is not at the end of the tube, but rather there is a part to protect from stray light.

It the tube tapers a bit, it most likely is a refractor.


What changes are being made to VIRGO and LIGO (if any)? Gravitational wave detectors VIRGO and LIGO are currently down for some updates, slated to be completed sometime early next year (they hope). What exactly are they doing? I hadn't heard it was down again after the last set of updates awhile ago. What are they updating now-- is that knowledge public domain?

Source: I went to an astronomy club meeting and it was stated in the presentation.

Currently, LIGO and Virgo are in what's known as a commissioning phase, a scheduled stage where the teams work on improving the sensitivity of the detectors. A big part of this is noise reduction, but there are other technical updates (an evolving plan also mentions increasing the power of the lasers and adding a "squeezed vacuum source"). Virgo in particular is replacing the steel fibers that hold up their mirrors with silica ones. The original silica fibers failed and were replaced with steel ones before last year's detection of GW170817, but now new silica ones are being added.

As of October, the Livingston site has reached low noise levels, while Hanford is still a bit away. Virgo isn't quite there yet. Soon, though, the three detectors should begin a couple of joint engineering runs, testing the hardware updates before O3 (the third, year-long, observing session) begins in February.


What is the official term for a relationship between a planet and its moons? Sorry if this is a dumb question, I could not find anything naming this in my astronomy books, and Google searches only seemed to show me pages about astrology, [sarc] because naturally, human relationships are influenced by celestial bodies. [/sarc]

I'm thinking along the lines of a parent-child relationship or a symbiotic relationship, but I couldn't find anything that specifically names this kind of relationship.

Is there an official term for this relationship?

I don't believe there's an official term but there are a few familiar/common terms.

Parent Body/Satellite is one.

Central Object/Orbiting object or Central Object/Satellite.

Star/Planet or Planet/Moon imply one orbits the other.   For a non orbiting Moon or Planet "Rogue" is used before their name.

A grey area comes into play when the two objects can be considered binary as opposed to one orbiting the other.   Some people define a binary orbit as one where the barycenter is outside the body of the more massive object, but I don't like that definition because by that definition, Jupiter and the Sun are a binary system and the Sun weighs 1100 Jupiters.   The Sun also has planets that don't meet that criteria, more distant than Jupiter.

Another problem with the Barycenter outside so it's binary argument is that when a star dies and goes white dwarf or even denser, then pretty much every planet now orbits a barycenter outside the star, but when it was a main sequence star, this wasn't the case.   The orbits didn't change, just the size of the central object.  That shouldn't change the definition of the orbital relationship.   I think the Barycenter argument, while convenient, is highly flawed for that reason.

Pluto/Charon could be called a binary dwarf planet, but because Charon was likely created from a collision on the Body that's now Pluto, I think that's a poor definition and I think Charon should be called a moon or collision moon.   That said, because four tiny moons orbit both Pluto and Charon, calling them a binary-system has some merit too.  There's no neat and tidy way to make a precise dividing line, besides the barycenter, which is neat and tidy, but as I said above, inaccurate.

Asteroids are sometimes found orbiting one another and I rarely hear that defined as a central asteroid with a smaller asteroid orbiting it, it's more often called a binary asteroid.  I've never heard it called a baby asteroid orbiting it's parent, but again, definitions fall into a grey area if one asteroid is quite a bit larger than the other.

This XKCD comic addressed circumbinary orbits and "the other kind", which doesn't have a name.   Not everything needs a name, and in this case, I don't there is an official one.  "Central body" "Central object" or "Parent" work just fine as familiar and common terms.


How can I validate star names and designations? While most star names and alphanumeric designations I've seen appear to be pure alphanumeric plus space, I have seen designations with both - and + characters in them too.
Is there a reference or standard anywhere for what characters are valid for designations and star names?
I've had a look around for this information, but I can't find any references which would allow me to write a comprehensive BNF syntax or a regular expression to parse and/or validate star names and designations.
In particular for a project I'm working researching, I would like to know if either a , comma or a | pipe character has or might ever be used in a star name or designation.

As far as I know, there is no standard that defines valid characters for a stellar designation. Sometimes people write using Greek letters (e.g. "α Centauri") and there are many odd catalogue notations. I would not trust that star designations could not contain commas or pipes (aka vertical bar, |), although I think it would be rare.
The IAU has stated that star names are separate from the catalogue designations, and in regard to designations "it is standard practice to identify them with an alphanumeric designation. " But standard practice does not guarantee that somebody will not disregard it, and there are clearly plenty of designations already with non-alphanumeric symbols.
So, one should probably not assume too much about what characters are in the string. Presumably for safety and generality one needs to assume a Unicode string and some robust way of escaping entries.


Calculating and mapping the best visibility of celestial occurrence Recently I found a fantastic website in-the-sky.org, from here we can simply pick up any astronomical event and check its visibility in any part of the Globe.
For occultations, for example, we have very nice maps like this below:

There are a lot of conjunctions, occultations, eclipses, and so on described fairly in detail. I think it's the best website so far for people making Astro calendars.
The problem is, that if I checked some conjunction i.e. Mercury with Mars on August 19, 2021  I spent quite a lot of time checking which located around the Globe is the best for watching this event. I took into consideration the solar depression, not lower than 6 degrees (end of civil twilight), and an altitude of these 2 bodies above the horizon (not lower than 3 degrees due to atmospheric extinction). Finally, my hand-sketched maps are looking like this:

plotted in the Day & Night Map at timeanddate.com

sketch plotted in Google Maps

Circumstances checked with stellarium-web.org
So basically is quite a lot of work by checking which location is the most appropriate to watch the moment of conjunction ideally (I mean the moment of biggest approach these 2 planets, which lasts maybe...30mins or so). Concluding I would like to ask about the possibility of auto calculate stuff like this. If for example, I would put in one column the min solar depression, in another column the min altitude of these planets, some tool would bring me the map as presented above?
Is it possible i.e. with Python or other (I am only basic with soft)?
Or do you know web services, which do the calculation such as this for you?
I fund some query here:
How to calculate conjunctions of 2 planets
but it applies to calculate the dates and geometrical circumstances of the conjunctions. I would like to have something in the map as presented above.

Partial answer to

Is it possible i.e. with Python or other (I am only basic with soft)?

Yes!
Use Skyfield.
As long as you can muster a little Python you can search for events, make topographical maps of event times and elevations, or even put it in a loop and find optimized locations.
The nice thing about learning to use Skyfield is that you can then do all your event searches, plots, predictions etc. this way in the future, and it's a great way to improve Python skills as well.
Skyfield also has a Github page where there are discussion and issues pages that are both very active.
You can also view other Stack Exchange questions tagged with Skyfield here and in Space Exploration SE.

See also:

Sunset on [Mountain] from [Viewing Point]
How to determine when Sun/Moon is aligned to two location on Earth's surface?
Where can I find the positions of the planets, stars, moons, artificial satellites, etc. and visualize them?
Inverse of the sunrise equation - finding locations with a given sunrise time on a given day


Eddington luminosity in various plasmas So I know that the Eddington luminosity is given by:

$L_{Eddington} = 4\pi GMc/\kappa$.

I want to calculate this luminosity for a plasma of purely ionized helium, as well as for an electron-positron plasma.

How do I find $\kappa$ in each of these cases? I know sometimes this is approximated as $m/\sigma_T$, but I'm not sure when to invoke this approximation, and what the respective mass would be.

I think you mean that kappa = sigma / m.   The sigma is the "cross section," like the area you expose when you slice a watermelon in half.  The m is the mass of the particle that has the cross section in question (it's not literally the cross section of the physical particle, but an effective cross section for interaction with light), or more often, the mass of all the particles that come along with the cross section in question (often there is one particle contributing most of the cross section, but several particles that come with it which provide the mass).  For example, if you mix protons and electrons, the electrons have a larger cross section because their low mass makes them interact more easily with light, but that lower mass also means it is not the electrons, but the protons, that provide the "m" in the above formula.

So these quantities depend on the composition of the gas you have in mind.  It's easy for an electron-proton [edited] plasma, because if you don't worry about resonant interactions in the plasma, you can just consider the cross sections of the individual particles, and you get "Thomson opacity" of 0.4 square centimeters per gram (that's sigma/m for the sigma of an electron and the m of a proton, rounded to one significant figure because nothing is ever really a pure electron-proton plasma).  Purely ionized helium is also easy, because if you again ignore any resonant interactions between the electrons and the nuclei, it's just the same Thomson opacity except reduced by the extra neutrons [edited] in the heavy helium nuclei.  Since there is one neutron per proton, that reduces 0.4 by factor of 2, yielding 0.2.  [edited for forgetting that the 0.4 already includes the protons.]


Why is the Earth's center still hot after millions of years? Why didn't the center of the earth cool after millions or billions of years? What keeps it hot?

There is a nice article from Scientific American, but the main point is:

  There are three main sources of heat in the deep earth: (1) heat from when the planet formed and accreted, which has not yet been lost; (2) frictional heating, caused by denser core material sinking to the center of the planet; and (3) heat from the decay of radioactive elements.

Other planets may have more or less radioactive material and this will make a difference over time as to whether they continue to have a molten core, or become volcanically and tectonically inactive.


Where can I find a good solar irradiance chart for the infrared? I'm trying to understand the results of the ExoMars Trace Gas Orbiter vs the Mars Express in terms of their abilities to find methane on the surface of Mars. The solution that I'm coming to is that it might be a result of the Sun's spectra masking what is actually there. Is there a place that has a complete infrared spectra of the Sun, focusing in on the region around 3-4 um? Specifically, I'm interested in wave numbers ($cm^{-1}$) 3000-3100 or so, something with a resolution of 1 wave number. Some things that would help would be anything along the following lines, so long as they apply to the true spectra, and not the one as seen from Earth.

A generally accepted solar spectra (NASA, ESA, NIST, or some other body)
A time varying solar spectra.

Thanks!

Thanks to @PearsonArtPhoto's comment data with 1 cm^-1 wavenumber resolution is available in the link labeled MODTRAN data here: https://www.nrel.gov/grid/solar-resource/spectra.html

Here's a quickie plot and script for the downloaded ASCII data.

There are six columns of spectral intensity data (Watts/m^2/nm) with labels 'MCebKur', 'MChKur', 'MNewKur', 'MthKur', 'MoldKur', 'MODWherli_WMO'. The plot shows them to be very similar in the thermal IR (not surprising) and differ substantially in the visible and UV where differences in the spectrometers will show up in the region rich with spectral emission and absorption lines. This is illustrated in the second plot, showing a randomly chosen zoom in on a few nanometers of visible light, and the Fraunhofer "A" line.

import numpy as np
import matplotlib.pyplot as plt

fname = 'AllMODEtr MODTRAN.txt' # MODTRAN data https://www.nrel.gov/grid/solar-resource/spectra.html

with open (fname, 'r') as infile:
    lines = infile.readlines()

lines = [line.split() for line in lines[19:-1]] # skip a few lines with missing data

print('line lengths: ', set([len(line) for line in lines]))

data = [[float(x) for x in line] for line in lines]

data = np.array(zip(*data))

print('data.shape: ', data.shape)

# data[0]: wavenumber (cm^-1)
# data[1]: wavelength (nm)
# data[2:8] MCebKur, MChKur, MNewKur, MthKur, MoldKur, MODWherli_WMO

labels = 'MCebKur', 'MChKur', 'MNewKur', 'MthKur', 'MoldKur', 'MODWherli_WMO'
wavelength = data[1]

if True:
    plt.figure()

    plt.subplot(2, 1, 1)

    for (thing, label) in zip(data[2:], labels):
        plt.plot(wavelength, thing)
    plt.xlabel('wavelength (nm)', fontsize=16)
    plt.ylabel('Watts/m^2/nm', fontsize=16)
    plt.yscale('log')
    plt.xscale('log')
    plt.xlim(190, 2E+05)

    plt.subplot(2, 1, 2)

    n700 = np.argmax(wavelength > 700)
    for (thing, label) in zip(data[2:], labels):
        plt.plot(wavelength[:n700], thing[:n700])
    plt.xlabel('wavelength (nm)', fontsize=16)
    plt.ylabel('Watts/m^2/nm', fontsize=16)
    plt.yscale('log')
    # plt.xscale('log')
    plt.xlim(190, wavelength[n700])

    plt.show()

if True:
    plt.figure()

    plt.subplot(2, 1, 1)

    n1 = np.argmax(wavelength > 516.5)
    n2 = np.argmax(wavelength > 519.5)
    for (thing, label) in zip(data[2:], labels):
        plt.plot(wavelength[n1:n2], thing[n1:n2], label=label)
    plt.xlabel('wavelength (nm)', fontsize=16)
    plt.ylabel('Watts/m^2/nm', fontsize=16)
    # plt.yscale('log')
    # plt.xscale('log')
    plt.xlim(wavelength[n1], wavelength[n2])
    # plt.legend()

    plt.subplot(2, 1, 2)

    n1 = np.argmax(wavelength > 757)
    n2 = np.argmax(wavelength > 760)
    for (thing, label) in zip(data[2:], labels):
        plt.plot(wavelength[n1:n2], thing[n1:n2], label=label)
    plt.xlabel('wavelength (nm)', fontsize=16)
    plt.ylabel('Watts/m^2/nm', fontsize=16)
    # plt.yscale('log')
    # plt.xscale('log')
    plt.xlim(wavelength[n1], wavelength[n2])
    plt.title('Fraunhoffer "A" line')
    # plt.legend()

    plt.show()


What is the largest object on which the Yarkovsky effect has been observed? The Yarkovsky effect is responsible for changes in the rotation and orbit of some celestial bodies, most notably asteroids. It has been measured on asteroids, such as 6489 Golevka and 1999 RQ36.

What is the largest object on which the Yarkovsky effect has been observed? Scholarpedia has an excellent article and list of asteroids, but the list isn't necessarily complete, and I don't know if the effect has been detected on other (non-asteroid) bodies.

According to Vokrouhlicky et al. 2015 Yarkovsky forces can be measured for small bodies with diameters up to 30-40 km. The largest object they have in their list of Yarkovsky detections is 4179 Toutatis with a diameter of (only) 2.8 km. I am not aware if Yarkovsky forces have been measured on anything larger than asteroids.


Unable to locate Big Dipper through Polar Axis Finder I have recently purchased a CG-4 Polar Axis Finder for my CG-4 mount.

This PAF has markings on the lens for aligning with Big Dipper or Cassiopeia, which looks like this:

I have aligned the PAF to the mount during the day, and I am now attempting to use it at night. My understanding is that I need to rotate the mount in RA to match the image in the PAF to the actual stars in either Big Dipper or Cassiopeia. This will give me the correct position to then re-target at Polaris to find NCP.

I have been trying for 2 nights, and still no luck! The Big Dipper and Cassiopeia are in front of me - I can see them very clearly with the naked eye. Yet when I look through the PAF, I cannot see any star patterns resembling either of my targets. There are stars, but it's like the magnification is too high, maybe? No stars forms the pattern I am looking for, in any orientation. I cannot derive the connection between what I see with the naked eye right in front of me, and what I see through the PAF. I understand that the image in the PAF will be mirrored vertically and horizontally - still no luck. I can easily find my target through the Finder Scope on my main tube, but not through the PAF.

I have devised an experiment. I have positioned my tripod under a power line running high above me. I have aligned my view at Alkaid (western tip of the Big Dipper handle) with the wire, so I can see it in the PAF. Good news - I can see it in the PAF, and I can see Alkaid (it's the brightest in the area, so I am fairly sure that I can use it as a reference point between what I see with the naked eye and what I see through the PAF).

Bad news - no matter how I rotate my mount in RA while keeping the handle tip aligned with Alkaid, there's nothing that matches the rest of Big Dipper...

What is going on? I can't even explain this with a
"Defective PAF Theory"...

My guess is that the drawing is a "cartoon" and not to scale.

The declination of Polaris is +89° 15′ 50.8″ so it is only 0.746° away from the pole, (where the "+" is in the center of your drawing).

Since the inner circle's 143 pixel diameter corresponds to 1.472°, the outer circle's 824 pixel diameter is only 8.48°, or 85.76 North declination. The big dipper and Caseopia are at 60° to 50° North declination, way way outside the view of your scope.

They are shown only to provide a general direction to help decide how to rotate your finder.

 Source


Difference in redshift between 2 interacting galaxies I have a galaxy 'A', say at redshift 1. Let's suppose this galaxy has no peculiar velocity. What would be the redshift of another galaxy 'B', that has a radial velocity of 500 km/s, relative to A?

All this in the standard (Planck) model.

Any tools to do get this easily (an python code, astropy?)

From eq. 10 in Hogg's classic paper, assuming that the peculiar velocity $v_\mathrm{pec} \ll c$:
$$v_\mathrm{pec} = c \frac{z_\mathrm{obs} - z_\mathrm{cos}}{1 + z_\mathrm{cos}},$$
where $z_\mathrm{obs}$ is the observed redshift, and $z_\mathrm{cos}$ is the redshift from cosmological expansion only.

Let me invert that and wrap it up in Python for ya:

def zobs(vpec,zcos):
  c = 3e5
  return (1+zcos) * vpec/c + zcos


How are boulders formed on asteroids? For example: Are they soft landed meteorites? Or do they form from melted material during a violent impact? Or are they the result of some kind of erosion process?

It looks like you are asking about rubble piles, asteroids that are made up of a large number of different sized objects that are weakly held together by gravity. A few of the component objects are large, but most are very small (down to grains of sand).

By way of analogy, think of playing pocket pool. Rack the 15 target balls but leave the rack on. The cue ball bounces off when you strike the rack with the cue ball, but that's about it.

Now let's try again, but this time with the rack removed. To make the target balls a even more rubble pile-like, we'll use a piece of cardboard to add a bit of space between the target balls. Now something very different happens when the cue ball strikes the target balls. The balls are only loosely connected to one another. This makes them very good at absorbing the momentum of the cue ball and at distributing the energy and momentum throughout the rack. Given a low to moderate cue ball velocity, the collision will be close to purely inelastic.

And that's how you get a rubble pile. It's one inelastic collision after another after another. Over the course of 4.6 billion years, you have a pile of dust and sand with some rocks and a few large boulders mixed in.


Equation to find distance between objective and eyepiece I have a home made astronomical telescope with 100 cm objective lens and 5 cm eyepiece.when viewing an object in infinity the distance between eyepiece and objective is 105 cm. So how could I calculate distance between objective and eyepiece for and far away object.For example a planet 1 AU from earth how much should be the distance between objective and eyepiece ?

1 A.U. is same as infinity. The difference in terms of eyepiece position is infinitesimal, you can't measure it. Anything beyond a few kilometers away is pretty much "at infinity".

Regardless of that - from the practice of designing and building telescopes, calculations only offer you a starting point. You do the math, and the distance is 105 cm. But in practice lenses will deviate from the ideal focal length. Even if they didn't deviate at some temperature, put them in a cold environment, and the focal length will change a fraction of mm.

So take the calculations as a starting point, and build the instrument in such a way as to allow fine adjustments of the position of the eyepiece. There's a device called focuser that allows such fine adjustments. Or simply rely on friction to move the eyepiece back and forth until the image looks best, and hold it there.

When using the instrument in practice, you'll forget the ideal distance. What you will do is adjust the position of the eyepiece until the image looks best. You will do that every time you observe, and often multiple times during the same observation.

If you want some math, take a look at the thin lens equation, and apply it to the objective lens.

f = focal length of the lens

o = distance from lens to object

i = distance from lens to image

Then the thin lens equation is:

1/f = 1/i + 1/o

i = 1/(1/f - 1/o)

If o = infinity, then i = f.

But what happens if o = 1 A.U.?

i = 1/(1/1 - 1/(1.5 * 10^11)) = 1.0000000000067 meters

The difference is something like 6.7 * 10^-12 meters. It's smaller than an atom.


On analogies between gas and stellar systems Analogies between (typically) ideal gas and stellar systems are not only intuitively valid to some extent, but have been established and used in the studies of stellar clusters and galactic systems, most often as a simplification to collisionless Boltzmann equations.

The idea behind the analogy is that if a stellar system can be represented as a set of point masses, and if the number of point masses is large, then we can consider them from the point of view of kinetic theory of gases. One thing to remember here, though, is that stellar gas system is neither relaxed, nor can be relaxed.

I am curious here: How far can the described analogy be pushed?

For example, there is a range of gas-specific phenomena (or we could be talking about plasma, if you may prefer), which would be fascinating to imagine for stellar systems, such as shocks, turbulence or viscosity. Can such, or some other, characteristic phenomena exist in stellar systems and are there actual systems exhibiting such a behavior? (of the named ones, viscosity analogue exists and is rather common)

The analogy is rather weak and not really useful.

So-called collisionless stellar systems (those for which relaxation by stellar encounters has no appreciable effect over their lifetime), such as galaxies, can be described by the collisionless Boltzman equation, but never settle into thermodynamic equilibrium (only into some dynamical or virial equilibrium). Thus, the only other systems with somewhat similar behaviour are collisionless plasmas.

Sound, turbulence, viscosity etc are all effected by close-range collisions (not mere encounters) between the molecules. These also maintain thermodynamic equilibrium and a Maxwell-Boltzmann velocity distribution. Stellar systems have none of these processes and their velocities are in general anisotropically distributed and don't follow a Maxwell distribution.

Gases are in some sense simpler to understand, because their dynamics is driven by local processes and because statistical methods are very useful. Stellar systems are driven by gravity, i.e. long-range non-local processes, and intuition from the physics of gases is often very misleading (for example, a self-gravitating system has negative heat capacity -- this also applies to gas spheres, such as stars).

Note also that the number of particles in a gas is much much larger ($\sim10^{26}$) than the number of stars in a galaxy ($\sim10^{11}$), though the number of dark-matter particles may be much higher.


Extra-solar identification of binary planets Pluto and Charon orbit about a common barycenter that isn't inside of either planet. Let's assume that this relationship was scaled up to the point where it could be detected by a search for extrasolar planets. Could any of the methods we currently use tell us the difference between one massive body vs two bodies of nearly identical mass?

Yes indeed there could, especially in the case of a transiting planet system. Whilst the radial velocity curve would be nice and smooth, reflecting the position of the barycentre of the double planet, the transit light curve would show structure associated with the two planets obscuring the disc of the star. Essentially the transit shape would vary depending on the orbital phase of the double planet and on occasion the transit would occur in two steps as first one planet then the other
passed in front of the stellar disc. No such objects have been found.

People are already looking for this in the context of searching for "exo-moons" - for example,
the "Hunt for Exomoons with Kepler" programme. Finding a double planet with equal sized components would be comparatively easy compared with the tenuous signals expected from exomoons.


How fast would we have to go for the red(/blue)shifts of galaxies ahead of us to differ from those behind us with statistical significance? Here, we are looking for a statistically significant difference between the mean redshifts of galaxies ahead and those behind, with reference to a prior-specified direction. For example, suppose that we were aboard an advanced spaceship that had been accelerating in that direction at (say) 1 $g$ for some years. How soon into our journey would we notice that the galaxies ahead were bluer than the galaxies behind? Clearly this depends on our existing model, based on prior observations, for the distribution of galaxies' redshifts, and on some reasonable kind of weighting for each individual galaxy (perhaps according to the cosine of angle from our direction of travel, but not according to the galaxy's distance). However, in this analysis, we are ignoring individual data about any particular galaxy acquired before our present observation. For simplicity, let us also suppose that there is no statistically significant difference between the mean redshifts forward and back in the line of our journey before we began it. For the sake of definiteness, if it is needed, let us take a significance level of 1%.

First off, I'm not going to calculate an answer to the "significance level of 1%" part. This is more a rule of thumb kind of answer.

We're moving in a spaceship and want to see

  a statistically significant difference between the mean redshifts of galaxies ahead and those behind

In other words, the red- and blueshift due to our motion must exceed the peculiar motion of the individual galaxies. Cosmologists have been dealing with a very similar problem trying to measure the Hubble constant.

I remember from a cosmology class (can't find a source at the moment) that the Coma cluster is the first cluster whose redshift is dominated by the Hubble flow as opposed to peculiar motion. This is mainly due to the fact that the local group is moving towards the nearer Virgo cluster. From the above wikipedia link: Distance ca. $100 \textrm{MPc}$, apparent recession velocity ca. $7000 \textrm{km s}^{-1}$. So, at that speed, you would definitely see a systematic difference in redshift of galaxies ahead of and behind you. How long to get to that speed at constant acceleration of $10 \frac{m}{s^2}$?

\begin{equation}
 a = \frac{v}{t} \Rightarrow t = \frac{v}{a} = \frac{7\cdot 10^6 m s^{-1}}{10 m s^{-2}} = 7 \cdot 10^5 s \simeq 8\, \textrm{days.}
\end{equation}
Note that this is a worst-case scenario. People have used much closer galaxies to determine the Hubble constant. This paper's abstract says

  Due to the linearity of the expansion field the Hubble constant $\textrm{H}_0$ can be found at any distance $>4.5$ Mpc.

This is all very local, so we'll just assume a Hubble constant of $\textrm{H}_0 = 70\textrm{km}\,\textrm{s}^{-1}\,\textrm{MPc}^{-1}$ (Planck says 67.8 and Riess et al. say 73.8) and calculate redshift and hence apparent recession velocity at that distance using the Hubble law

\begin{equation}
 v = \textrm{H}_0 \cdot d = 70\,\textrm{km}\,\textrm{s}^{-1}\,\textrm{MPc}^{-1} \cdot 4.5\, \textrm{MPc} = 315\,\textrm{km}\,\textrm{s}^{-1}\,.
\end{equation}
At constant acceleration of 1g you'd get to that speed in about 9 hours, but you might need more time to do your data analysis on the galaxy spectra you'll have to take.


Light patch in the night sky I am so sorry for being ambiguous. I'm not an astronomer and have have never actually even bothered to look at the sky before. I don't have a telescope nor camera.

Yet, I'm really really curious about what it is I saw in the sky tonight.

Towards, the east I first noticed a "constellation" the looked much like what is described to be the big dipper (It is possible that it could have been Andromeda and Pegasus). It was squarish and had somewhat of a ladle towards it's north eastern corner. The most distinguishable feature of the structure was that it had 3 stars in a straight line. It was the straightest line in the entire night sky.

About a hand's length to the west was another "constellation", my guts said it's name was Orion. Again, I have never seen, let alone distinguished, a constellation properly in my life. It was like a triangle with it's nose pointing towards the east. The sides that converged to the nose seemed to extend a bit backwards like antennas.

And to the west (a few inches north to the Orion was this strange glow.
At first I thought it was my eyes playing tricks on me as sometimes whenever you stare into light bulb or some other light source, a faint glow in that area of your vision often persists. And as I looked directly at it, it slowly faded away into darkness and all that was distinguishable was an extremely tiny star or two. But whenever I looked to something near it (like a tree or constellation) , the patch reappeared. Then, I noticed that there was cluster of tiny little stars. I couldn't make out much. What caused that light patch? It seemed to glow in and out like it was breathing. I am sure that my eyes weren't playing tricks on me because even as I turned around and tilted my head and jumped up and down in the process, the patch remained in the same spot in the sky.

The location which I observed this is from Ernakulam, Kerala, India. The nearest current sky map I could find is the following from Chennai (which is really far away):

I can't make head or tail of it. Please help and no I'm not crazy. I know it sounds like one of those crazy UFO stories but I assure you it's not.

Is there anything like what I've said observed in the night sky before?

Given the description, that light patch was probably Pleiades.

It is a star cluster in the constellation of Taurus which is inspired from a popular Greek mythology of Seven Sisters. You can read more about it here.

EDIT: One of the great softwares, free and open source, for amateur level observational astronomy, though professionals use it as frequently is Stellarium. It's easy to use and should clear all your doubts.


Might someone see changes to the corona during a solar eclipse? I've seen many pictures of the corona during a solar eclipse, and the structure and delicacy is amazing. Clearly, the appearance would change over time, depending on the fine details of the solar wind and the structure of the mass shed from the solar surface. I wonder, though: might the appearance, to the unaided eye, change during a single eclipse?

This could actually be treated as two questions (all example durations and times taken from the August 2017 eclipse):

a) Might the corona's appearance visibly change during totality at a single location (a maximum of 2 minutes 40 seconds)?

b) Might the corona's appearance visibly change between the first Earth-wide totality (16:48 UTC, when the Moon's shadow touches down in the Pacific) and the last Earth-wide totality (20:02 UTC, when the Moon's shadow last leaves the Atlantic)?

Searching for solar wind velocities yields a broad range of values, but $400km/s$ seems to be a common value. With the solar diameter being about $1{,}400{,}000km$, that's about a solar diameter per hour, which suggests there will be no visible change at a single location, but there certainly could be changes when viewed across the entire 3+ hours of totality.

So, can we expect changes in the coronal appearance during this eclipse, either at a single location or across the entire eclipse path?

Yes. There is a chance of one or more solar flares or CME's occurring during the eclipse and these would be noticeable during totality. There are actually two NASA jets equipped with telescopes and high-speed cameras to film the Corona and any such event. The plane will track the eclipse throughout its duration.


How is the average distance between 2 objects orbiting around a third object calculated? I want to know the average distance between Io and Europa knowing that Io's semi-major axis (around Jupiter of course) is 421,800 km and Europa's semi-major axis is 671,100 km.
At first I thought it's the average of the closest approach (671,100 - 421,800 = 249,300 km) and the farthest approach (671,100 + 421,800 = 1,092,000 km), but the average of those is exactly 671,100 km, which is Europa's semi-major axis, and I find that hard to believe.
Assuming the orbits are co-planar and perfectly circular, which they more or less are, surely there must be a simple formula to calculate the average distance?
I asked this on another site and the answer was "run a simulation!", which is a very good answer, and I would've already done that if I knew how lol.

If we set the radius of Io's orbit to 1, then Europa's is about $a=$1.591. Since they are in a 2:1 orbital resonance we would expect that number to the 3/2 power to be exactly 2. It's close (2.007) but there's enough of a difference to make it interesting; since Jupiter rotates rapidly I'm guessing that it's related to this.
Okay based on @JamesK's idea of keeping one fixed I tried to get the analytical integral
$$<r_{12}> = \frac{1}{2 \pi}\int_0^{2 \pi}\sqrt{(a-\cos \theta)^2 + \sin^2 \theta} \ d\theta$$
from Wolfram Alpha but I got a

Standard computation time exceeded...

message which I've never seen before, (screenshot) so I did it in Python.
While @JamesK's answer is "the greater of the two" which here would be 1.591 or there would be 671,100 kilometers, because this is a 2D and not a 1D problem and Pythagoras has something to say, I get a different value.
('ratio: ', 1.5910384068278804)
('d.mean(): ', 1.7524934914237922)
('James_K: ', 1.5910384068278804)

The Python script below returns 1.752 or about 739,200 kilometers (solid line) versus the mean projected 1 dimensional distance (dashed line).

import numpy as np
import matplotlib.pyplot as plt

a = 671100. / 421800
print('ratio: ', a)

theta = np.linspace(0, 2*np.pi, 100001)[::-1] # don't double-count the endpoints
d = np.sqrt((a - np.cos(theta))**2 + np.sin(theta)**2)
print('d.mean(): ', d.mean())
theta_degs = (180/np.pi) * theta

plt.plot(theta_degs, d)
plt.xlabel('phase angle (deg)')
plt.ylabel("distance normalized to Io's SMA")
plt.plot(theta_degs, d.mean() * np.ones_like(theta_degs), '-k')
plt.plot(theta_degs, a * np.ones_like(theta_degs), '--k')
plt.ylim(0, None)
plt.show()

James_K = ((a-1.) + (a+1.)) / 2.
print('James_K: ', James_K)


What is there in the intergalactic space? What bodies can be encountered way outside galaxies - far beyond the farthest edges of galaxies, in the deep space between them? Are there single, galaxy-less stars, giant clouds of gas more dense than that the lower-than-elsewhere content of free hydrogen in space, or any other phenomena that span the void between the galaxies?

There can be stars (and small star systems). Stars need not be found only in galaxies.

There can be gas clouds.

Most nebulae are in intergalactic space. Indeed, for a while, both galaxies and nebulae were termed as "nebulae" until the differing nature of galaxies was discovered.

Almost any (small) structure that can be present in a galaxy can be present in intergalactic space, for that matter. Black holes (neutron stars, white dwarfs, brown dwarfs, ... ), star clusters, star systems, etc can all be present.

Finally, there's a very rare (rare in the density sense) plasma, mainly of hydrogen, that makes up almost all of the intergalactic medium. Zero pressure is an unattainable ideal case.


What's the difference between optical telescopes and solar telescopes? Solar radiation is strong. Following problems for solar telescopes may be telescope site selection and temperature control.

I wonder the telescopes themselves and their instruments are different?

Solar telescopes are optical telescopes, and it is quite possible to use an optical telescope to observe the sun. The usual way is to use the telescope to project an image of the sun, by placing a card at the focus of the eyepiece.

A professional telescope is a complex piece of engineering, it is designed for a particular task, such as observing very faint objects. It isn't designed for solar observation, and would most likely be rapidly damaged if it were pointed at the sun.

Solar telescopes have plenty of light to observe. The technical challenges involve controlling that light, so that it doesn't damage the equipment, and filter it, so particular aspects of the sun can be observed. The engineering problems of a solar and "nocturnal" telescope are different, so you can't use the same professional telescope for both. Analogy: an F1 race car and a rally car are similar in some ways but have been designed to overcome different technical challenges. An F1 car would never win a rally, nor would a rally car win at F1.


Pluto- Current theories regarding its geological nature? The images of New Horizons from Pluto will take more a year to arrive from space, for the moment with have some compressed images as a preview.

Nasa has advanced some information regarding the geologically inactive zone, but there has been no information regarding the possible geologically active zones, on the formation of the plateaus and the mountains.

What forces could be driving geothermal activity of what nature on Pluto? What can be learnt from theories of the moons of Jupiter and Saturn to understand activity inside of Pluto? What is the theoretical temperature of the center of the dwarf planet?

Geothermal activity can originate from a combination of:

Residual heat from planet formation: During the formation of a planet, half of the potential energy of
the parent region of dust and gas can be theoretically converted to
kinetic energy---this is known as the Virial Theorem.
The kinetic energy of the particles translate to a temperature.
Internal radioactivity: Around half of the $4.5 \times 10^{13}$W of heat that come from the Earth's interior is driven by radioactive decay.  Should Pluto have the same proportion of radioactive materials in
its composition? Some would assume so, but others would say that the
heavier radioactive materials should have fallen towards the centre
of the solar system during its formation and would thus exist mostly in the inner planets. Note that geothermal activity on
Mars has now ceased despite it being much larger (Mars has a radius of $3400$km while that of Pluto is $1200$), so a combination of residual heat and radioactive decay is
perhaps unlikely in the case of Pluto.
Tidal effects: Tidal forces basically apply whenever a part of a planetary body experiences a changing gravitational field with time (see tidal heating)---a number of processes can cause this:

the moon having an elliptical orbit;
extra moons in the vicinity (relevant to Io);
moon's orbital period and planet's rotational period not being synchronised;
non-uniform density in planet.

With time, the New Horizons mission should shed more light on these $3$ possibilities.

Note that the geothermal activity on Pluto likely refers explicitly to substances such as Nitrogen, Methane, etc., where far less energy is required to drive activity; that is to say, the ability to melt silicates has long since passed.


If the Universe is infinite, why isn't it of infinite density? If we make the assumption that the Universe is infinite, and has an infinite number of hydrogen atoms, then why is it not of infinite density - because, under Schrodinger's wave equation the probability of an electron being at any given point is non-zero and any non-zero number multiplied by infinity is itself infinity?

Is the answer (a) I have made some basic error in physics, (b) the Universe is provably not infinite because of this - effectively a version of Obler's Paradox or (c) the Pauli exclusion principle means that electrons just cannot be anywhere?

I would like to point out that any information (even quantum mechanical) travels at most at the speed of light. (There are some problems with entangled systems etc, but we can assume most systems to not be entangled, which is a fair assumption, imo). So, if you consider the age of the universe to be finite, any point will have only finitely many overlapping wavefunctions (those within the range of visibility, and the probability can be very very small at most points). So that means that there is never an infinite amount of atoms in the visible region at any finite time, meaning that the density never reaches infinity (or does so only at t=inf).


Existence of planets larger than their host star? The mass region of objects between ~ 0.5 Jupiter masses and 80 Jupiter masses (gas giants through to brown dwarfs and red dwarfs) is typified by an almost flat relationship with object diameter. There are planets out there which are larger than some of the smallest stars.

The smallest (currently fusing) star known, EBLM-J0555-57, is estimated to be slightly larger than Saturn (at about 59000 km radius with 85 times Jupiter's mass).

One of the largest planets known that isn't a suspected brown dwarf, WASP-79b is estimated to be twice Jupiter's diameter at 0.9 times Jupiter's mass. Many Hot jupiters and puffy planets with similar measurements are known.

How likely are there to be systems where a planet is larger than its host star? Are there any examples known?

I am looking for currently fusing stars only, which rules out pulsar planets, etc.

Since the smallest stars are still the size of gas giant planets, the question ends up coming down to whether gas giants exist around stars at the bottom of the main sequence. Close-in gas giant planets are rare around low-mass stars, though there do seem to be long-period ones. This means the largest planetary radii for the systems in question are going to be similar to Jupiter, rather than inflated hot Jupiters. An exception would be the case of very young systems before the planets cool and shrink but in that case the star would also still be contracting so you probably don't win there.

A problem is that these stars are extremely faint, so the radial velocity method is tricky - this may change a bit once more RV instruments that operate in the infrared (e.g. the Habitable Zone Planet Finder) come online. The long orbital periods for giant planets around these stars would also require longer observation times to make a detection. Unfortunately the long orbital periods would make transits unlikely, so most probably we wouldn't be able to determine the planet's radius and would not know for certain that the planet is larger than the star.

Direct imaging has spotted a few objects of a few Jupiter masses at fairly wide separations from objects near the hydrogen-burning limit, e.g. 2MASS J02192210-3925225 with an object at the deuterium-burning limit is located about 150 AU from a 0.1 solar mass star. It's not entirely clear what to call these objects and they may be very low-mass brown dwarfs rather than planets. Furthermore these systems are so young that the stars have not yet contracted to their main sequence radii. For low-mass stars this can take several billion years, by which time the planets will have cooled off and become much fainter (and less detectable). These kind of wide-separation systems may also end up being disrupted by stellar encounters.

The other approach that works for detecting these kind of systems is gravitational microlensing, which tends to find objects near the system snowline, i.e. on scales more similar to our planetary system. An example of the kind of system that might have a planet larger than its star is KMT-2016-BLG-1107Lb, where the parameters suggest a ~3.3 Jupiter mass planet orbiting a ~0.087 solar mass star at ~0.34 AU. Unfortunately the uncertainties in the parameters are typically large because the lens systems are usually invisible. This means we also don't have radius information, so we can't say for sure that this system definitely has a planet larger than its star.

So it looks like systems do exist where a planet can be larger than the main-sequence star it orbits, though so far there is no confirmed case due to the difficulty of making the necessary observations.


Difference in energy released in stellar mass black hole merger and supermassive black hole merger Super massive black holes are usually millions of times more massive than stellar mass black holes. I have read on SE and over internet that 3M☉ worth of energy is released in black hole mergers (not sure which type of merger). I have tow related questions:

What is the difference in energy released from a stellar mass black hole merger vs. a supermassive black hole merger?
How much energy will be released in the super massive black hole merger when Milky way and Andromeda will merge in few billion years?

Too long for a comment, but it's an incomplete answer.

The gravity waves detected were from a stellar mass binary black hole merger, sometimes abbreviated bbh for binary black hole.

The two black holes are thought to be about 36 and 29 solar masses with a final combined mass of about 62.  So, roughly 5% of the black hole mass turned into into gravitational wave energy.   Source.

and from Wikipedia article (which can be taken with a grain of salt)

  As the orbiting black holes give off these waves, the orbit decays,
  and the orbital period decreases. This stage is called binary black
  hole inspiral. The black holes will merge once they are close enough.
  Once merged, the single hole settles down to a stable form, via a
  stage called ringdown, where any distortion in the shape is dissipated
  as more gravitational waves.3 In the final fraction of a second the
  black holes can reach extremely high velocity, and the gravitational
  wave amplitude reaches its peak.

  The existence of stellar-mass binary black holes (and gravitational
  waves themselves) were finally confirmed when LIGO detected GW150914
  (detected September 2015, announced February 2016), a distinctive
  gravitational wave signature of two merging stellar-mass black holes
  of around 30 solar masses each, occurring about 1.3 billion light
  years away. In its final moments of spiraling inward and merging,
  GW150914 released around 3 solar masses as gravitational energy,
  peaking at a rate of 3.6×1049 watts — more than the combined power of
  all light radiated by all the stars in the observable universe put
  together.3[4][5] Supermassive binary black hole candidates have been
  found but as yet, not categorically proven

Supermassive bbh are thought to have been observed, see here and we may see one in our lifetime, not sure how often they happen.  But beyond that, I have no way of knowing how much more energetic a supermassive BBH merger would be other than to say, I would think, a whole lot, as it would have to scale upwards by some formula.

With the case of Andromeda and the Milky Way, we're talking Andromeda's 100 million solar mass black hole and the Milky way's 4-6 million solar masses.  Maybe someone here can estimate, but if the energy output is even 5%-10% of the smaller of the two, that's still a few hundred thousand solar masses of energy, an absolutely crazy energy output.  Even if it's far smaller than a few hundred thousand solar masses, it's still enormous energy.

I'm also not sure if it's a dangerous form of energy output as it basically squashes things back and forth maybe a couple times before returning them to normal.  I have no idea what the safe distance is from that kind of merger and gravity wave creation.    Interesting question though.  Fun to think about.


Stellar nurseries in the "Shedding New Light on the Whirlpool Galaxy" video Captions in the Hubble Space Telescope YouTube channel video Shedding New Light on the Whirlpool Galaxy say:

(visible) Along the dark dust lanes, bright pink nebulae are the birthplace of new stars.
(X-ray, lower energy) Before leaving these stellar nurseries, the most massive stars die in supernova explosions, which heat the surrounding gas to X-ray temperatures.

I'm not very familliar with star formation processes.
These might be considered as separate questions, but I've put them here together because they all refer to the same two sentences in this video, and it's likely that those familliar with nurseries, or wanting to know more about them, will have something to say or learn about all three.

Do stars tend to leave "these stellar nurseries" after a while, and it's only the short lifetime of the most massive stars that keeps them from leaving before going supernova?
What impact does the heating of surrounding gas to X-ray temperatures have on the formation and evolution of other stars within a given "nursery"?
Are there really such things as spatially well defined "nurseries"? Are they distinct and roughly countable, or is this a subjective popular term? Can one point to something and say "this little blob here at x, y, z in the spiral arm of the Whirlpool Galaxy, it's a classic nursery"?

Do stars tend to leave "these stellar nurseries" after a while, and it's only the short lifetime of the most massive stars that keeps them from leaving before going supernova?

Yes. The lifetimes of very massive stars (10-50 Myr) are comparable with the dispersion timescale for young clusters and associations. So massive stars tend to die near where they were born and they will be surrounded by their (more numerous) lower mass siblings. Lower mass stars have long lives and end up dispersing and making up the general population of a galaxy.

  What impact does the heating of surrounding gas to X-ray temperatures have on the formation and evolution of other stars within a given "nursery"?

It is unclear. The injection of energy and heating of gas ought to make it less susceptible to collapse and fragmentation. On the other hand that doesn't matter isf most of the gas that was going to turn into stars has already turned into stars. On the other hand, it is possible that the shock waves and outflows from supernovae actually compress surrounding structures and trigger new star formation.

  Are there really such things as spatially well defined "nurseries"? Are they distinct and roughly countable, or is this a subjective popular term? Can one point to something and say "this little blob here at x, y, z in the spiral arm of the Whirlpool Galaxy, it's a classic nursery"?

To some extent yes. There are some massive clusters of young stars that can be observed in other galaxies and can be certainly identified as the birthplaces of tens of thousands or even millions of stars. On the other hand, in our own galaxy it appears that although most stars are probably born in clusters and associations, there is no such thing as a "typical" cluster and that star formation takes place at a range of scales and at a range of densities. i.e. Much of the star formation taking place in other galaxies may take place away from some of the obvious blobs of star formation.


Solar Analemma - but with a star instead We (homeschool students and I) are trying to find the answer to this question.  Does a star also create Solar Analemma figure 8 when photographed daily for a year?
Has anyone published an experiment where the same star is photographed every night at the same time?
We tried answering this ourselves by googling it, but only come up with websites mentioning the sun.   Is this because it is only possible with the sun?

An analemma shows the position of the Sun in the sky from a fixed location on Earth at the same mean solar time. It gets its north-south shape because of the tilt of Earth's axis makes the declination of the sun change across the year, and the sideways shape due to the orbit nonuniformity.
The star analemma would get a point at the same time every sidereal day (slightly different from the solar day). To a first approximation that fixes the star's right ascension: it will not move along the celestial equator. The celestrial equator of course rotates one turn per year as seen from the ground, so in one sense the analemma is just a circle around the pole of the sky. But if you look at it in the coordinate system of the celestial sphere the star is fixed.
...Except that there will be some stellar parallax due to Earth's different locations along its orbit during the year. The star will seem to move along a tiny ellipse when compared to distant stars in the background. I think the parallax ellipse is the closest counterpart to the sun analemma.


Why are we so quick to proclaim the geological inhospitability of other planets based on extremely minimal information? Now, I'm not questioning claims that any planet in the Solar System is atmospherically or externally inhospitable, but claims made that other planets have geology that is extremely hostile to colonization (or even, in the case of Venus, further exploration).
Some of these claims are:

Mars's core is frozen.
Mars has no recent volcanic activity.
There are no large deposits of carbonates or other carbonaceous minerals/materials on Mars.
The total quantity of water on Mars is less than 1% that on Earth.
A perchlorate layer covers the entire Martian surface.
The soil of the Moon, Mars, and Venus would need to be massively modified to support plant life.
Venus was volcanically resurfaced in its entirety.
There are never any breaks in Venus's cloud layer, no matter how small or infrequent.

Judgements like this seem very premature given our lack of hard data, especially that of direct measurements of rock strata. For instance, about the first claim, only one functional siesmometer has been sent to the surface, which has only been there for a year and lacks any impact tests, and the only instrument sent to measure internal heat has so far malfunctioned. The 2nd and 7th claims are almost exclusively based on crater counts, which can give tremendously different age values depending on the expected impact rate. The 3rd is based exclusively on remote sensing methods unable to identify underlying strata, the 5th is based on a handful of landings, and the 6th has been called into question by research old and new. For the 8th, no modern space mission has even carried the instrumentation required to confirm this (that is, a high-resolution visible-light camera). All of these seem only possible to confirm or deny with much more extensive exploration, especially on and under the ground.

So, then, what am I missing, if anything? Why is it acceptable to make judgements like these off the information we have? I mean, imagine if a textbook of Earth's geology was writen solely on the observations of a handful of satellites as well as 9 pseudo-randomly-dispersed geologists allowed only a couple tens of kilograms of shallowly-penetrating tools and analysis devices (some defective) each, of which 5 of them are buried up to their knees in rock.

It is not simple to address all these points since they are simple expressions for complex processes.

1.) Mars's core is frozen

Translating frozen as solid. It is still unclear if Mars' core is solid or liquid, see @userLTK's answer: it is curently seen as being viscous. A liquid core could help maintaining a magnetic field. Mars has a very weak magnetic field that does not shield it like the earth's magnetic field does. This is adverse to the development of complex organic molecules and the basics of simple life. Maybe InSight brings us more insight into this one.

2.) Mars has no recent volcanic activity.

That appears to be incorrect. Mars has no plate tectonics that offer cycles (e.g.carbon). One can speculate that tectonis are helpful for a biologic evolution and complex life, offering renewal of needed elements, thermostats, being helpful in case of planetwide overfreezing, ... but this is debated and speculative.

There is possible polar volcanism and recent lava flows in the calderas of the Tharsis Montes (Olympus Mons and neighbours).

3.) There are no large deposits of carbonates or other carbonaceous minerals/materials on Mars.

There are carbonates, but not organic. That means that in the past organisms have not built up sequences of sediments like on earth. And it is true that remote sensing will not suffice for a qualified final judgement. But there is nothing more to do atm.

4.) The total quantity of water on Mars is less than 1% that on Earth.

Unclear, but probably not totally nonsensical. Though there is water, or rather brines. Water isn't exactly rare in the solar system. Mars probably had a water ocean early, but may have lost it qickly to space. Otoh it can be debated if amounts of water have been sequestered in the Martian mantle. This water could sum up to several meters worth of water coverage.

5.) A perchlorate layer covers the entire Martian surface.

Exaggerated, but perchlorates were found in samples of Marsian regolith and under UV radiation result in a bacteriocidal environment. No potatoes for Marc ...

6.) The soil of the Moon, Mars, and Venus would need to be massively modified to support plant life.

Well, that is indeed a belittlement. It is far beyond our capbilities to mobilize the necessary masses and energies. One could imagine greenhouses; and test runs have been/are being made in Antarctica. But who wants greenhouse stuff every day ;-). There is this study concluding that even if we could mobilize all the CO2 in all available reservoirs including the upper crust of Mars, that would only rise the atmospheric pressure by a few percent. Not enough to significally warm the atmosphere or walk around without a pressure suit (oxygene supply allways needed anyway).

7.) Venus was volcanically resurfaced in its entirety.

I have no idea, but so are large parts of Earth, constantly actually. But on the Venusian surface there are ~450°C and 95bar atmospheric pressure. The atmosphere is almost pure CO2. Excluding life until further notice is a valid guess.

8.) There are never any breaks in Venus's cloud layer, no matter how small or infrequent.

Ok.

We could address these points one by one and search for proper publications of data from spacecraft, remote sensing and rovers and apply the principle of uniformity (that's what NASA does, but don't use it as a religion ...) and discuss further. But this has all been done multiple times. All in all, for Venus the judgement "is dead" is pretty natural, given the conditions. Mars may have seen microbial life in its beginning, let's say its first few hundred million years (speculative !), but today this is unlikely, though not impossible. More data needed, as you say.


At what density does helium burning start in a star? I have seen several references that say that helium burning begins in a star once the core temperature reaches $10^8$K (such as here) but nowhere that says what density that corresponds to.  Does anybody know a reference that has this value?  And if it makes a difference, I would like to know the density for quiescent helium burning, not helium flash helium burning.

The short answer: $\sim10^4$ grams per cubic centimeter.

From this webpage, I have a few statistics regarding required mean density and during each phase of fusion (the fusion of lighter elements may happen in the "shells" outside the core).
$$\begin{array}{|c|c|}
\hline \text{Fusion phase}&\text{Mean density (g/cm}^3)\\
\hline \text{Hydrogen} & 5\\
\hline \text{Helium} & 700\\
\hline \text{Carbon} & 200,000\\
\hline \text{Neon} & 4,000,000\\
\hline \text{Oxygen} & 10,000,000\\
\hline \text{Silicon} & 30,000,000\\
\hline
\end{array}$$
This is data for a star of $25M_{\odot}$.

Note, however, that this is mean density in the star, not the density in the core, where fusion is taking place. That is on the order of $\sim10^4$ grams per cubic centimeter (see e.g. here). There may be a sharp density dropoff starting from the center of the star, showing that only the hot, dense inner regions can fuse the main element in each stage.


Tidally locked, and yet spinning? Reading about Uranus almost 90° tilt, I was wondering if some rocky planet with mass concentration at one pole could possibly spin around its own axis, while still being locked to its star? Which means the more massive pole always points toward the star?

I think what you are envisioning is having one pole always pointed towards the primary star. So the planet would rotate about that pole, but then the direction of the pole would change over the course of a year to keep the pole pointing towards a star.

This phenomenon of the direction of the pole changing is called "precession". The Earth does it over a period of 26,000 years, but the pole only traces out a fairly small circle in the sky, rather than twisting about a perpendicular line like you envision.

I think your scenario is improbable at best. Planets are like gyroscopes and resist having their axes of rotation be twisted about a perpendicular axis like that. Even a planet with mass concentrations at both poles (maybe a long cigar shape) to maximize tidal force would probably end up losing the perpendicular rotation to tidal friction, and just end up rotating slowly about an axis nearly parallel to the axis of the orbit.


What is the largest possible size for a brown dwarf? What is the largest possible size for a brown dwarf before it has enough mass, capable of sustained fusion, thus becoming a star?

I think what you are asking is what is the radius of an object that has the maximum mass to be classed as a brown dwarf?

The mass threshold for this is about $0.075 M_{\odot}$. The boundary is a bit fuzzy - there is still some hydrogen fusion, but not enough to produce the luminosity of the object), it also depends slightly on the chemical composition of the object.

However, the fact that you can still see (with a telescope!) brown dwarfs raises a more fundamental problem with your question. Their luminosity comes from gravitational potential energy; they are contracting all the time.

So you can only ask what is the radius of the most massive brown dwarf at a given age?

The oldest (about 10 billion years, though there is no good way to estimate the age of a brown dwarf in the field, or measure its mass), most massive brown dwarf's should be about the size of Jupiter. A similar brown dwarf in a star forming region, born a few million years ago, should be several times bigger.

The plot below (from Nelson, Rappaport & Joss 1986 - newer models are available, but show the same behaviour) shows the radius of substellar objects as a function of time. The plateau at early times is caused by Deuterium fusion in object more massive than about $0.012M_{\odot}$.


Is it possible to get a glimpse of the Big Bang through gravitation waves? I read in an article announcing the detection of gravitational waves by LIGO that it will be possible to detect them from the Big Bang. Is this true?

Gravitational waves from the big bang may be "heard" but not by LIGO. The waves emitted at or around the inflationary epoch of the big bang are expected to be at much lower frequencies (milli-Hz or lower) than those announced today by LIGO. There are various sources of noise that make LIGO insensitive to GWs at frequencies below about 10 Hz.

It will take space-based interferometers like the proposed LISA, with longer interferometer arms and well away from terrestrial sources of noise to stand a chance of detecting such GWs.

If they are detected - they might "sound" something like this (if upshifted into the audible range) - from the LIGO website. It sounds like white(ish) noise because of the broad continuum of frequencies expected.


Non-thermal Sunyaev-Zel'dovich effect Exactly what is the non-thermal Sunyaev-Zel'dovich effect? From what I understand from reading several papers by Mark Birkinshaw and Sergio Colafrancesco, I get the rough idea that the non-thermal SZ effect has something to do with it being in the relativistic realm.

Papers by Sergio Colafrancesco:

Polarization of the Sunyaev-Zel'dovich effect: relativistic imprint of thermal and non-thermal plasma
The non-thermal Sunyaev-Zel'dovich effect in clusters of galaxies
Non-thermal phenomena in galaxy clusters: cosmological relevance

Review by Mark Birkinshaw:

The Sunyaev-Zel'dovich effect

To clarify, I'm not referring to the kinematic SZ effect.

There appears to be a distinction by the authors between the SZ effect due to hot thermal electrons and relativistic electrons. I find the nomenclature ambiguous, as temperature is essentially kinetic energy on a smaller scale, so why would relativistic electrons that have more kinetic energy be 'non-thermal'?

Lastly, is the key distinction between them using a relativistic vs. a non-relativistic formulation?

The non-thermal S-Z effect is caused by inverse Compton scattering of the CMB photons from a non-thermal population of electrons - i.e. electrons that have high energies not because they are hot, but because they have been accelerated non-thermally. The usual mechanisms are accelerating by electromagnetic fields and the Lorentz force.

The rest-mass energy of an electron is 0.511 keV. In order to attain "relativistic energies" then the electrons must have kinetic energies similar to this or higher. The average kinetic energy of a particle due to its temperature is just $3k_{B}T/2$. If we equate this to 0.511 keV then the temperature required to have thermal relativistic electrons is $T > 4 \times 10^{6}$ K.

Gas at this temperature does exist in the intracluster medium of massive galaxy clusters. But in addition there are populations of non-thermal electrons that are accelerated to relativistic speeds for instance in the jets and radio-emitting lobes of active galaxies.

The distinction is important when studying the S-Z effect because the energy distributions of thermal and non-thermal populations can be quite different. Non-thermal populations are usually characterised by a power-law, whilst thermal electrons have a Maxwell-Boltzmann distribution. This results in a different inverse Comptonisation spectrum from electrons of the two populations that are often (usually) spatially unresolved. The non-thermal S-Z effect is essentially a contaminant that needs to be accounted for when using the thermal S-Z effect to investigate the structure and parameters of the intracluster gas and using the S-Z effect as a cosmological probe.


Are there equal number of planets, stars, galaxies etc in observable universe spinning in both directions? Just because we observed that our milky way galaxy is spinning in a certain direction therefore we assume it is applicable to all other galaxies, I am curious to find out if hypothetically most of the celestial objects such as natural satellites, planets, stars even galaxies within our observable universe are spinning/rotating in the same direction as the milky way what kind of implications can we say about the condition in the early universe? or is it just an coincident?

Angular momentum of the entire universe remains constant. Assuming that the big bang was the only  thing present initially, it wouldn't  posses any angular momentum. Now, if there are unequal number of planets, galaxies, stars,etc. in the observable universe spinning in both directions, there'd be some net angular  momentum which would violate the conservation of angular momentum. Hence, in my opinion, there are equal number of celestial bodies spinning in both directions.


Redshift observation at different wave length Can one star be observed at different wave length show different redshift ?

It's not impossible, but does require a bit if a special set-up.

Normally, the light from a star is redshifted mainly due to its velocity toward/away from us (a small, but important, contribution comes from gravitational redshift, when the light climbs up the potential of the star). Because stars tend to rotate, light coming from the side of the star rotating away from us is slightly more redshifted than the light coming from the side rotating toward us. If a large prominence is present on one side, then because the prominence is hotter than the average surface temperature of the star and thus emits at shorter wavelengths, the combined spectrum will exhibit a larger redshift at short wavelengths.
Since the flux from the prominence alone is, after all, small compared to the total flux, the effect would be rather small, however.

A more common mechanism that may cause a differential redshift is stellar outflows. If large amounts of gas are being expelled (e.g. in protostars or AGB stars), then atoms and molecules in the outflowing material will absorb some of the light from the star. These absorption lines are then blue shifted wrt. the "systemic" velocity (i.e. the velocity of the star wrt. us), again skewing the redshift as a function of wavelength. A spectral line may even be seen both in emission and absorption, known as a so-called P-Cygni profile. The figure below (from the Wiki article linked to) shows the same intrinsic wavelength (here H$\alpha$) both redshifted and blueshifted (by rotation and thermal motion), but the blueshifted light is absorbed by the outflowing atmosphere:


What's the terminology of a meteor "ditch" when impact happens at an angle? When a meteor hit the surface of a planet, it creates an impact crater. When an meteor hit the surface of a planet at an angle, like it usually happens in the movies, what do you call the long "ditch" that is formed before the actual crater where the meteor came to rest?

I think the answer to this is that it doesn't have a name because such "ditches" don't occur for real meteor impacts. In movies and tv shows, these ditches are often shown as being caused by the meteor first hitting the ground at some angle, then sliding across the ground, digging out a ditch along the way, until they come to their final resting point where the crater is.

When you stop to think about it, this scenario doesn't really make sense. These types of images (e.g., this one or this one) usually show a thin tail or ditch where the meteor first impacts which gets wider and deeper as the meteor scrapes on the ground, resulting in a final, large crater. But, the most energy a meteor imparts to the ground comes from the first instance it hits. If it were to scrape along the ground as portrayed in many movies, the crater would come from the point it hit the ground and the tail would be in the direction the meteor was traveling. The "ditch" or "tail" would get thinner and shallower as the meteor lost energy scraping across the ground. Generally the opposite is shown in movies.

But all that is moot anyway because meteors don't scrape along the ground at impact. That would just violate conservation of momentum and energy. You really have one of two scenarios.

The meteor hits the ground with such force and energy that it mostly destroys itself and you wind up with just a crater. Such an example is the meteor crater in Arizona - in a stroke of brilliance called Meteor Crater. I would hazard a guess that almost all meteor impacts are of this form, be it on Earth or elsewhere.

The other option is that the meteor isn't destroyed when it hits the ground. In this case, rather than dragging or scraping on the ground, your meteor will skip like a rock on water and create another crater on its second impact. In theory, it will keep skipping until it is finally destroyed or runs out of energy. This scenario requires that the impacting meteor is hitting at a very shallow angle with very little force and generally means that it is hitting a smaller body (but larger than itself) such as an asteroid/comet/moon. An example would be the Messier Crater on the Moon, linked by Andy in his comment. These types of craters are unlikely though, as they require pretty specific conditions to occur.


Time vs magnification in a binary lens For a single lens: we got

\begin{equation}
 u(t)=\sqrt{\left(\frac{t-t_0}{t_E}\right)^2 + u_0^2},\end{equation}

so the magnification is

\begin{equation}
A = \frac{u^2+2}{u\sqrt{u^2+4}} \end{equation}

Therefore the magnification for a single lens depends on three parameters: $u_0$ (minimum separation lens-source), $t_0$ (time where the magnification is maximum) and $t_E$ is the characteristic event timescale, which is the time it takes for the source to move with respect to the lens by one Einstein ring radius.

For a binary lens, however, the formulae of $u$ and $A$ above no longer hold. $A$ can be calculated for a point $u=(u_1,u_2)$ using numerical methods (Press et al. 2002) but, how is calculated $u$ for a certain time $t$? According to Tsapras (2018) $u$ depends on $u_0$, $t_E$, $t_0$ but also the angle $\alpha$ at which
the source trajectory crosses the binary axis, the mass ratio between the two components, $q$, and the separation between them, $s$, projected on the lens plane. ¿How these last three parameters come into play in the calculation of $u$ for a binary lens?

This answer applies to the simplest case: a static binary and a point source.

In the binary case, $u(t)$ describes how close each point in the source trajectory comes to (what you have defined as) the origin of the binary axis.

The solution is non-trivial. It involves finding the roots of a 5th order complex polynomial. You can look for example at how Etienne Bachelet's pyLIMA package codes it in Python. If you want to do it yourself, you first need to identify the location of the caustics and critical curves for the given arrangement. For that you need your two masses (or just the mass ratio) and their separation in units of the Einstein radius. The coefficients of the polynomial (A, B, C) are described in Schneider & Weiss 1986 (eqn 9b).

Then you need to define the trajectory of your source relative to the binary axis. You also have to choose your origin (some people use the midpoint between the masses, others use the largest of the two masses or the barycenter).

For each point in the trajectory (instantaneous source position) you have to evaluate the corresponding magnification, that is, find the roots of the polynomial for that position. You will then get five solutions, which correspond to the images of the source. However, not all 5 solutions correspond to real images. To find out which are the real ones, you have to substitute them in the inverted equation and see if they map back to the given source position. You will always have three (outside the caustics) or five (inside the caustics) real images.

You can see an example below.

You can see how different source trajectories generate different light curves at this link.


When will the next 'Super Blue Blood Moon' occur? I missed the sight yesterday (1 feb 2018) because I live right in the region where the sight was not visible. So when will the next Super Blue Blood Moon occur?

If you are looking for the perfect 'Super Blue Blood Moon', then, according to this article (assuming you live in the US):

  The next Super Blue Blood Moon won't happen until Jan. 31, 2037, and it will be visible in North America, Europe, Asia, Australia and parts of Africa.

However, if a Super Blood Moon is enough for you, you can see the next one on Jan. 21, 2019.


What color is earthshine? What color is earthshine (e.g the average color of earth that shines on the moon)?  I am making a solar system exploration game, and would like to know this for the lighting of my moon level at night, with a "full earth".

Edit: With your answers, this is what I get:

Edit:
Here is a video including the moon level, bathed in earthshine as the specified color in the answer at "night time" (clip is 12 seconds into the video):
https://www.youtube.com/watch?v=HKGCtkps8gk&list=PL9Bk1v7iJfdCpRaQ6vTGYOM-lXAO7RAQ1&index=1

If interested in my game I am making, here is a link to it:
https://jonathanlcopeland.wixsite.com/planetary

In my answer to Color of planets I estimated the colour of the Earth as #2f6a69 (based on averaging the colour in various images of Earth, and adjusting for albedo), but noted that it is the hardest of the planets to give a single colour to.

If you were on the near side of the moon with no sun the cones in your eyes would not be fully active: you would be have Mesopic vision. Also your eyes would adapt to the blue light conditions. As a result you probably wouldn't notice blueness of the light much.


How do we know the order of the new Trappist-1 planets? Using transit photometry astronomers were able to discover Trappist b through h. Based on this question we learn that the naming of planets is based on their distance from their star (b being the closest).

But how do we actually determine the distance from the star? From my understanding with transit photometry we basically just see a shadow against the backdrop of the star. That can tell us the planet exists, but how do we know the distance between the planet and the star?

Using Kepler's laws.
We can determine the orbital period, $P$, each planet has by just looking at the time between transits for a given planet. Each planet has a distinct transit so its easy to distinguish which planet is transiting and we can calculate a period pretty easily.
Kepler's law then tells us that if you're orbiting with a specific period, you have to be orbiting at a specific distance (based on parameters of the system). The general equation is given by
$$P^2 = \frac{4\pi}{GM_{star}}a^3$$
Where $G$ is just the gravitational constant, $M_{star}$ is of course the mass of the star and fairly well known, and $a$ is the radius at which the planet orbits. Simply calculate $a$ for each of your planets and put them in the correct order. You could even do this yourself using data from the paper.


Term for altitude of the sun? The sun travels in an arc across the sky. Where I live, during the summer the arc rises higher, but in the winter the arc is lower. Once might speak of highest altitude or elevation the sun reaches during any given day. In the old days this was called "high noon" when the sun had reached the highest point in the sky for that day. The town clock would be set to 12 at this point.

Is there a term for the elevation of the sun in the sky?

The term for when the sun is at its highest is "solar noon".

https://en.wikipedia.org/wiki/Noon#Solar_noon It is the moment the sun crosses the meridian. The meridian is an imaginary half-circle that goes from the northernmost point on the horizon to the highest point directly above you and then to the southernmost point on the horizon. The sun is always at its highest point in its daily path when it crosses the merdian.

You're right that in earlier centuries, each town would set its clocks at noon for when the sun was at its highest point. Those of us who are familiar with astronomy and history would call that type of timekeeping "apparent solar time". You can't guarantee an exact 24 hour day with "apparent solar time", so some people used "mean solar time" instead. (Historical note: Having each town choose its local noon became a nightmare for railway companies that wanted to set train schedules. So the railway companies urged the creation of 4 time zones in America and encouraged each small town to use "standard time" instead of "apparent solar time".

And as rgettman already mentioned, the term for the sun's height above the horizon is "altitude". Astronomers use the term "elevation" for a person's distance above sea level.


How to calculate the period of a lunar mansion? What is the period of a lunar mansion or station referring to and how is it calculated? Wikipedia says the following:

A lunar station, also called a lunar mansion or lunar house, is a segment of the ecliptic through which the Moon passes in its orbit around the Earth. The concept was used by several ancient cultures as part of their calendrical system.

For example, the period days of first lunar station is from April 23rd to May 10th and the period of the last lunar station is the days of April 20th, April 21st and April 22nd.
Please note that the following table is included in the Wikipedia page of Lunar Mansions and also the beginning day of each period is only listed here. For example the duration of the first mansion's period is from April 5th to April 18th. It's from April 18th to May 1st for the second Mansion and so on.

If I understand the concept of "mansion" correct, it is similar to an astrological sign, and astrononomically simply refering to a certain zone in which a certain object (here: the Moon) can be seen on the sky.
More specifically, a Lunar station - [Manazilu ʾl-Qamar منازل القمر] according to Islamic astronomical system seems a certain sector of the sky and the sky is divided into 28 of theses sectors. This defines a celestial coordinate system with $x$-axis being the ecliptic, the celestial longitude. The longitude is measured in degrees east of the vernal equinox (the ascending intersection of the ecliptic and equator):
An algorithm to determine the Lunar station at a given time would have as input parameter only the position of the Moon on the sky (actually only the Ecliptic longitude $\lambda$ of the Moon) and check in which interval $\lambda$ lies. The lower boundary of each mansion is given in the 3rd column in the Wikipedia-table shown in the question in a rather inconvenient format, namely in degrees and minutes from a start of a zodiac symbol.
In a first step, you would have to convert the Wikipedia list to a intervals with real celestial longitudes. You would end up with 28 if-clauses in your algorithm to determine a string $s$ containing the name of the lunar mansion:
$s_{\rm lunar~mansion}(\lambda) = \left\{ \substack{ {An-Nath} {\rm ~if~}
  0 \leq \lambda < 12^\circ 51' \\
\vdots \\
Butnu 'l-Hut {\rm ~if~} 0 \leq \lambda < 347^\circ9' = 330^\circ +17^\circ 9'
}\right.$
Here we used the fact that Pisces starts at $330^\circ$ celestial longitude.
Since you are after the begin and end dates for a each lunar mansion you have to calculate at which time the Moon celestial longitude $\lambda$ equals to the boundaries of the 28 intervals. I would do it vice versa and calculate for each day  of the year at 00:00:01 local time the longitude of Moon and then use $s(\lambda)$. You will end up with a table of 365 or 366 date- string-pairs. In the last step, you discard all lines of the table where a string repeats and reduce the list to 28 entries, with the start dates in the first column.


What are these data in light curve generator I'm generating light curves for some variable stars on the AAVSO website (see https://www.aavso.org/lcg ) . I can choose what type of data must be plotted. Can you explain what they are?

Thank you in advance!

The file format for submitting observations to AAVSO sheds some light on this.

"Visual" data are estimates by visual comparison to nearby reference stars of similar brightness.

U, B, V, R, I data come from CCD cameras using standard filters in the Johnson-Cousins photometric system, with passbands ranging from near ultraviolet to near infrared.
The J and H filters pass longer wavelengths in the infrared.

"Unfiltered w/(V|R) zero pt" are also from CCD cameras, not using one of the above filters, and calibrated using published V- or R-band magnitudes of reference stars.

Tri-R, Tri-G, Tri-B refer to the RGB channels of a color (e.g. consumer DSLR) camera.


Does the Moon have an aurora? If the Moon has a magnetic field and can possibly receive solar wind, then does it have an aurora? If Earth has an aurora, and Saturn has an aurora, then could the Moon possibly have an aurora?

Technically, yes, the moon does have an atmosphere that gets ionized by the sun.
NASA: Is There an Atmosphere on the Moon?

  our moon does indeed have an atmosphere consisting of some unusual gases, including sodium and potassium, which are not found in the atmospheres of Earth, Mars or Venus. It's an infinitesimal amount of air when compared to Earth's atmosphere. At sea level on Earth, we breathe in an atmosphere where each cubic centimeter contains 10,000,000,000,000,000,000 molecules; by comparison the lunar atmosphere has less than 1,000,000 molecules in the same volume.

Pretty thin soup. Sodium and potassium get kicked up by photons hitting the surface. There's also argon, helium and other minor components.
As shown in this figure from the first link:  The sodium in that atmosphere does glow; (Rayleigh unit definition). At least some of the glow is due to full fledged ions rather than charge-neutral fluorescence:

  It is confirmed that the ions include oxygen, sodium and potassium.

So, whether by ionic or fluorescent emission, the moon's atmosphere does glow. Unless one wants to argue about the glow not being restricted to the poles by a magnetic field, or airglow, that glow counts as an aurora.