How is spectroscopy used to deduce what an object is made of? Spectroscopy is an analysis of light (or other EM wavelengths) that is often used by scientists to examine what an object is made from or contains.
Apologies if this is a stupid question, but this sounds effectively like saying “this thing is absorbing this wavelength or colour, therefore it is this substance”.
I’m confused as to how this works in practice. As a familliar example: light bouncing off leaves in summer can be a completely different colour to leaves in winter. Water when frozen looks to be a different colour to when it is liquid. Copper is shiny brownish unless it gets a bit rusty, then it’s bright green, etc etc.
Is it possible to explain how we can say with any amount of certainty that a given set of dips in EM wavelengths translates into identification of substances?

This is not exclusive to spectroscopy applied to astronomy but general.
Matter can interact with electromagnetic waves spanning a very wide range of frequency (energy). Also matter can emit electromagnetic radiation when in a kind of excited state.
Due to the internal mechanism of absorption/emission it happens that the spectral characteristics can be peculiar to the chemical nature and physical state of the matter under analysis.
This is basically what you are aware of.
Your concern likely arises by over-focusing on colour, that per se in not the most powerful identification tool, or even by thinking that the particular state of the matter does not count, or changes are neglected.
Let me take your example of leaves. The fact that they colour undergoes changes does actually means that their composition changes. This is already an information rather than a problem.
Imagine that observing a planet one detect, say, carbon monoxide, it does not mean that its atmosphere won't change. Eventually different observations would prompt a planetologist to ask himself why, perhaps concluding that a kind of volcanic activity or degassing is ongoing , just to say.
A planet looking green then brown on a regular pattern would certainly suggest the presence of plants or anyway photosynthesis based on chlorophyll, providing that the green spectrum closely resembles that one we know, and does not come from narrow spectral features that would otherwise indicate, for instance, the presence of chlorine.
In other words, probing a sample, in astronomy as well as on a lab bench, leads to information about that sample in that moment. This is quite philosophical rather than a problem in spectroscopy or spectroscopy applied to astronomy. Moreover spectroscopy doesn't come alone and certainly requires considering the scenario.
But at its core is the existence of peculiar features, they can be single lines or more or less complicated spectra, and those are linked to the composition of the sample, elemental or molecular depending on the frequency window used.
I am not sure if this answer your question, but again this passage
"this thing is absorbing this wavelength or colour, therefore it is this substance”
is both correct and wrong. It must be taken with a grain of salt, or things must be analysed in depth.
What is certainly true is that there are specific lines typical of elements, or other spectral features typical of molecules. Explaining why it is so is way more complicated (for me) to be done in few lines here. But the reason resides on the discrete electronic structure of matter, as well as molecular shapes combined with limitations on which transitions can take places. Combining the two leads to a high specificity.
Unfortunately not the best example for astronomy, but consider that a given compound virtually has its own IR vibrational spectrum, different from that of any other compound!
You might want to read about spectroscopy in general, and have a look at Wikipedia's Astronomical spectroscopy; Chemical properties


J2 perturbations and orbits I am trying to solve a problem where I need to calculate a satellite's orbit, but first I would like to ask for some clarifications from someone here that might know this stuff. I need to design an orbit so that no maneuvers (one part of the problem) are necessary to maintain it, and the hint is that there are J2 perturbation only and that the orbit is elliptical. I don't really understand this, so can someone explain what they mean with only J2 perturbations and how it is relevant here? (just asking for an explanation)

Thanks!

Due to the oblateness of the Earth (the Earth's equatorial bulge), a geocentric satellite's orbital plane will precess (rotate) relative to inertial space.
The rate at which the line of nodes moves owing to this bulge is given by
$$
\dot\Omega = -\frac{3}{2}J_2\left(\frac{r_E}{ℓ}\right)^2 n\cos\iota
$$
where $J_2$ is the is the zonal harmonic coefficient ($1.08262668\times10^{-3}$ for Earth), $r_E$ is the body's equatorial radius ($6\,378\,137$ m for Earth), $ℓ$ is the orbit parameter (the semi-latus rectum), $n$ is the mean motion, and $\iota$ is the inclination of the orbit.

For a given orbit parameter ($ℓ$) and mean motion ($n$), the inclination of a geocentric satellite orbit can be selected to obtain, for example, a Sun-synchronous orbit ($\dot\Omega=360^\circ$ per $365.26$ days, or $0.9856$ degrees per day).

Coordinate System

This Wikipedia article (and diagram from that article) describes the coordinate system used.

The orbital plane (yellow) intersects a reference plane (gray). For Earth-orbiting satellites, the reference plane is usually the Earth's equatorial plane.  The intersection is called the line of nodes, as it connects the center of mass with the ascending and descending nodes.  This plane, together with the vernal point ($\gamma$), establishes a reference frame.

Two elements that define the size and shape of the elliptical orbit
are the semi-major axis, $a$, and the eccentricity, $e$. The
semi-latus rectum is related to $a$ and $e$ by $ℓ=a(1-e^2)$.
Two elements define the orientation of the orbital plane in which the
ellipse is embedded: the inclination, $\iota$, and the longitude of the ascending node, $\Omega$.


The reason behind Big Bang It always amuse us to research about things around us and we always start our research with a question that - what must be the reason for happening of that phenomenon?

As we know that the formation of universe is being postulated with theory of Big Bang.
But now, I want to ask that what was the reason for Big Bang. I mean why it happened, what must be the circumstances or what made it happened?

WHY implies a reason, which is venturing in to the religious realm.

The circumstances under which an event such as the Big Bang occurs are guess work at best. Since the Big Bang is a singularity from which time itself started there is no real before the big bang. That's the first problem. The second is that because of the spatial singular nature of the big bang no information from 'before' it could ever pass through to our current universe and provide us with any hints.

There are a number of oddball theories that explore the idea of physics before the big bang. Some investigate what occurs on scales of time shorter than that of the Planck time, where quantum mechanical processes may give us hints in to the cause or mechanics of a big bang event. Proving or, indeed, disproving these theories is currently impossible experimentally.


Composition of ice giants After reading the paper "The Measured Compositions of Uranus and Neptune from their Formation on the CO Ice Line", I was left with doubts which I would like to clarify.

Firstly, the paper proposes that Uranus and Neptune were created in the CO ice line of the Solar System, which explains several of their unusual characteristics (abundant carbon, depleted nitrogen, etc.).

In the paper, an explanation is proposed for the low D/H ratio of Uranus and Neptune, which is not consistent with that of the comets in their neighborhood, which suggests that the water inside them was not accreted from the protosolar nebula:

  Finally, coupling the D/H observations in Uranus and Neptune with our model where only a small fraction of the water present in the planets interiors is of nebular origin, and the rest originating from the transformation of CO into H2O, leads to a higher D/H ratio for the
  proto-ices that formed the planets. The value found is compatible with internal structure models and the
  formation location of the planets in the same region as
  comets.

Instead, water would be created by reacting the accreted CO with the H2 in its atmospheres. In other words, water would be created within them.

According to the paper, the composition of the CO ice line after 100,000 years was mostly CO, while water represented 1.9% of the total composition. This makes me wonder, why was water scarce in the CO ice line? Is water depletion in the CO ice line related to the high abundance of carbon in that zone?

On the other hand, the authors mention that the large amount of carbon-rich solids allowed the creation of the nuclei of these planets:

  Since CO is the major C-bearing volatile in the PSN [protosolar nebula], its ice line should be very rich in solids, explaining the origin of the high volumetric density of solids needed to form the planets. The high CO abundance in the building blocks implies that planets forming in this region should be very rich in carbon in bulk.

...

  In this paper we showed how the formation on Uranus and Neptune on CO iceline resolves many issues related
  to these planets. The diffusive redistribution of vapor across the icelines increases the local solids density allowing the formation of these planets from carbon rich
  solids but nitrogen poor gas, and lead to planetary interiors consistent with recent D/H measurements.

But what do the authors mean when they say "carbon-rich solids"? Does this mean that the nuclei of Uranus and Neptune are poor in silicates?

All this makes me think that the nuclei of these planets are similar to the carbon planets, which are believed to be made up of carbides, could this be the case of the nuclei of Uranus and Neptune?

However, the authors considered an environment with C/O ~ 1, but carbon planets are expected to form in environments with C/O > 1. Anyway, I can't think of anything other than carbide when the authors mention "carbon-rich solids"...

There is a few things one has to consider when talking composition:

It is usual to talk about relative abundances, and usually the solar composition is taken as the measure for this in the assumption that its composition is mostly prestine with a few exceptions. Now you can compare observations of different bodies and look at ratios of different materials, say nitrogen vs. carbon.

Now, materials have a different condensation temperature, and that is one of the main points of the paper. In the sun everything is in gas phase and thus has about pristine ratio.

Planets on the other hand form from solids. Thus - assuming a planet forms at distance R from the sun - it forms only from the materials which already solidify at the temperature at the given distance. (This is simplified due to radial mixing in the PPD and planetary migration, but the point is still valid). While the overall chemical composition of the PPD is the same, the chemical composition of the solids is different, the high(er)-temperature condensates are enriched, thus they are also enriched in the planets forming there

Carbon dioxide condenses from gas phase at slightly higher temperature than nitrogen. That means that you enrich the solid phase of the PPD in carbon and oxygen. Planets form from solids and only accrete gas when they have grown sufficiently - a threshold which Uranus and Neptun only barely reached. At the same time the gas of the PPD has to be in pressure eqilibrium, thus a flow towards the condensation zone exist, leading to slightly further enrichment of the condensing matter in the solid fraction - which is only partially balanced by the radial drift of the solids inward where they evaporate again.

In essence, due to different condensation temperatures, and the region the two outer gasous planets formed, they are enriched in carbon when comparing to nitrogen due to carbon dioxide ice condensing in the solar nebular. It doesn't mean that anyone took away the silica nor the water ice in the formation - as such.

I don't find there any support in the paper that the ratio of C/O can be enhanced beyond 1: the most abundant solids are slica, water ice - and the point of the paper at that distance CO which is increasingly enhanced during the formation process due to transport processes of solids and gas and condensation in the vicinity of the CO snowline (see figure 4 therein).


Why did supernova 1987A's "String of 'Cosmic Pearls'" appear to be so lumpy 20 years later? Is it still? NASA's A String of 'Cosmic Pearls' surrounds an exploding star is beautiful and the page says:

This image shows the entire region around the supernova. The most prominent feature in the image is a ring with dozens of bright spots. A shock wave of material unleashed by the stellar blast is slamming into regions along the ring's inner regions, heating them up, and causing them to glow. The ring, about a light-year across, was probably shed by the star about 20,000 years before it exploded.

Did the ring break up into "pearls" or lumps due to some kind of instability? Why so lumpy? The image was taken 20 years after the supernova was first observed, does the ring still look like this?

Also see https://en.wikipedia.org/wiki/File:HST_SN_1987A_20th_anniversary.jpg

The "lumpiness" is (mostly) inherent to the ring, and is probably the result of instabilities in the outflowing gas that gave rise to it in the first place. E.g., Akashi et al. (2015):

We suggest that clumpy dense outflowing equatorial rings around
evolved giant stars, such as in supernova 1987A and the Necklace
planetary nebula, are formed by bipolar jets that compress gas towards
the equatorial plane. The jets are launched from an accretion disc
around a stellar companion.... we perform 3D numerical simulations,
and show that bipolar jets expanding into a dense spherical shell can
compress gas towards the equatorial plane and lead to the formation of
an expanding equatorial ring. Rayleigh-Taylor instabilities in the
interaction region break the ring to clumps.

What you're seeing in the image is emission due to heating from the impact of the expanding supernova shock wave. Some of the clumpiness may be exaggerated by the fact that denser clumps of gas can radiatively cool more efficiently than diffuse gas, as explained by Fransson et al. (2015):

If the density of a clump is sufficiently high, radiative cooling will
cause the clump to collapse to an even higher density. The result will
be an optically emitting hotspot (Pun et al. 2002). If instead, the
density of a clump falls below the threshold density for radiative
cooling, the gas behind the transmitted shock will radiate X-rays and
very little optical radiation. This threshold density is a sensitive
function of the velocity, ${{V}_{{\rm clump}}}$, of the shock entering
the clump. Thus, at any given time, the requirement for radiative
cooling acts as a high contrast filter, limiting optical radiation to
only the denser clumps.

The brightness of the ring has faded somewhat since that image was made (more on the east side than on the west), as shown in this composite of HST images (Figure 3 of Larsson et al. 2019):

The figure in the paper itself includes an animation of the evolution.


What is the process for vetting the 4,175 candidate planets Kepler has discovered? In the National Geographic article about NASA's announcement of new planets discovered by the Kepler spacecraft, it states that there are 4,175 candidate planets. What is the process for vetting these candidate planets? How do we know they exist without knowing whether they are planets? Or are they candidates because the data hints that a planet might be there but we need more detailed data or more analysis before we can confirm it?

Planet "candidates" are Kepler Objects of Interest (KOIs)that have a transit-like light curve and have passed a number of observational tests. They are candidates, because although they do show a transit in the light curve of the star in question, there is no independent confirmation of a planetary mass.

One problem to overcome is that of "false positives". There are other astrophysical phenomena besides planets that can mimic an exoplanetary transit in a Kepler light curve. For instance a grazing incidence stellar binary can produce what looks like a transit in a light curve; so too can a chance alignment of a star with a background eclipsing binary star. There are also a number of instrumental anomalies, such that a signal in one part of a CCD or the Kepler field can produce a "ghost" at another position that might look like a transit.

If you can obtain detailed spectroscopy including accurate radial velocity measurements you can usually rule out most of these false positives, largely by getting a mass constraint for the companion.

Even where you have a very clean transit signal and can estimate a planetary radius, a further problem is that a wide range of masses produce objects with very similar radii. ie. more massive brown dwarfs have very similar radii to exoplanets. Again, only a mass estimate, either through radial velocity measurements or sometimes through "transit timing variations" if the object is in a multiple exoplanet systems.

Now the problem with the KOIs is many of these stars are way too faint ($V>14$) to do the kind of detailed spectroscopy that is easily possible on the much brighter exoplanets around stars found in say the HATNET or WASP ground-based surveys of bright stars.

So, what you can do is tackle the problem statistically, by identifying the kinds of false-positives you might have, quantifying their influence, and throwing away suspect objects (see for instance Batalha 2012). Section 4 of this paper describes in detail some of the tests that are done: e.g. comparing the depths of odd and even numbered transits to look for asymmetries that would indicate grazing incidence binaries; looking between transits for a secondary eclipse that would also indicate a stellar companion; the shape of the transit is diagnostic but cannot easily rule out a planetary candidate; searching for motion of the "photocenter" of the source - if the photocenter moves during a transit it could indicate a background, diluted, eclipsing binary lightcurve.

An early paper by Morton & Johnson (2011) claimed on the basis of a population synthesis approach, that that astrophysical false positives were limited to less than 10%. However, a recent paper by Coughlin et al. (2014) discusses how instrumental effects can be tested for by comparing the transit periods with the periods of other known objects in the Kepler field of view. They claim that around 30% of the KOIs may in fact be false positives. Either way it looks like the big majority of the KOIs are indeed exoplanets, but identifying which ones aren't will require detailed follow-up.


Why are there so few supernovae in M31 (Andromeda)? Estimates of the supernova rate in the Milky Way put it at a few per century, but very few of these are visible from Earth (at least with the naked eye) because of intervening gas and dust clouds). On the other hand the Andromeda galaxy (M31) is sufficiently face on that we should see at least most supernovae there, and is several times more massive than the Milky Way, so one would naively expect to see at least one every few decades. Nevertheless, we have seen only one supernova in M31 in the last 150 years (SN1885a).

Are these accepted (or even seriously proposed) explanations for this?

The low supernova rate in M31 can be directly attributed to the fact that the galaxy's star formation rate is much lower than the Milky Way's.

Andromeda is currently in a relatively quiet phase in terms of star formation, currently experiencing rates of $\sim0.40M_{\odot}\;\mathrm{yr}^{-1}$. The Milky Way, on the other hand, has a star formation rate several times higher; as such, it contains more massive, short-lived stars which are supernova progenitors. This leads to a correspondingly higher supernova rate than Andromeda. Estimates of the supernova rate in M31 vary, but a value of 0.5 to 1.0 per century is reasonable. This in turn matches well with observations.


If all stars rotate, why was there a theory developed that requires non-rotating stars? According to Penrose's research, a non-rotating star would end up, after gravitational collapse, as a perfectly spherical black hole. However, every star in the universe has some kind of angular momentum.

Why even bother doing that research if that won't ever happen in the universe and does it have any implications for the future of astrophysics?

In a similar way, we could ask...

  No beams can be exactly 1 meter long. No beams can be exactly
  straight. The material making up a beam cannot be truly isotropic.
  So why should we bother calculating the stress in a 1 meter straight
  beam having isotropic material?

Because knowing how to perform this calculation is a building block for doing more complex calculations.

The non-rotating black hole calculation also provides a limiting solution.  The solution for a spinning star's collapse will approach this solution as the spin approaches zero.

Similarly, Newton told us that as external forces approach zero, the path of a moving object will approach a straight line.  This is useful to know even though there is no place in our universe that doesn't have gravitational influence.


What does an Einstein-De Sitter universe look like? I know an Einstein-De Sitter universe is a "flat" universe, i.e. with a K ("bendiness", sorry, don't really know what to call it in English) factor of 0, but does that entail anything as to its contents? The Wikipedia page is quite lackluster on this aspect, and my astronomy course textbook merely slightly less so (it says it's made up mainly of "non-relativistic, dust-like matter").

Bendiness = space-time curvature.

And yes, it is flat (k=0) for the EdS model. Essentially it is the epoch at which only matter is thought to dominate (no contributions from radiative pressure or dark energy, $\Lambda$).

It is only a model. The EdS universe is thought of as a static Universe which is expanding indefinitely. It just makes solving certain equations in Cosmology a little easier, but it was perhaps due to Einstein's stubbornness in accepting a dynamic Universe.


How do I align my finder scope National Geographic 76/700 EQ Telescope :  National Geographic 76/700 EQ

I tried aiming my telescope at the moon but I just couldn't do it, it was so hard to do, my finder scope isn't helping at all and I watched a bunch of videos saying to use the screws to align the finder scope but the screws on my finder scope don't do anything. Any suggestions?? I really need help tonight is cloudy and I only get like 5 minutes every hour to look at the moon

The moon is generally big enough to not need a finder scope. In general, The easiest way to aim a telescope directly at something is to look parallel to the telescope, right above the edge. If you can just see the object you are aiming at, it should be at least visible in the finder scope (if properly configured, see below). In the case of the moon, try to make just the top half visible when looking parallel to your telescope.

If you are having trouble using a finder scope, it might not be properly aligned. A finder scope has two wires forming a cross. A properly aligned finder scope will have an object in the middle of the telescope's view if it is exactly on the cross of the wires. If this is not the case, the position of the wires can be adjusted using the screws. This is best done at daytime by aiming the telescope at a recognizable landmark (somewhat) nearby, such as a tower.


Is the gravitational field of the sun uniform? I understand that rocky bodies in the solar system all exhibit gravitational anomalies. Does the sun exhibit any gravitational anomalies?  If so are they distinct enough that it effects the orbit of the Parker Solar Probe?

The Sun rotates, taking about 24.5 days to complete a revolution at the equator, a bit longer at the poles. This makes the Sun have a bit of an equatorial bulge, which in turn means that the Sun's gravity field is not quite uniform. The Sun's J2 is very small and the effect is well known.
Very large stars are asymmetric due to being close to the Eddington limit. The Sun is too small of a star to have the kind of gravitational anomalies that very large stars and rocky planets exhibit.


What is the composition of the Solar Wind? Is the composition of the Solar Wind known? I'm especially interested in the heavy metals present. Most accounts deny the existence of anything other than electrons, protons, and some alpha particles; but it seems to me that if we can identify most of the known elements in the Sun's photosphere, then they are likely to exist in the Solar Wind at some concentration. If not, what is the detection limit (ppm? ppb? ppt?) we have so far established? Have any limits been established for atom clusters (dust?)? As a secondary question, I guess that (neutral) hydrogen and (negative hydride) H(-) do not exist in the solar wind due to its temperature being too high. Is this correct, and if so, is it true throughout the heliosphere or does the solar wind cool enough for the formation of bound species?

We have very good data on the heavy metals in the solar wind from the Charge, Element, Isotope Analysis System (CELIAS) on SOHO:

Some of these elements were previously known; others were observed for the first time. The new ones are phosphorus, chlorine, potassium, titanium, chromium, and nickel. They were detected in smaller amounts than, say, carbon, oxygen or calcium.

Now, the seeming overabundance of heavier elements, with the peak at iron, might seem surprising. One would think that the lighter metals - carbon, oxygen, etc. - might appear in higher quantities, given their substantially lower masses, which make it easier for them to escape the Sun's atmosphere. However, this is due to experimental bias. The instruments on SOHO were designed to search for these particular heavier elements, which of course led to the detection of several new isotopes. We now have a much better picture of what heavy metals can be found in the solar wind, but the chart above should not be taken as evidence of the relative quantities, as a whole.

Additionally, there actually is some neutral hydrogen, both in the solar wind and the solar atmosphere (see Olsene et al. (2004) and Collier et al. (2001)). It should be present in the corona, and can be detected and modeled by Lyman $\alpha$ scattering. It was also detected and studied by the Low Energy Neutral Atom (LENA) imager on IMAGE.


Signal-to-noise in inverse angstrom for spectroscopy? In a paper I came across the description of the signal-to-noise ratio (SNR) for observations with a spectograph. This was reported as $10\:1/\mathring{A}$. I am rather new to spectroscopy, so could someone clarify these units for me? Why is it used and how should I read it?

A spectrum imaged onto a CCD or other detector consists of photons spread out along a wavelength axis. Signal-to-noise (S/N) depends on how many photons you have from the source, how many from the background, intrinsic noise from the electronics, etc. -- and what kind of bin you're adding up the photons in. If you summed up all the photons across the spectrum (over all wavelengths), you'd get one number with a very high S/N, but no spectral information. If you divided the spectrum into N different wavelength bins, you'd get a lower S/N per bin, but more spectral information.

What the S/N ratio you mention means is that if you divided that spectrum into bins that were 1 Angstrom wide, you'd have enough photons in each bin for a S/N of 10 in each bin (at least for some region of the spectrum, probably near the central wavelength). You can then have some idea how the S/N would improve for bins larger than 1 Angstrom in size, or how it would get worse for smaller bins. S/N per Angstrom is conventional for optical spectroscopy, both because Angstroms are traditional and because moderate resolutions spectrographs often have scales of a few tenths to several Angstroms per pixel along the wavelength direction.


How deep in Mars would a person not need insulation and pressure? How deep in Mars' surface would one have to go to both not need a pressurized suit and be warm enough to just wear clothes? in other words is there a dept Goldilocks where you would only need an oxygen supply?

According to this paper, there are various but enough good estimations for the temperature gradient of the Martian soil. Note, direct measurements will we have first with the next Martian lander, the InSight:

Image from here

The for us important part of this estimation is this:

  Depth penetration of the annual temperature wave at $120^\circ E,
> 20^\circ N$, using data from the NASA/MSFC Mars GRAM as the surface
  boundary condition and assuming a planetary heat flow of 20
  $\frac{mW}{m^2}$. The snapshots of the temperature as a function of
  depth are given for the models with

  (a) $k_\infty = 0.02 \frac{W}{m\cdot K}$ and
  (b) $k_\infty = 0.1 \frac{W}{m\cdot K}$.

  Heat flows derived from the soil temperatures given in Figures 3a and
  3b for models with
  * (c) $k_\infty = 0.02 \frac{W}{m\cdot K}$ and
  * (d) $k_\infty = 0.1 \frac{W}{m\cdot K}$.

  The snapshots (gray lines) show the local heat flow. The area inside
  the envelope (black lines) represents possible heat flow values that
  can be obtained by a single measurement. The heat flows derived from
  the annual mean temperatures are indicated by squares. Note that in
  order to calculate heat flows, the thermal conductivity was assumed to
  be known.

What we can see here, is similar to the Earth:

there are significant temperature differences in the upper soil, depending on the geographical position, yearly and daily cycles
however, around from 4m depth, the soil temperature is roughly constant.

Extrapolating the upper two graphs, we can expect a pleasant earth-like temperature not very deeply, roughly around 20-40 m.

However, according to this answer, the Earth-like pressure happens much deeper, around 20-40 km below the surface. This answer uses the Barometric formula to calculate the required depth, which is a very good estimation. It seems probably unreachable with the current technology, although it is not very far away from it: the main problems of the digging of deep holes are

cooling
water incursions

The first is much easier, the second is non-existant on the Mars.

Note, the Martian atmosphere is mainly carbon dioxide, thus spacesuits won't be needed, but some oxygen tanks still will be.

There is no such depth where both the temperature and the pressure would be comfortable for us.

P.s. actually, 16% pure oxygen is already enough for us to breathe, which makes the required depth to around 10-15 km.


Definition of stellar core? This is a basic question, but I may as well ask it. I had always thought that the core of a main-sequence star is defined as the part hot enough for nuclear fusion. Some dictionaries seem to agree with this.

However, many books say that protostars and pre-main-sequence stars also have cores, though they are not undergoing hydrogen fusion.

So what exactly is the definition of a stellar core? If it doesn't necessarily have to be hot enough for fusion, what separates it from the rest of the star?

I think that there isn't a strict answer to this question. However, I believe the answer is that there's a difference between the core of a hydrogen-burning star and the core of a protostar or star-forming, gas cloud.

For a hydrogen-burning star, the core, as you say, is the region of the star where fusion is taking place. This is surrounded by the radiative and convective zones (which one comes first depends on the mass of the star). For true stars, the concept of the core is well defined.

For things like protostars and star-forming gas clouds, the concept of the core is less well defined and more a nomenclature for a region of the object rather than a strict definition. I don't think it is correct to assume that because one is talking about the core of a protostar, that they are referring to the core as it is defined for a hydrogen-burning star.

So what does it mean to be a core in a protostar or star-forming gas cloud? I will first point out that protostars can still be fusing. In the pre-main sequence stage, most stars will be fusing deuterium and we can consider the core to be the region where this is occurring. A protostar does not become a fully fledged star until it begins hydrogen burning, but deuterium fusion requires lower temperatures and pressures than the full proton-proton chain of hydrogen fusion (of which deuterium fusion is a part) and so can occur in protostars.

We might also distinguish a core from outer regions based on a density or compositional change. If we plot up something like the density (or really any property that changes with radius), we are likely to see a drastic jump signifying some sort of boundary. Cores for star-forming regions may be defined by highly dense regions, high temperature regions, or regions "where the physics changes" because we've passed some critical threshold at some radius. These cores are less well defined and can't be likened to stellar cores very well.


Closest star system to Alpha Centauri? The closest star system to our Solar System is Alpha Centauri.

But is our Solar System the closest star system to Alpha Centuari?

If not, which star system is?

The sun is the nearest star to Alpha Centauri (unless you count Proxima Centauri, which is really part of the same system).

There is a very small and dim pair of brown dwarfs, called Luhman 16 that are closer, at about 3.6 light years from Alpha Centauri. Brown dwarfs are not true stars, but they do glow from their own heat. They were only discovered in 2011. It is possible that there are other very dim objects, but these would not be stars either in the strict sense.


How to tell a crater is old or not? Based on Wikipedia, we can estimate the age of a planet's surface.

How to tell a particular crater is newly formed or not? It may have sharp edge.

Different astronomical objects may have different kinds of environments which may make this more complicated.

Are there any peer-reviewed papers?

One criterion that works well is the presence or absence of smaller craters inside. If the crater is clean, it's probably new. If it's full of smaller craters, it's old. This applies to planets and satellites with no atmosphere, or with a rarefied atmosphere.


Red shifting galaxies I am an amateur astronomer please correct if any of my understandings are wrong. We all know that from the Hubble's ultra deep field image the most distant galaxies which were created shortly after big bang looked to be red shifted. This is because of the process of expansion of the universe these lights are reached its highest visible wavelength. So in near future (in terms of astronomy) the galaxies which appears to be normal today become red shifted?  and those are already appeared as red shifted become invisible? If it become invisible still can we see it through infrared telescopes right?

Assuming an open model of the universe and a long enough timeline galaxies which appear "normal" today would become more red shifted over the course of observation.  I put normal in quotes because there are no galaxies which are relatively static to ours.  Any galaxy which has movement will have some "shift" to them, and all galaxies are moving away from us.

It is possible that eventually the light from them could move into the infrared and even the microwave in extreme cases.


Number Density of Dark Matter Halos Is there a way to calculate the expected number density of Dark Matter Halos above a given mass, in a certain redshift range, and in a certain area?

The function you're requesting — i.e. the number density $N$ of DM halos above a given mass $M_\mathrm{h}$ — is called the cumulative halo mass function (cHMF). It is obtained by integrating the halo mass function (HMF) from a given mass to infinity. The HMF, in turn, is thus the function that describes the (differential) number density of DM halos of a given mass.

In other words,
$$
\boxed{N(>\!\!M_\mathrm{h})
= \int_{M_\mathrm{h}}^\infty \!\!\!dM_\mathrm{h}'\, \frac{dN}{dM_\mathrm{h}'}.}
$$

Halo mass function

So, the problem is to determine the HMF, i.e. $dN/dM_\mathrm{h}$. This was first calculated, analytically, by Press & Schechter (1974) assuming spherical collapse of structures from an initial, smoothed density field. It may be written as
$$
\frac{dN}{dM_\mathrm{h}} = \frac{\rho_{\mathrm{m,0}}}{M_\mathrm{h}}
                    \left| \frac{d\ln\sigma}{dM_\mathrm{h}} \right|
                    f(\sigma),
$$
where
$\rho_{\mathrm{m,0}}$ is the present-day average mass density of the Universe,
$\sigma = \sigma(M_\mathrm{h},z)$ is the rms fluctuations of the (smoothed) density field, and
$f(\sigma)$ is the "multiplicity function" (note that because the number density decreases so fast with halo mass, for computational purposes often the HMF is expressed as $dN/d \ln M_\mathrm{h}$ rather than $dN/dM_\mathrm{h}$).

If you want, I can give you more details about how to calculate $\sigma(M_\mathrm{h},z)$ and $f(\sigma)$. You can also find details on this in sec. 2.1 of Laursen et al. (2018), but note that there's an error in Eq. 1. If you're happy with using a "black box", you can get both the HMF and cHMF for your favorite cosmological parameters using this online HMF calculator.

Only in the Press-Schechter formalism can an analytical form of $f(\sigma)$ be derived, and it was subsequently found that it over(under)predicts the collapsed fraction at the low-(high-)mass end (see e.g. Governato et al. 1999); in general one must obtain it by fitting halo abundances in cosmological $N$-body simulations.

Defining a halo

This is what N. Steinle describes in his answer, but actually you don't need to assume a density profile of the halos. So, how do you count halos in a simulation? There are several ways, arguably the two most popular ones being the spherical overdensity (SO) and the friends-of-friends (FoF) method.

Spherical overdensity

In the SO method, you first calculate the center of mass (CoM) of a clump of particles in the simulation, and then you calculate the average density $\bar{\rho}$ of particles in successively larger spheres centered on the CoM. As you increase the radius of the sphere, $\bar{\rho}$ drops because you include less and less dense regions. When the density has reached a certain factor $\Delta$ times the average density $\rho_\mathrm{m}(z)$ in the Universe you stop, and the total mass of all particles inside that sphere is then the halo mass. The overdensity factor $\Delta$ is usually chosen to be around 200, but other choices exist, e.g. 500 which then gives slightly smaller masses (because you stop counting earlier).

A variant of this method is using ellipsoids rather than spheres, allowing for more realistic results for elongated structures.

Friends-of-friends

In the FoF method, you start at an overdensity and count all particles that are "linked" together, meaning they are within some chosen distance (the "linking length") of each other. This method may give more realistic results for very non-spherical structures, but also tends to include particles in filaments streaming into the galaxies, which perhaps shouldn't be considered a part of a galaxy.

The figure below (from Klypin et al. 2011) shows halos from the Bolshoi simulation identified with the two methods; SO (red points) and FoF (blue points), compared to an extension of the P-S HMF (solid black line) to allow for ellipsoidal structures (Sheth & Tormen (1999, 2002). At all masses, FoF halos are seen to be more massive than SO halos.

Redshift range and area

Re-reading your question, I think maybe you're interested not in the number density, but in the absolute number in a volume spanned by a redshift range $dz$ and area $dA$. If that is the case, then you simply multiply your $N(>\!\!M_\mathrm{h})$ by the cosmological volume given by $dz$ and $dA$. Let me know if you also want to know how to calculate that.


Supernova in Hertzsprung–Russell diagram If you could put a supernova in the Hertzsprung–Russell diagram. Where would it be? Would it be near the white dwarfs or near the super giants?

I know that a supernova isn't a star but rather the explosion of a star, but if you technically could. Where would it be located?

Thanks!

It would be located way off the diagram to the top and left  i.e. moderately hot and very, very luminous. Of course it then changes with time as the supernova fades and cools.

This paper by Faran et al. (2017) shows plots of luminosity and temperature versus time for type II supernovae. They start at 15,000K and luminosities of about a billion suns and then fade to about 5000K and by an order of magnitude in luminosity after 50 days.


Measuring misalignment between two positions on sky Let's say I have the (RA,Dec) for two positions on the sky. I want to measure the position angle between these two positions. In other words, if I had the Cartesian coordinate vectors for these two positions (say [x,y,z]) then I think the position angle PA would simply be the dot product of the two vectors, so basically cos(PA). However, RA and Dec are spherical coordinates (corresponding to $\phi$ and $\theta$ respectively), not Cartesian coordinates. How do I get cos(PA) between the two positions on the sky if I only have their (RA,Dec) instead of [x,y,z]?

https://en.wikipedia.org/wiki/Position_angle

  Position angle, usually abbreviated PA, is [a] convention for measuring angles on the sky in astronomy. The International Astronomical Union defines it as the angle measured relative to the north celestial pole (NCP), turning positive into the direction of the right ascension. In the standard (non-flipped) images this is a counterclockwise measure relative to the axis into the direction of positive declination.

Assuming you mean the angle between the meridian line through A and the great circle that goes through points A and B, then it goes something like this.

Define vectors from the origin to A and B assuming they lie on a unit sphere, such that $x_A= \cos \delta_A \cos \phi_A$, $ y_A = \cos \delta_A \sin \phi_A$ and $z_A= \sin \delta_A$, and similar for B. Here $\phi$ refers to right Ascension and $\delta$ is declination.

The great circles in question define planes that pass through the origin. A normal to the plane defined by OAB is given by the vector product $\vec{n_1}=\vec{A}\times \vec{B}$. Similarly a great circle passing through the O, A and the NCP $(0, 0, 1)$ has a normal of $\vec{n_2}= \vec{A}\times (0,0,1) = (y_A, -x_A, 0)$.

The angle you are looking for is the angle between these two normal vectors, which can be found from scalar product in the usual way.
$$\cos \theta = \frac{\vec{n_1}\cdot \vec{n_2}}{|n_1||n_2|}=\frac{\cos \phi_{A}(y_{A}z_{B} - y_{B}z_A) + \sin \phi_{A}(x_Az_B - x_Bz_A)}{|\vec{A}\times \vec{B}|}$$


Venusian polar surface temperatures I've stumbled across several articles about how the Venusian polar high atmosphere is really cold. What these articles appear to fail to specify is what the surface temperatures of the poles are. I am interested in knowing the polar surface temperatures. I would think that convection would lower the polar surface temperature to lower amounts, but I don't know a lot about Venus's poles to say anything about this.

Venus's surface temperature is hot everywhere at about 460⁰C. There may some small differences due to latitude, but not nearly as pronounced as on Earth or Mars. The supercritial CO2 that forms the lower atmosphere is a good conductor of heat, keeping surface temperatures very stable.

The article you refer to notes that models of the Venusian atmosphere predict somewhat higher temperatures at high altitude and latitude than can be inferred from measurements made during aerobraking. This tells us that the models of the atmosphere need to be tweaked. It doesn't mean that there is a region of cool temperatures at the poles.


Why does this nucleogenesis table not label s and r-processes for all elements (not-labmade) past Fe? I'm reviewing nucleogenenesis and came across the table below. I like it because it actually labels the s and r-process elements, but I became confused as to why the neutron capture processes begin at A = 38. I thought anything with an atomic number greater than 26 has to be formed by neutron capture? What is my confusion here? Thanks in advance!

If you go back to the sourced article in your graphics by Jennifer Johnson it has a more verbose colour legend. For the grey part it explicitly states

very radioactive elements. Nothing left from stars.

and her figure caption more verbosely

Each element in this periodic table is color-coded by the relative
contribution of nucleosynthesis sources, scaled to the time of Solar
System formation. Only elements that occur naturally in the Solar
System are shown; artificially made elements and elements produced
only through radioactive decay of long-lived nuclei are shown in gray.
The data plotted in this figure are available in table S1.

And that pretty much sums it up:
The colour gives the source of the elements as found on Earth.
Thus the colour does NOT indicate how the elements can be formed in general, but the origin of the isotops as found on Earth (or present on formation of Earth, thus still long after nucleosynthesis in their progenitor stars). The lifetime of the longest isotope of technetium is 4.2 million years, and of promethium of only 17 years. Thus basically all of those grey-coloured elements are decayed long ago and none of the naturally occuring specimen on Earth are anymore of primordeal origin but result of fission of higher-order elements.
EDIT to add: As to the 2nd question in your posting which is quite distinct from the title

"why the neutron capture processes begin at A = 38. I thought anything with an atomic number greater than 26 has to be formed by neutron capture?"

Those elements can actually be formed by fusion of the lighter elements in the core of the supernova due to the high density and temperature (basically similar to how we can create heavier elements in the lab, colliding heavy ions) - but that fusion will consume energy instead of releasing energy.


How is the Gould Belt younger than the sun? Our sun is located in the Gould Belt, a  group of stars which is thought to be 30 - 50 million years old. However, the sun formed 4.6 billion years ago.

Did the belt form around us?

Everything is in motion in our Galaxy. The Sun has executed some 20 laps of the Galaxy since it was born and may have migrated inwards or outwards to some extent. The Sun's location has nothing to do with the Gould belt or vice versa.

The Gould belt stars formed just 30 million years or so ago. The position of the Sun relative to the Gould belt is a coincidence and it will not be in the Gould belt in another 30 million years or so, because it has motion relative to it.


Does time dilation increase within overlapping gravitational fields? If a spaceship was to travel to the barycenter of a binary star (the stars having identical size and mass) and come to a stop there, would the people on board this spaceship find that time is moving slower there (relative to the passage of time experienced outside of the gravitational fields of this binary star) due to the two stars overlapping gravitational fields at this point in space?

Does time dilation increase within overlapping gravitational fields?

Gravitational time dilation depends on the observers' relative positions in the gravitational potential.

For relatively weak gravitational fields the rate at which a clock ticks for observer A compared to the clock rate for observer B is given by
$$\frac{d \tau_{\rm A}}{d\tau_{\rm B}} \simeq \sqrt{1 + \frac{2\Delta \Phi_{\rm AB}}{c^2}} \sim 1 + \frac{\Delta \Phi_{\rm AB}}{c^2},$$
where $\Delta \Phi_{\rm AB}$ is the difference in gravitational potential between observers A and B.

Gravitational potential is a scalar quantity, so the basic answer to your question is yes - the effects of the two neutron stars would be summative. However, I would hesitate to use the approximation above when dealing with the strong gravity near neutron stars.


How significant are the recent results that Scholz’s Star has perturbed several observed hyperbolic objects? The Gizmodo article A Visiting Star Jostled Our Solar System 70,000 Years Ago refers to the the three year old ApJ. paper The Closest Known Flyby of a Star to the Solar System (also arXiv) which describes Scholz’s Star and it's pass close to our solar system about 70,000 years ago.
The Gizmodo article then discusses the newly published paper in MNRAS Where the Solar system meets the solar neighbourhood: patterns in the distribution of radiants of observed hyperbolic minor bodies. However, while I can access the earlier paper, the new result is paywalled and I'm not able to access it (at least not soon).
The second half of the abstract in particular is confusing me.

Here, we perform a systematic numerical exploration of the past orbital evolution of known hyperbolic minor bodies using a full N-body approach and statistical analyses to study their radiants. Our results confirm the theoretical expectations that strong anisotropies are present in the data. We also identify a statistically significant overdensity of high-speed radiants towards the constellation of Gemini that could be due to the closest and most recent known fly-by of a star to the Solar system, that of the so-called Scholz's star. In addition to and besides 1I/2017 U1 (‘Oumuamua), we single out eight candidate interstellar comets based on their radiants’ velocities.

I've heard of a radiant of a meteor shower - it's an apparent position of the source of meteors referenced to the position of the Earth at the time of the shower. But I've= never heard the term applied to the orbit of a minor body unrelated to the Earth's position. What is the "radiant" of a minor body with a hyperbolic orbit in a simulation? Could it be the asymptotic incoming direction of the hyperbola?
But my main question is simply how "statistically significant" is this result in reference to the enhancement in the direction of Gemini? I can't see the data. Is it just a tiny fluctuation, or a fairly obvious and robust feature?
A screen shot of the data would be most welcomed!
Possibly helpful: List of hyperbolic comets.

Not an answer, but just on radiants:

Radiant means angle of approach.   It's applied to meteor showers because the Earth intersects the dust trail that causes the meteor shower at a specific place in orbit and dust trail has a specific angle of intersection relative to Earth and Earth's orbit.

Source of picture.

  What is the "radiant" of a minor body with a hyperbolic orbit in a
  simulation

Radiant can't be applied to elliptical orbits though extremely elliptical orbits kind of have a radiant, but it can be applied to objects approaching the solar system.  A hyperbolic orbit generally implies an object that came from outside the solar-system though it could also be a gravity assisted object from inside the solar system that was accelerated from an elliptical to a hyperbolic orbit.

Here's an article that mentions radiant in association with an exo-solar object

  astronomers looked for the radiant it seemed to originate from.
  Calculations determined that A/2017 U1 came from a radiant located
  close to (R.A. = 18h 41m 25s ; Dec=+34° 15′) coordinates, which is
  near the actual position of Vega

exo-solar objects approach the solar system in a mostly straight line until they get close enough for the sun to bend their path.   Where they came from before their direction was curved by the sun's gravity is their radiant.


Questions about spiral galaxy arms I have 2 questions related to spiral galaxies.

Firstly, how did the arms form? Why would the stars accumulate into those specific areas? And secondly, why are they still intact?

The inner parts of the arms must be revolving more rapidly than the outer parts, so surely the would become stretched and then no longer resemble arms, but simply a disk around the galactic center.

Actually, the stars and nebulae that make up the spiral arm are only temporarily part of that spiral arm. Spiral arms are more like sound waves where individual particles move around a more or less stationary position. (Look for instance at the animation of longitudinal waves from Dan Russel, the red dots move a bit to the left and to the right around a stationary position). Dust, gas and stars move towards or away from another just as longitudinal waves. Where the dust, gas and stars come close together (and where, therefore, the density increases), spiral arms can be seen as more stars are close together increasing the brightness at that position in the galaxy.

This effect is, furthermore, much increased because the increased density of dust and gas in the spiral arm causes protostars to form. The brightest stars burn up their energy so fast that they will cease to exist even before the longitudinal wave (the spiral arm) has passed. These very bright stars only exist for a small portion of their orbital period around the galaxy's centre, and only while they are in the spiral arm. The large majority of stars exist much longer, but are also much dimmer and contribute only little to the overal brightness of the galaxy.

This causes the spiral arms to be so much brighter than the rest of the disk, where also a lot of stars exist. But these can hardly be seen as they are much dimmer.

Of course, the stars do not revolve around a stable position in the galaxy (as the red dots in the wave animation) but follow their own orbits around the centre of the galaxy. Sometimes a bit faster, and sometimes a bit slower depending on the position relative to the spiral arms.

Because the spiral arms are waves, it does not matter that stars near the centre move faster than the stars at the edge. It just means that they will be part of the spiral arm for a shorter period of time.


Understanding date of astronomical events I have a masters in chemistry but pretty much, a layman in astronomy.
So, can you please explain to a novice like me, about this paragraph taken from the Wikipedia article on Makar Sankranti:

There are two different systems to calculate the Makara Sankranti date: nirayana (without adjusting for precession of equinoxes, tropical) and sayana (with adjustment, sidereal). The January 14 date is based on the nirayana system, while the sayana system typically computes to about December 23, per most Siddhanta texts for Hindu calendars.

Am I correct to understand that when the date was assigned in Hinduism some thousand (?) years back, the winter solistice used to be on 14th/15th January?

Precession of equinoxes means that the North pole of the Earth is changing its direction. This also means, that the dates of the seasons (seen from outside the Solar System (= sidereal)) are changing. Nirayana calculates the date of Makar Sankranti with adding years to the first Makar Sankranti, but sayana calculates the date of Makar Sankranti relative to stars (sidereal).
In a nutshell: nirayana is on the same date as the first event (first Makar Sankranti), but sayana is on the same event as the first Makar Sankranti (winter solstice). Yes, winter solstice was once on the 14 January.


Get a table of Moon phase angle per day Where can I get a table with the Moon phase angle for each day ?

It's available  here for a given day, but I would have to input each day of a year to get a full table.

=== NEW EDIT : 2019-09-18 ===

Actually, I'm preparing a calendar of lunar phase with corresponding Moon photo for each day and for a whole year. For this, I downloaded a set of images here from Jay Tanner's website. The name of these images correspond to the phase degree, but when I associate these images with the data from JPL HORIZONS suggested by @Mike G, it doesn't match what I see in the Sky.

How can I associate a set of photo of Moon phases to each day of a given period of time (for instance, the current year) ?

JPL HORIZONS can do that.
With settings like these:

  Ephemeris Type : OBSERVER
  Target Body : Moon [Luna] [301]
  Observer Location : Geocentric [500]
  Time Span : Start=2019-09-12, Stop=2019-09-19, Step=1 d
  Table Settings : QUANTITIES=10,23,24

it returns results like these:

 Date__(UT)__HR:MN       Illu%    S-O-T /r    S-T-O
***************************************************
 2019-Sep-12 00:00      95.688 155.9731 /T  23.9640
 2019-Sep-13 00:00      98.620 166.4750 /T  13.4888
 2019-Sep-14 00:00      99.814 175.0444 /T   4.9422
 2019-Sep-15 00:00      99.231 169.9061 /L  10.0670
 2019-Sep-16 00:00      96.874 159.5743 /L  20.3723
 2019-Sep-17 00:00      92.791 148.7668 /L  31.1541
 2019-Sep-18 00:00      87.074 137.7510 /L  42.1469
 2019-Sep-19 00:00      79.858 126.5419 /L  53.3370

where Illu% is the illuminated fraction $k$, and S-T-O is the sun-target-observer phase angle $i$.
These quantities are related by
(Meeus 41.1)
$$ k = \frac{1 + \cos i}{2} $$

An observer location on the surface of the Earth instead of the geocenter gives slightly different results due to parallax.

Tanner's rendered images appear to be indexed by the difference between lunar and solar ecliptic longitude.
The sun-observer-target elongation angle S-O-T is a close approximation in most cases.
Where the /r column is /T for trailing, use that value directly.
Where /r is /L for leading, subtract S-O-T from 360°.

A single cycle of Moon images cannot capture libration effects as the NASA SVS images do (see SpaceBread's answer), so Tanner's images look a little different from the actual Moon.


Inconsistent online radius value for Proxima Centauri I was looking up the radius of Proxima Centauri and got a funny result.

Google says it's about 100,000 km, while WolframAlpha says its about 200,000 km.  Are the error bars that big, or does someone have some bad numbers?

Wikipedia quotes $0.1542\pm 0.0045$ solar radii which is $107276\,km$ with an error of about $3130\, km$.

They also give a reference to a 2017 paper available on Arxiv Proxima's orbit around Alpha Centauri, P. Kervella, F. Thévenin, C. Lovis that gives this value.

Wolfram's estimate is too far off to be an experimental error, IMO, and I think someone has just inadvertently used the diameter (twice the radius) rather than the radius.


Is the motion of the Sun around the Galaxy a result of gravitational pull? Does the orbit of the sun (and other stars within the Milky way) around the galaxy result directly from radial gravitational force toward the objects in the center of the galaxy, or is there additional forces at play?

I would say the answer to your question is yes and no. Yes that the orbit of our Sun in the Milky Way is due solely to gravitational forces as you suggest, but no in that they are not all radial towards the center of the galaxy.

The motion of the Sun around the center of our galaxy can be broken into two motions. The first is an "azimuthal" orbital motion around the center of the galaxy due to radial gravitational forces from mass interior to our orbit (be it stars, gas/dust, dark matter, dragons, etc.). The other type of motion is an oscillation into and out of the plane of the milky way. This is also caused by gravitational forces, albeit not radial forces from the center of the milky way. As the sun moves "above" the plane of the Milky Way, there is more mass below than above and it gets pulled "down". When it is in the plane it has residual energy from "falling down" and continues to fall "below" the plane where it then gets pulled back "up". This type of oscillatory motion is constant and analogous to a mass on a spring.


What was the length of the solar day 73 million years ago? How could this be estimated, or how accurately could it be extrapolated from a present-day measurement of the Earth's spin-down rate?

There is evidence from Silurian coral fossils that, 430 My ago, there were 420 daily rotations in each annual season, compared to 365 days per year now.  If we assume that the year (fixed by mean Earth-Sun distance and Kepler's Laws) hasn't changed much in that interval, but that instead the day has gotten longer due to the Earth-Moon tidal interaction, that means that 430 My ago there were about 20.9 hours in each day.

Linear extrapolation in between says that only about one-sixth of that change has taken place in the past 73 My, which would give a day length of about 23.5 hours.

In a comment, JohnHoltz cautiously extrapolates your currently-known slowing of 0.0016 seconds/century over that interval, which gives an ancient day length of closer to 23.7 hours.

JohnHoltz's estimate is probably better. Tidal slowing is occurring as the mean distance between the Earth and Moon increases, which makes all tidal effects (including tidal slowing) weaker. So a linear extrapolation from today's well-measured rate of rotational slowing is probably more accurate for recent times than a linear extrapolation over a much longer period that probably includes more rapid slowing in the past. It inspires confidence that the two methods come out close to each other, though.


The face of the moon at moonset It appears that the face of the moon "rotates" clockwise from the time the moon rises to the time it sets. Tycho's crater seems more to the left and the "Rabbits head" looks like it's facing down more.

I know that is not actually the case but I am having trouble visualizing why this appears so. Can anyone explain?

Actually, it is rotating relative to your perspective. (The other answer relating to liberation occurs over a longer period of time).

Here is a simulation from Sky Safari for later tonight (moonrise) and tomorrow (moonset) for my location. Note how the angle of the lit hemisphere rotates between the pictures:

Moonrise:

Moonset:

It looks like this for me because I am at 43 south. If I was at the equator, the moon would appear to have rotated 180 as it travelled from horizon to horizon.

It is easier to think about on the equator. Say the moon rises, and you consider the bit at the top to be "up". It continues on up, right over your head, and down to the horizon... But on the way down, the "up" side of the moon is now looking down. It was "up" until the zenith, but then it is "down" all the way to the horizon. It doesn't rotate at all, but the result is a 180 degree flip in appearance from horizon to horizon.

Or consider the perspective at a pole, while the moon is up. The moon travels right around the sky, always facing the same direction, with no apparent rotation (and while it is up, no moonrise or moonset, it is up all day).

Latitudes in between see an in-between effect; some apparent rotation of the moon between moonrise and moonset.


Why is a star at its highest point when local sidereal time = RA (right ascension)? I'm currently taking a course called Introduction to Astronomy at Coursera. It's not very formal so they didn't present a proof of the statement in the title. I understand why logically one could argue that when a star lies on the projection of the observer's local meridean onto the celestial sphere (I understand that this projection defines the observer's local sidereal time) then this star is at its highest point on the sky.

I haven't found any mathematical proof of this statement and also do not know how to approach the problem geometrically (either euclidean geometry or analytic geometry).

I appreciate any hint or direct answer on how to approach the problem. Thanks.

At some geocentric latitude $\phi$ and longitude $\lambda$, the elevation or altitude $a$ of a star with right ascension $\alpha$ and declination $\delta$ is given by
$$\begin{aligned}
\sin a = \sin\phi \sin \delta + \cos \phi \cos\delta \cos h&&&&&&(1)
\end{aligned}$$
where
$$\begin{aligned}
h=\theta_\phi - \alpha\qquad&&\qquad&&\qquad&&\quad\,&&(2)
\end{aligned}$$
is the hour angle to the star, expressed in terms of the local sidereal time $\theta_{\phi}$ and the right ascension $\alpha$.

Differentiating (1) with respect to time yields
$$\begin{aligned}
\cos a \frac{da}{dt} = &
\phantom{+}\,(\cos\phi\sin\delta - \sin\phi \cos\delta \cos h)\,\frac{d\phi}{dt} \\
& + \,(\sin\phi \cos\delta - \cos\phi \sin\delta \cos h)\,\frac{d\delta}{dt} \\
& - \cos\phi \cos\delta \sin h\,\frac{dh}{dt} &\!\!\!(3)
\end{aligned}
$$
While not quite zero, the time derivatives of latitude $\phi$ and declination $\delta$ are negligibly small compared to the $2\pi$ radians per sidereal day time derivative of hour angle $h$. For all practical purposes, the above thus reduces to
$$\begin{aligned}
\cos a \frac{da}{dt} = - \cos\phi \cos\delta \sin h\,\frac{dh}{dt} \quad\!&&&&&&(4)
\end{aligned}
$$
The left hand side of (4) is zero at extrema of elevation angle. Thus we're looking for conditions that make the right hand side of (4) equal zero. Since $dh/dt$ is nonzero, the right hand  side is zero only if one or more of $\cos \phi$, $\cos \delta$, or $\sin h$ is zero. The first two cases ($\cos \phi = 0$ and $\cos \delta = 0$) represent conditions where elevation is constant. The only condition of interest is $\sin h = 0$, which means an hour angle of 0° or 180° (hour angle is constrained to lie between 0° (inclusive) and 360° (exclusive)).

Since latitude $\phi$ and declination $\delta$ both lie between -90° and +90°, the condition $h=180^{\circ}$ represents the minimum possible elevation, while $h=0$ represents the maximum possible elevation. From (2), $h=0$ means $\theta=\alpha$, or local sidereal time being equal to right ascension.


Can there be an infinity of humans in the Universe? I was reading this question about if the number of stars can or cannot be infinite.
The answer to this question is:

"if the universe is considered infinite, the number of stars can be infinite, otherwise not."

So, I came across a mental problem: If the universe is considered infinite, and therefore we can consider that the number of stars is too, then, we can consider that the number of humans (example) is also infinite, or the number of anything is also infinite?

If the answer is No, please describe why u think this is not a real affirmation.

IMO, this sounds more like a philosophical question rather than an astronomical question, but since I like both subjects, I'll give it a shot.

  Note: This is hypothetical question, so this answer is purely subjective (and hypothetical).

Infinity

If the number of stars is infinite, so would the numbers of humans.

I believe that in every system where an entity of infinity is introduced, all other entities will (eventually) be infinite. But, (and this is the fun "part") you cannot measure infinity. It would give you infinite results over a time span of infinity.

Take your example for instance. If there were infinite numbers of stars. Picture youself flying around in a spaceship with the goal to find out if this question is true or not. What do you see? "Worse case" scenario; you see only stars. Wherever you go. Forever. The opposite;  only humans.

One might think that it's the "in between" that is the most likely scenario. But given the probability theory, we should flatten out at approx. 50%.

Finite

If there is a finite numbers of stars then I think it's "safe" to conclude that there ain't an infinite number of humans as we're all made of starstuff.

Conclusion

  Yes: If there's an infinite numbers of stars.

  No: If there's a finite numbers of stars.


Mini black holes, a possible result of the LHC experiment at CERN A scientist at CERN LHC (Large Hadron Collider) was asked during an interview about the possible results and consequences of operating the LHC at full power of collision in the near future, one of the results he literally said :

  One of the theories that predicts the consequences of operating the LHC at full power collision is that mini black holes might form, but do not be afraid of those black holes, they will not start expanding and destroy the earth, they will instantaneously disappear.

I know that black holes create disturbance in space-time. And they actually appear when matter massively gets pressurized into a small size of volume in space which causes gravity to increase insanely which in turn initialize a black hole that even light its self can not escape away from.

So how can a mini black hole disappear anyway?
What in the world would cause a small size, a mini size, a tiny little black hole to vanish or disappear?

This result is due to Hawking radiation.

Due to random quantum fluctuations, particles are radiated from a black hole.

When the black hole has a mass less than the Moon, it will evaporate.

EDIT

I should add that any black holes created can only have the mass of the particles involved in the collision - two protons. So it's not going to do any harm before it evaporates. However, we would learn a lot from the event.


How far have individual stars been seen by radio telescopes? Writing this answer got me thinking.

As far as I understand it, stars themselves radiate most of their energy at optical wavelengths (near-IR through near-UV).

Various types of stellar objects may flare in various ways when in-falling matter from an accretion disk or companion is heated in magnetic fields or undergoes transient nucleosynthesis, but I'm excluding these types of processes and asking only about radiation from the stellar object itself, in steady-state.

Question: How far have individual stars been seen by radio telescopes?

Some types of red giant stars are susceptible to intense water and silicon oxide MASER activity in their outer envelopes. This results in intense radio emission. Examples of such maser activity have been observed in the Small Magellanic Cloud,at a distance of $\sim 60$ kpc  (e.g. van Loon 2013).

 Click for full size.

IRAS 05298−6957 (van Loon 2013): Note the logarithmic wavelength axis; the water maser peak lies at about 18 cm / 1670 MHz.


What is the highest recorded temperature in space What is the highest recorded temperature in space? I'm not asking about Planck temperature that is a fraction of a second before the Big Bang. I'm asking about the temperature that has been recorded by an instrument.

Well this infograhic puts gas heated by a supernova at about 55 million Celsius.

And that's not even the highest temperature we can just "find" out there, even if we discard supernovae and stellar cores.  The gas in a cluster of galaxies (the ICM) can have temperatures on the orders of 10 million to 100 million Kelvin.  Such a high temperature gas emits high energy photons such as X-rays via bremsstrahlung radiation, and these are observable (and have been observed) by X-ray telescopes.

There's this review article from 2003 that covers the basic methodologies and measurements made on ICMs, including (but decidedly not limited to) temperature.


Puzzling quotes from astronauts about earth size I have no doubt that we have been to the moon. This question has nothing to do with a moon landing hoax.  But, there are two quotes from two different astronauts regarding the size of the earth as viewed from the moon that are puzzling to me. Both quotes talk about how small the Earth looked. Shouldn’t the Earth look very large when viewed from the moon

It suddenly struck me that that tiny pea, pretty and blue was the Earth. I put up my thumb, shut one eye and my thumb blotted out the planet Earth. I didn't feel like a giant. I felt very, very small. — Neil Armstong
As we got further and further away it [the Earth] diminished in size. Finally it shrank to the size of a marble, the most beautiful you can imagine. That beautiful, warm living object looked so fragile, so delicate that if you touched it with a finger it would crumble and fall apart. Seeing this has to change a man. — James Irwin

I know the term large is subjective, but still, the comments seem off. Please let me know what I’m missing.

The Earth is 4 times the diameter of the Moon. The Earth viewed from the Moon will therefore appear to have 4 times the angular diameter of the Moon viewed from the Earth.

The Moon is easily obscured by a thumb at arm's length (by a factor of 3-4).

Now bring your thumb closer (because you can't fully extend your arm in a bulky space suit) and put on the biggest pair of ski gloves you can find.

It is not a great stretch of the imagination to think your thumb, in a spacesuit, would easily obscure something 4 times the size of the Moon.


Horizontal to Equatorial Conversion - Code Following this tutorial I have been able to convert from Equatorial to Horizontal Coordinates and am now searching for a way to do the reverse.
I understand this kind of question has been asked and answered using mathematics, but I have been unsuccessful in implementing the provided algorithm in code. Below is my C Sharp code for Equatorial -> Horizontal conversion, which I'm looking to reverse.
public static HorizontalCoords EquatorialToHorizontal(EquitorialCoords equatorialCoords, GeographicCoords geographicCoords, double localSiderealTime)
{

    double ha = (localSiderealTime - equatorialCoords.rightAscention) * hours2deg;

    double x_sid = Cos_d(ha) * Cos_d(equatorialCoords.declination);
    double y_sid = Sin_d(ha) * Cos_d(equatorialCoords.declination);
    double z_sid = Sin_d(equatorialCoords.declination);

    double x_hor = x_sid * Sin_d(geographicCoords.latitude) - z_sid * Cos_d(geographicCoords.latitude);
    double y_hor = y_sid;
    double z_hor = x_sid * Cos_d(geographicCoords.latitude) + z_sid * Sin_d(geographicCoords.latitude);

    double az = Atan2_d(y_hor, x_hor) + 180;
    double alt = Atan2_d(z_hor, Sqrt(x_hor * x_hor + y_hor * y_hor));

    return new HorizontalCoords(alt, az);
}

public static EquatorialCoords HorizontalToEquatorial(HorizontalCoords horizontalCoords, GeographicCoords geographicCoords, double localSiderealTime)
{
  //*hmmmmmm what goes here..
}

HorizontalToEquatorial would be like EquatorialToHorizontal in reverse, something like this:

(x, y, z)_hor = rectangular form of (alt, az)

(x, y, z)_sid = (x, y, z)_hor rotated by geographic latitude

(ha, dec) = spherical form of (x, y, z)_sid

ra = local sidereal time - ha


Why telescope mirror glass shipped as randomly broken chunks of a constant size in cardboard boxes? The video MIRROR LAB: Preparing for Casting GMT's Mirror 6 shows the unpacking several hundred boxes full of broken glass from OHARA, packed in styrofoam.
The glass chunks are a fairly uniform size of perhaps 15 cm, and of compact shape; there are no long slivers or sheets; they are all very roughly cuboids.
This seems to be deliberate. It could have been ground to a finer, pourable size, or even smaller for filling the nooks and crannies of the support web at the bottom of the mold, or in much larger sheets or bars. But these roughly block shaped pieces are stacked like bricks by hand, one at a time, into the mold.
Why is this so?

more screen shots (in case video disappears) click for full size:

The material used for the mirror is indeed E6 Borosilicate manufactured by Ohara corporation as pointed out by @notovny. The fabrication process of a borosilicate glass honeycomb  mirror has remained almost unchanged since the first one, an 8.4m LBT mirror, was cast in 1997 (here is the article of the casting). Quoting the article:

E6 is a good match to our process because it is manufactured in appropriate volumes with good quality control, and because the broken surfaces of the chunks melt together smoothly without discontinuities.

This somewhat more modern article (2019) goes deeper into detail:

A significant advantage for our process is that Ohara delivers the glass as blocks broken out of a set of one-ton melts. All surfaces are pristine fracture surfaces which melt together seamlessly in the honeycomb mold, leaving no trace of the original blocks.

And this work from the Arizona University explains further:

...E6 borosilicate glass... is melted in clay pots,..., with vigorous strirring that yields high homogeneity and low striae. It is supplied to us in the form of roughly cubical blocks with smooth, uncontaminated fracture surfaces and weighing typically 4 kg each.

So using pristine chunks of E6 borosilicate seems to greatly reduce the possible contamination (in comparison to using powder or not pristine chunks), seems to melt rather very smoothly and is probably an easy size to transport. The reason of why they use this material is explained in depth in all 3 articles mentioned.


How does the Hubble Space Telescope "Drift and Shift"? The Phys.org article Mystery of the universe's expansion rate widens with new Hubble data says:

Astronomers have been using Cepheid variables as cosmic yardsticks to gauge nearby intergalactic distances for more than a century. But trying to harvest a bunch of these stars was so time-consuming as to be nearly unachievable. So, the team employed a clever new method, called DASH (Drift And Shift), using Hubble as a "point-and-shoot" camera to snap quick images of the extremely bright pulsating stars, which eliminates the time-consuming need for precise pointing.
"When Hubble uses precise pointing by locking onto guide stars, it can only observe one Cepheid per each 90-minute Hubble orbit around Earth. So, it would be very costly for the telescope to observe each Cepheid," explained team member Stefano Casertano, also of STScI and Johns Hopkins. "Instead, we searched for groups of Cepheids close enough to each other that we could move between them without recalibrating the telescope pointing. These Cepheids are so bright, we only need to observe them for two seconds. This technique is allowing us to observe a dozen Cepheids for the duration of one orbit. So, we stay on gyroscope control and keep 'DASHing' around very fast."

I understand that the technique skips the use of guide stars, but I'm wondering exactly what does happen. What does the word recalibrating mean in "..move between them without recalibrating the telescope pointing..."
Do they just execute a blind change in direction using Hubble's attitude control system of gyros and reaction wheels, expose, and move on to the next field, and hope the target object was imaged?
For a little background see Hubble's one-gyro mode; how does it work for attitude control, stabilization, and slewing? and answer(s).

The "drift-and-shift" (DASH) mode was described in a paper by Momcheva et al. (2016), and works the way you supposed: a sequence of nearby images is taken using blind offsets without guide-star recalibration: move to the first field and take an image (possibly first acquiring a guide star), move to a nearby target field and take another image (no guide star acquisition), repeat...

Guide-star "calibration" means correcting the internal model of "where in the sky HST is pointing" by locating a bright star with well-known coordinates, tweaking the pointing of HST to put the guide star in the right position within the telescope's focal plane (so that the center of the focal plane is now pointing where the observing proposal specifies), and setting up a monitoring process where the position of the guide star is continually tracked during an observation to make sure the telescope pointing is not drifting (and correcting it when it is). The whole acquisition-and-setup process introduces an overhead of about six minutes; since a typical HST observing window is only about 50 minutes (before the spacecraft's orbit carries it around to the other side of the Earth and it can't see the target any more), trying to change target fields multiple times would rapidly eat up your actual observation time.

(In some [most?] cases, it might make sense to do guide-star acquisition for the very first field, to which HST has likely just made a very large slew, to ensure the initial pointing is accurate and that the (smaller) offsets to new fields will be reasonably accurate.)

Not having a guide star does impact the stability of the telescope pointing during an observation: guiding using just the gyros means a drift of about 0.001 to 0.002 arc seconds per second of time. So long exposures are not a good idea, because they'll be smeared by the telescope drift: an exposure of 100 seconds means a typical drift of several pixels during that time. But since Riess et al. were taking very short exposures (just a few seconds), this wasn't a problem for them.


How have we measured the radius of the Earth (old and new)? I'd imagine ancient methods are fun exercises in geometry. how has the measurement has evolved over time?

The first method is credited to Eratosthenes. He knew that during the summer solstice in Syenne the angle of the Sun overhead at noon was $0^\circ$. Following this he made the same measurement in Alexandria and measured the angle of the Sun overhead using shadows and calculated it to be $\approx 7^\circ$ which is approximately $1/50$ of a circle. Hence, both the circumference and the radius are easily calculated and quite accurate for such crude methods.

This is a pretty broad question so I'll limit myself to describing one instance of how the radius of the Earth is measured. Specifically, I'll talk about how it's measured today, with current technology.

As technology has progressed, our ability to precisely measure facets of the Earth has drastically improved. At this point, we can measure the exact shape and size of the Earth to such precision that asking about the "radius of the Earth" is no longer meaningful. Primarily because we know the shape of the Earth to such precision that we know it is not a perfect sphere with a fixed radius.

The current standard used to describe the exact shape of the Earth is the World Geodetic System, the latest edition of which is referred to as WGS84. In effect, this is a coordinate system centered on the Earth that precisely describes the shape of the Earth. This is done by using sensitive satellite measurements to fit the spherical harmonics to the Earth's geoid. The current, most updated version of WGS84 has more than 4.6 million harmonic terms with an accuracy in "radius" at any given point of 10 km. That is, you could pick any precise location on the Earth and use WGS84 to calculate the radius of the Earth at that exact point to an accuracy of 10 km. This radius would of course vary as you moved about the Earth.

If you really want to break this down into a simple number, the WGS model, at the crudest level, considers the Earth to be an oblate spheroid with an equitorial radius of $R_{eq} = 6\:378\:137\:\mathrm{m}$ and a polar radius of $R_{p} = 6\:356\:752.3\:\mathrm{m}$.


Why are (Type II) supernovae so bright? The vast majority of energy from a supernova is emitted as neutrinos and high-energy radiation, both of which being invisible to the naked eye. Yet a supernova can outshine its galaxy in the visible spectrum for weeks.

How is a supernova generating so much visible light that nuclear fusion pales in comparison?
What is the ratio of visible and invisible energy emitted by a supernova, and how does it compare to stars' normal operation?

The difference is based on the different efficiency of the processes.
We can describe the luminosity by:

$$L = \eta m c^2$$

where $\eta$ is the conversion efficiency, and describes how much matter can be converted into luminosity (photons).
Main sequence stars (if you mean this by "normal operation") extract energy from matter by nuclear fusion.
The efficiency of nuclear fusion in stars is of the order of $\eta = 1\%$.

The other competitive mechanism, much more efficient than nuclear fusion, is conversion from gravitational potential.
In core-collapse SNe, this is the mechanism that brings to the explosion.
Gravitational potential energy is defined as $U=-\frac{GMm}{r}$ where m is the mass of a particle, at a distance r, from a large object of mass M; G is the gravitation constant.

If you consider the SN scenario, $r$ is the distance of a particle that is falling from the external layer towards the center (center at $r=0$). So the particle goes from $r_1$ to $r_2$ with $r_2 < r_1$. Then the system lost part of the potential energy, converted to kinetic energy.
All the external matter collapse in a very brief time (order of seconds), from the external shell to the compressed nucleus, bringing more compression and then generating energetic shock in the explosion.

The virial theorem says that half the change in gravitational energy stays with the star, while the other half is emitted as luminosity.
The efficiency coefficient for gravitational conversion is $\eta\sim10\%$, i.e., 10 times larger than the nuclear fusion efficiency.

From this reference, you can check that the ratio between the invisible against visible emission is of the order $\sim10^7$ (I don't know what kind of reference is that, but the authors are totally trusty).

Something more here and here.


Inner Workings of Neutron Stars What are future steps that can be taken in order to learn more about the inner workings of a Neutron Star such as "nuclear pasta" and the materials in the inner core?

An incomplete shortlist would be:

(i) If you can measure the maximum possible mass of a neutron star (the most massive neutron star gives a lower limit to that), then it tells you how "hard" or "soft" the equation of state (the relationship between pressure, density and composition) is in the interior (especially at the core), and therefore tells you something about the matter composition and the nature of the strong nuclear force at small separations. Nuclear pasta is unlikely to have a dramatic effect on this.

(ii) Measuring the masses and radii of neutrons stars would directly tell you about the equation of state at different depths inside a neutron star. Again, I think nuclear pasta does not have a major bearing on these diagnostics.

(iii) Measuring the rate at which neutron stars cool, tells you about the interior composition. Quark matter and boson condensations in the core would allow for faster cooling. Abrupt changes to the cooling rate can tell you about superfluid phase transitions. Cooling can also be accelerated by nuclear pasta phases by allowing the URCA process to operate.

(iv) Measuring the response of pulsars to glitches tells you about superfluidity in the interior and crust and the coupling of crust and core will depend on the properties of what is in between - i.e. nuclear pasta.


Simulation packages or theory to work with gravitational collapse of massive molecular clouds? So, I am getting interested in gravitational collapse of large molecular clouds that fragment and collapse into multiple stars. Are there well-known popular academic simulation packages that simulate these, for research purposes? Or are there papers or references I can use to write my own?

This sounds very ambitious! I think your way in to this topic might be to have a look at the works of two authors - Matthew Bate and Mark Krumholz.

The reason I suggest these two names is that they are representative of the two basic approaches to simulating the collapse of molecular clouds (which has little to do with n-body simulations). These approaches are known as Smoothed-Particle Hydrodynamics (SPH) and Adaptive Mesh Refinement (AMR).

Crudely put, SPH treats the fluid as discrete particles whose properties are smoothed over the size of a kernel - the resolution is controlled by the number of particles in the simulation and the smoothing length. AMR is a more "traditional" grid-based approach where the size of the grid is varied adaptively with time and space to get the requisite resolution.

A quick google reveals a number of public codes -e.g. for SPH there is SPHYSICS or GRLAB; for AMR there is ENZO or PARAMESH.

One of the main activities in model simulations these days is trying to incorporate "feedback" into star formation. i.e. the winds and radiation from newly born high-mass stars and the outflows from protostars. Such things do not form part of standard codes.


Have we sent radio signals to exoplanets that may be habitable? I would like to know please whether or not we have sent radio signals to exoplanets that may be habitable.

Thanks in advance !

Short answer : Yes
Long answer : Yes
We have actually sent radio signals to distant exoplanets that are thought to be capable of hosting (hopefully intelligent) life.
Some examples?

The radio signal directed at a world 12 light-years away included music and math lessons from Earth
Are There Any Habitable Exoplanets That Can Hear Us?

The second link only 'mentions' a planet that had been sent radio planet :

Those waves, which are all electromagnetic like light, would have since traveled about 70 light years away from Earth. The newly confirmed Kepler 452b, at 1,400 light years away, will not be seeing 'I Love Lucy' for more than a millennium.

Hope this answers your question.


What wavelengths are used to search for distant solar system objects like KBOs and Oort cloud members? What wavelengths of light are used/most suited to search for distant solar system objects like KBOs and Oort cloud members? I suppose they are brightest in reflected sunlight, so they are best searched for in visible and near infrared. Is that correct?

Virtually all KBO searches use mosaic CCD cameras operating in the visible part of the spectrum, usually with a red filter like SDSS-r' (centered at approx. 622nm SDSS filters) on big (~4m telescopes). This is what we did with the OSSOS survey I was (lightly) involved with (http://www.ossos-survey.org/about.html). Although cold KBOs are brightest in the infrared, the background from the atmosphere is much higher which means you are less sensitive, unless you go to space (very expensive).

Also IR detectors are smaller and less sensitive than optical CCDs and much harder to make into mosaic cameras and keep cold (to increase sensitivity). This means you can't cover as much sky area per night which makes finding rare and faint KBOs much slower. A CCD and red filter is a good balance between brightness of the objects you are looking for, the sensitivity of your detector (CCDs get less sensitive as you move more to the red or blue of the green-red central part of the optical spectrum) and a low background from the atmosphere.


What's the brightness of Alpha Centauri from Proxima Centauri? Self-explanatory, but I would like a comparison as well. Is the light enough to see by? How disrupted will the pitch darkness on the spot opposite of the 'solar pole' be?

Not close to being able to read by.

Proxima Centauri is about 13,000 AU from the two binary Centari stars.   Together they have about twice the luminosity of the sun but at 13,000 AU, that's roughly 2/169,000,000 the visible light that the Earth gets from the Sun.

The brightness variation of the full moon to the Sun is about 1 to 440,000, so, some rough math, the two stars would shine about 1/190th as bright as the full moon.   That would make those 2 stars by far the brightest stars in the Proxima Centauri sky, but far short of reading light.   Together, the two stars would be about 10 times as bright as Venus at Venus' peak.  (Venus is about 1/2000th as bright as the moon, -4.4 apparent magnitude to -12.6 for the moon).

That would, I think, be bright enough to be visible during the day under an earth like sky a lot of the time.

The two stars would be quite close to each other too, maximum visible distance between them would be roughly 1/4 the diameter of the full moon, where they would still be visible separate stars when far apart, but they would pass close to each other too, perhaps appearing to touch to the naked eye.

The two stars complete a full orbit around each other in 79.9 years, so the variation would be noticeable over a human lifetime.


Why do we need the "mean" in mean free path? I was introduced to mean free path in my astro physics class,
and the professor posts a question for us to ponder: "Why do we need the "mean" in mean free path?"

This further makes me to wonder what is the mean free path for, and how is it used?

In every context we talk about "mean free path", we talk about particles. Particles usually bounce around a lot, from collision to collision. In between two bounces a particle moves in a straight line. That is the expected behaviour from Newton's laws of motion.

Between one collision and the next, a particle therefore moves a distance. That is the "free path". So why do we need to include "mean"? The thing is, you can never be sure about how far the particle moves after a collision. It might as well immediately bounce into another particle, as well as move a considerable distance. However, if you measure really many particles, their average is going to be pretty stable and predictable. That gives a nice, usable number. The "mean" here is for average. (In case you wonder, yes, this applies to optics too, but the concept requires a little more abstraction).


Exoplanet radius density relation according to NASA exoplanet archive I downloaded the info from NASA exoplanet archive at: https://exoplanetarchive.ipac.caltech.edu/cgi-bin/TblView/nph-tblView?app=ExoTbls&config=compositepars

I named the file "NASA.Composite.Planet.Data.csv". I had to edit the file to remove the header which was preventing the program below from running. (I put the header at the top of the program below)

I then plotted it with Matplotlib using this python (anaconda) program: https://planet.wikia.com/wiki/User:Granpa/Python_program

I got this image:
https://i.imgur.com/1057YvQ.png

Can anyone explain what I am seeing

What you are seeing is a combination of several things as you move across the diagram from left to right with increasing planet radius. As this diagram  from a talk by Cayman Unterborn at the recent "Know Thy Star - Know Thy Planet" conference shows, is a transition from rocky (like Mars, Venus, Earth; the 'Ma', 'V' and 'E' on the diagram) exoplanets with increasing density as ~1.5 Earth radii is reached to "Neptune-like" gas giants with increasing amount of a gas envelope, possibly with a denser core. (The size and type of Jupiter's core is not a totally settled question for example and so the wider range of exoplanets could have a wide variety of core properties). There is a lot more information in this blog post on 'Which small exoplanets are rocky' which talks about what we can learn about planets in the 0.5 to 4 Earth radius regime.

At higher radii (approximately 11 Earth radii/1 Jupiter radius) what you are seeing is the effect of electron-degeneracy pressure. This causes the radii of exoplanets with a mass of about Jupiter, brown dwarfs up to 80 times the mass of Jupiter and low mass M dwarf stars (with a mass of hundreds of Jupiters) all to have very similar radii but with widely varying densities. This causes the near-vertical line on the right hand side of your plot. This is also what makes it very difficult to know whether you have a star, brown dwarf or a planet if you only a measure of a transiting object's radius (from e.g. Kepler) and don't have a mass measurement (usually from radial velocities) to go with it.


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

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

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

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

So, my questions are:

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

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

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

Any help is appreciated!

Addressing (2) and (3) first:

In a case like this, your best option is to go straight to the source. In this case, that would be Blandford & Znajek (1977), the originators of the proposed mechanism. they have several figures regarding different magnetospheric structures depending on different magnetic fields. However, the most important one is Figure 1, the general case:

$D$ represents the accretion disk, while $T$ is the transition zone where matter is rapidly moving radially towards the black hole. The lines represent magnetic field lines, along which charged particles. Electrons (e-) travel in the direction of the medium arrows on each field line; positrons (e+) travel in the other direction. The field lines are closer together in the disk area closer to the black hole, indicating the stronger magnetic field.

If you want a good overview of the process, this is the paper to look at. That said, it is far from an easy read.

Regarding (1), I'm not an astronomer and not really qualified to tell you what the mainstream opinion among astronomers is. However, as far as I'm aware, the Blandford-Znajek process is currently accepted as a strong possibility for generating the magnetic fields observed near most black holes (including stellar-mass black holes).