Are the "extinct species" of meteorites originally from the "Barbarian" asteroids? I've asked earlierin this unanswered question about an "extinct species" of meteorite, now I've just read in Phys.org about Barbarian asteroids:

  Named after the first asteroid of this type discovered, Barbara (234), Barbarians are a key to understanding how the solar system first formed. Barbarians are extremely rare and ancient, and were present before the Earth was created. Only 13 Barbarians have ever been discovered.

Are these two different types of extremely rare materials, or are the "extinct" meteorites actually products of the "rare Barbarian" asteroids?

From: UWA Zadko Telescope helps reconstruct 'Barbarian' asteroids.

The answer is in the part of the abstract that you quote in your other question:

  "...This may be the first documented example of an ‘extinct’ meteorite, that is, a meteorite type that does not fall on Earth today because its parent body has been consumed by collisions."

What they're saying here is that there used to exist some asteroids of some particular type (here they mean formed from the pieces of a single body). After some time all asteroids of that type were destroyed in collisions, fell on planets or into the sun or were ejected from the solar system. Some of the pieces fell on Earth. As far as we can tell there are no pieces left in solar orbit and so none of these type of meteorite fall on Earth any more, hence it is called "extinct".

Since the Barbarian asteroids currently exist, they are by definition not extinct.


Source of T Tauri wind? What particularly causes the T Tauri star to eject the strong bipolar wind which clears the gases around the star?

If you want to trigger outflows, there are two main processes that can help:

magnetic field;
radiation pressure.

Magnetic fields is well-suited to launch such outflows, through magneto-centrifugal effects. Basically, if there is magnetic fields tighed to the disk surrounding the protostar and the angle between the field lines and the disk is right, a particle from the disk that follows the magnetic field lines can be ejected. This is the well-known Blandford & Payne (1982) mechanism.

Note that, at earlier stages of star formation, magnetic field could also trigger outflows by a "magnetic field tower" growth. Basically, during the collapse of the prestellar core into a protostar, the field lines are dragged and twisted (due to the rotation of the core), the twist propagating from the inner to the outer region of the core, that triggers outflows. This kind of thing is discussedd in Hennebelle & Fromang (2008).

By the way, these two mechanisms are complementary, because slow outflows (of the order of 10 km s$^{-1}$) are observed around young protostar, whereas "fast outflows" -- jets, of the order of 100 km s$^{-1}$ -- are observed around late protostars, and these two mechanisms explained well the former and the later.

For more massive stars, radiation pressure will plays a role in outflows triggering. The protostar radiates away a part of its accreting energy, and strong a radiation pressure can trigger the growth of a kind of "bubble", that is an outflow (you can see Hennebelle & Commerçon (2012) for a brief review of the question).

Regarding your comment on your own question, it is mostly radiation pressure that will clear up the gas around the new-born star, that is clearly not an outflow or anything alike.


How bright is the Crab Pulsar's 30 Hz modulation in visible light? What color is it? This answer to Has great eyesight been necessary for astronomers? mentions Astronomer Jocelyn Bell Burnell's recounting of a likely first visual observation of a pulsar. This can be found for example in Nature's Air force had early warning of pulsars

  The work preceded by several months the observations made by Bell Burnell, then at the University of Cambridge, UK, which led to the first paper on the subject. A Nobel prize for the discovery was subsequently awarded to her supervisor Antony Hewish, but, controversially, not to her. Schisler was not the only one to “pre-discover” a pulsar, though, according to Bell Burnell. “There are actually a lot of stories,” she says. In the 1950s, a woman visiting the observatory at the University of Chicago, Illinois, pointed out that there was a regularly pulsating source of visible light in the Crab Nebula. Elliot Moore, an astronomer at the university, dismissed the woman's claim, telling her that all stars seem to flicker. Another radio astronomer she knows of will, after a drink or two, confess to having dismissed observations of a pulsating source as the result of faulty equipment. “He's a bit embarrassed now,” says Bell Burnell.

This is also summarized in Wikipedia's Crab Pulsar:

  Jocelyn Bell Burnell, who co-discovered the first pulsar PSR B1919+21 in 1967, relates that in the late 1950s a woman viewed the Crab Nebula source at the University of Chicago's telescope, then open to the public, and noted that it appeared to be flashing. The astronomer she spoke to, Elliot Moore, disregarded the effect as scintillation, despite the woman's protestation that as a qualified pilot she understood scintillation and this was something else. Bell Burnell notes that the 30 Hz frequency of the Crab Nebula optical pulsar is difficult for many people to see.

Per Wikipedia the Crab Pulsar has an apparent magnitude (V) of about 16.5, but I don't know how much of that intensity is modulated at 30 Hz or if the modulation is concentrated in some specific part of the visible spectrum. I would guess that a neutron star's direct visible light would be quite small except for the pulses, but I don't know if that's what the 16.5 m refers to.

I'm imagining a small, low noise photodiode intercepting the light from the region containing the location of the pulsar, possibly with a color filter, with the signal amplified and the DC removed and then digitized with an ADC and a Raspoerry Pi. (assume that I'd read up on how to best do this) and then integrating for a few minutes or hours and looking for some power near 30 Hz with a Raspberry Pi.

But before I think further, I'd need to know how deep the visible light's modulation is and if it's stronger in some wavelengths or flat across the spectrum.

Question: How bright is the Crab Pulsar's 30 Hz modulation in visible light? What color is it?

The optical pulsations of the Crab pulsar have been studied closely since 1969. The observations are actually not that difficult (I did some myself with a photoelectric photometer as a student) and have been achieved with a variety of technologies.

A paper by Fordham et al. (2002) slices and dices the Crab pulsar's pulse shape into fine time and spectral bins in the optical regime. A phase-folded light curve for the full blue-to-red range is shown below. The pulse shape is actually extremely stable and it looks like this in many other papers. The pulse has been "background subtracted" using the signal in the "off" phase of the pulse. The unpulsed component amounts to less than 1% of the integrated brightness in the optical, so essentially "off" does mean off.

The same paper discusses the integrated energy spectrum and the wavelength-dependent pulse shape of the pulsar. The integrated spectrum is almost flat (after correction for interstellar extinction) - as in, if the spectrum $F(\nu) \propto \nu^{\alpha}$, then $\alpha \sim 0$; this result holds for the whole pulse, or if just either of the two peaks are considered (there is a tiny $<1$% variation in the ratio of the two pulses across the optical range).

Postscript - I notice that the Wikipedia page on the Crab pulsar has a slowed-down animation of the pulse as seen at 800nm (very close to optical). The two pulses and their difference in brightness are quite obvious, as is the "off" phase. It would not look much different at shorter, visible wavelengths.


Approximate conversion of redshift 'z' to a time and/or distance, when reading papers? I'm looking for some form of "rough and ready" formula to convert between redshift z value, years since BB, and distance, so that when I read an astronomy paper and it discusses an event that occurred at z=10+/-0.5, or a quasar at z=7, I can get a rough idea when the event occurred and how far away they are saying the quasar is, as context.

I'm aware that this is an inherently vague question, since the times and distances depend on the model and convention chosen, and also that I'm not specifying proper distances/comoving coordinates, etc.

My assumption is that most current models and their parameters,  that are mainstream accepted and used, will be based on very similar parameters of very similar models (if not the same model), such as latest Planck parameters, or similar. They might differ more due to assumptions about very early times, but redshift is inherently >~380 k years, and if they did vary a lot for times beyond that timeframe, we'd have real issues.   In other words, I suspect/hope that any differences in answers due to model variation, won't significantly change the answer to this question. So the only question will (hopefully) be, which convention or type of metric/distance will be appropriate.

If an assumption needs making (such as the meaning of 'distance' to be applied, or the zero point used for time: BB or end of inflation etc) please make an assumption  most likely to help me, and I'll edit the question to clarify if needed, once I see what is too vague in the question as initially worded.

Thank you !

Use one of the "cosmology calculators". The conversions depend on what you assume for the cosmological parameters.

Here's one that will do what you want. http://home.fnal.gov/~gnedin/cc/

e.g. For the default parameters, $z=7$ corresponds to a look back time of 13.01 billion years, whilst $z=10.5$ corresponds to a look back time of 13.33 Gyr, with the current age of the universe being 13.78 Gyr. Choosing the "luminosity distance" option, we that the object has a luminosity distance of 112 Gpc.

If you want the proper distance you could use http://www.astro.ucla.edu/~wright/CosmoCalc.html
According to this calculator the $z=10.5$ object is currently at a proper distance of 9.76 Gpc (31.8 billion light years).


Should this photo of the sun's surface actually be white? If I'm told correctly (eg. What Color is the Sun?) that the sun is actually white, should the photo on that page actually be white too? Is it just doctored to meet peoples expectations?:

Likewise for all the red photo's in a Google image search for "The Sun's surface".

The term "color" is a label that humans have assigned to denote the ratio between the intensity at various wavelengths in the three different wavelength bands, or regions, that the human eye is able to perceive. These bands are centered roughly at 430, 545, and 570 nm, but are quite broad and even overlap:

Human cone response, normalized to the same height. In reality, the response of the blue cones is significantly smaller, and the green is somewhat larger (from Wikipedia).

If an object emits light only at, say, 450 nm, the ratio is roughly 0.1:0.2:1 (in the order R:G:B); it then looks a special way to us, and we call it "blue", or maybe "violet". If it emits at 550 nm, or 650 nm, we call it "green" or "red". An object that emits light in a more continuous spectrum that covers the region 500–600 nm, we'd name something like orange-/brown-/olive-ish, depending on the exact spectrum.

The Sun emits photons at all wavelengths, but not in an equal amount at all wavelengths. The particular ratios between the three bands that we can see, we have labeled "white". However, when the Sun's light enters our atmosphere, some of the light is absorbed, especially at the blue wavelength. Filtering out the blue results in a spectrum that looks more orange to us. The figure below shows the Sun's "true" spectrum (in yellow), and the spectrum seen from the surface of Earth (in red):

The Sun's spectrum measured outside our atmosphere (yellow) and at sea level (red) (modified image from Wikipedia, with data from Global Warming Art).

Sometimes we want to observe the Sun in a wavelength region that is invisible to humans, for instance in UV or X-rays. This can be done with a telescope and a detector that is sensitive to light in that particular region, but in order for us to see it, we represent the image with a color that we can see. The image in the top of the link you provide is taken with the European spacecraft SOHO's instrument EIT at 19.5 nm, which we call "extreme UV", bordering on soft X-rays. Since this is invisible to humans, they arbitrarily chose to represent it using green. They might as well have chosen pink or brown.

The Sun in Extreme UV, during a particularly violent solar flare (from the SOHO gallery).

Several of the photos in your second link are images taken by the Japanese space telescope Hinode, which observes both in the optical (i.e. visible by humans), X-rays, and far UV. If these are shown in orange, again it's just to make them visible to us, and you may say that they have been "doctored to meet our expectation". In this way, I like better when they choose a color such as all green, so we know it's "false color".


Can a meteor shower happen simultaneously all around the planet? In the original book, the classic 1962 movie and the modern 2001 re-make for TV. The store "The day of the Triffits" depicts a meteor shower that happen all around the Earth at the same time, and leaves everyone who sees it blind the following days.

Given the nature of how the Earth rotates, moves around the Sun and a meteor field (required to create a shower of many meteorites). Is it really possible for such an event to happen everywhere at the same time?

This is kind of an important plot in the story, because if one side of the planet goes blind first they can warn the other.

Realistically, no, that cannot happen. Most meteor showers that we experience on Earth - the most famous being the Perseids and the Leonids - are a result of comets passing roughly through our orbit and leaving behind debris that was burned off as the comet passed by the Sun. We then come along, sweeping through this debris and from our perspective on Earth, we see a shower of meteors raining down on us.

That implies two important things. First, we primarily see meteors as we sweep through the debris from comets. They are not objects which have made a trajectory for Earth and hit us head on. Second, we only see meteors when we're on the side of the planet facing the orbital direction of the Earth.

That being said, for the sake of the story, one could envision an alien race of sufficiently advanced technology surrounding our planet with asteroid and comet debris and subsequently "dropping" these meteroids on us from everywhere all at once. I'm not sure if aliens are involved in the story you've linked, but aside from third party intervention, there's now way you're going to see meteors from every place on Earth all at the same time.


How are younger objects outside our observable universe when the older CMB is an observer's temporal "edge"? We know the observable universe is limited to objects whose light has had time to reach us and that an observer very far away will see a slightly different (assuming cosmological principle) observable universe with a slightly different (yet similar) CMB. We know that the CMB (cosmic microwave background or surface of last scattering) was released everywhere in the universe at once and is considered one of the earliest images of the universe. If objects (galaxies, stars et.) created after the CMB are outside our observable universe, why is the CMB our temporal edge? In other words, how are younger objects outside the older CMB? I understand that the universe is expanding, but wouldn't the CMB get redshifted then too?
edit:grammar

The part of the universe that we can see is a cone in spacetime (our past light cone) and there are young and old parts of the universe both inside and outside the cone.
Here's a picture from Ned Wright's cosmology tutorial that shows what's going on.

We're at the top center. The red lines are (a slice through) our past light cone. Ignore the wavy $\phi(x)$ line and imagine a straight horizontal line there instead. Below that line the universe was opaque, so our observable universe effectively ends at that line (just like our view of the sun ends at its surface). There are young and old galaxies, stars, etc. both inside and outside the cone.


What limits the use of the H-R diagram to measure distance (main sequence fitting), what distances is it useful for? Is it only possible to measure objects that form around the same time? Is it possible to measure clusters from distant galaxies other than our own?

It depends how precise you need to be. Main sequence fitting assumes that the star(s) in question is(are) on the main sequence. If you have a cluster of stars (at the same age) then defining what is on the main sequence and what isn't becomes much, much easier and of course you have lots of stars with which to beat down the statistical uncertainty.

In fact, for coeval groups of stars what you term "main sequence fitting" is rarely done. The process is the fitting of an "isochrone" (a line that links points in the HR diagram at a single age), so that both the distance, age (also extinction and metallicity) are possible free parameters.

The subtle distinction here is that what is termed "the main sequence" does not really exist in practice, or at least not as a uniquely defined locus in the HR diagram. Star begin their main sequence lives on the "zero age main sequence" (ZAMS) and end their main sequence careers at the "terminal age main sequence" (TAMS), gradually changing their luminosity and temperature as they do so.

Here is a diagram from Martignoni et al. (2014) showing the ZAMS and TAMS for stars of different masses. there is typically a factor 2-3 in luminosity between them (a larger difference at larger masses). That means whether you use the ZAMS, the TAMS, or something in between to determine the distance from a vertical displacement in the HR diagram, you could vary your answer for the distance by $\sqrt{2}$ to $\sqrt{3}$. In other words you need to know the age of a main sequence star before "main-sequence fitting" can give you an accurate distance.

Of course, lower mass stars are longer lived. Anything of say 0.7 solar masses or below has hardly moved from the ZAMS in the age of the Galaxy, so there would be little error in assuming a ZAMS locus. Conversely, the effects of age are far more rapid and therefore far more important on the main sequence at higher masses.

If you were to try to use main-sequence fitting to estimate the distance to individual stars then there are several hazards. For one, it can be nearly impossible to estimate the age of an individual star. Therefore if it has a mass greater than 0.7 solar masses then there will be an uncertainty in its position in the absolute HR diagram that leads to an inevitable uncertainty in estimated distance. Further, the intrinsic position in the HR diagram depends on the star's chemical composition. Such ancillary information might be available, but it might not, in which case that is another source of error. A further source of systematic uncertainty is stellar rotation. Fast rotating stars have extended lifetimes on the main sequence and somewhat different intrinsic positions on the HR diagram; again a source of systematic uncertainty that is especially problematic for high mass stars. Finally, it can be that what you think is an isolated main sequence star is in fact a binary system. A companion can increase the luminosity of the system and make a star appear closer than it actually is (by up to a factor $\sqrt{2}$).


Expected nature of LISA's data; will it be more like a forest of static peaks, or a series of individual events? @RobJeffries' clear answer to Which things “LIGO can see things that LISA can't”, and vice-versa? explains that the Laser Interferometer Space Antenna or LISA will only be sensitive to gravitational waves with frequencies below about 1 Hz and so will be sensitive to much slower rotating objects than those that LIGO records.

  Lower frequency GWs can only be seen with LISA. This would include stellar binary systems with orbital periods longer than about 10 seconds, merging supermassive black holes and maybe GWs from the big bang

This can might include "event-like" signals, for example (possibly) a merger of two supermassive black holes that are so large in diameter that even during the merger their orbital frequency is below 1 Hz, but it can also include signals from the rotation of bodies not yet in contact but are slowly losing angular momentum though continuous GW radiation. While these would be much weaker, they would provide a very stable and very narrow peak in a spectrogram with an extremely slow drift, so you could accumulate data for years in order to bring them up out of the noise.

While LIGO's detected events have lasted of the order of 1 second or less, it sounds like it is possible that LISA could potentially record continuous GW radiation from a large number of pairs at the same time since the "lifetimes" might be years or millennia rather than seconds, provided that the sensitivity to these weaker signals is sufficient.

Question: What is the expected nature of LISA's data; will it be more like a forest of fairly static or slowly moving peaks in frequency space, or a series of individual events? Presumably this has been modeled based on some predictions of the number of different kinds of pairs at various separations expected to be found nearby.

LISA's data will be very different from LIGO's. It will typically "see" many sources at the same time. Most prominently:

Mergers of pairs of supermassive blackholes. These will be very much like a scaled version of the events that LIGO sees (probably more variation in the mass-ratio and ecccentricity though). They will be much louder (SNR>1000) than any event seen by LIGO though. They will (potentially) enter LISA's sensitivity band months before merger. Event rates are uncertain with estimates ranging from a few to hundreds per year. Depending on where this rate is in nature, we may get many overlapping signals.
Wide binaries These are binaries of compact objects (mostly white dwarfs) that are far from merger. They evolve very slowly, and will therefore mostly show up as continuous almost monochromatic signals. There will be thousands of such signals "visible" at any one time.
There has been some suggestion that LISA may be able to see the earlier stages of GW150914 like events months to years before merger. The current design limitations make this somewhat unlikely though.
Extreme mass ratio inspirals These are mergers of stellar mass compact object with a supermassive black hole. Due to the very small mass-ratio their evolution is very small, meaning that they will stat in the LISA sensitivity band years before merger. Their event rate is even more uncertain than that of supermassive BH mergers with estimates ranging from 1 to 1000s per year. In all likelihood these signal will overlap.

Consequently, LISA will be observing thousands of sources at any one time, which will be a significant challenge for the data analysis.


Can one build a distributed radio telescope? I understand some radio telescopes are built as arrays of receivers. Could one build an array from a heterogeneous set of receivers in scattered locations? Suppose a large number of persons each operate a receiver, and data is gathered together; can it function as an array? Asking for a friend.

Yes, we can do radio astronomy with heterogeneous, geographically distributed antennas.  The VLBI is an excellent example.

Of course, the antennas have to be similar in some ways for it to work:

If the antennas are ground based, they need to be in the same hemisphere, or the Earth will prevent them from looking at the same target at the same time.
They must have extremely stable timing sources, since error or drift in the time tagging will result in dB losses for a detected signal and inaccuracies in angular resolution.
They must have accurate enough timing sources to allow synchronized collections.  The collection times need to be offset in time to account for path delays to the various antennas.
They must overlap in collection RF.  Any differences in center frequency and bandwidth will mean that some of the antennas will be picking up different signals than the other(s).  Practically this usually degrades the collection quality.
It's desirable to have similar antenna beamwidths or, again, the antennas won't all be picking up the same signals.
You need to synchronize the collectors and have accurate estimates for the distances between them.  The VLBI systems use methods described here: How are the atomic clocks synchronised between worldwide VLBI telescopes?,


Where/how are metals distributed in our universe? For one particular kind of element, what is the distribution in the whole universe?

Are most of the metals located in ISM, IGM, or stars? Maybe different metals have different distributions?
For example, could most of the Mg be found in white dwarfs?
Have all the natural elements have been found in stars?

From the big bang nucleosynthesis (BBN) page is a handy chart of the sources of elements:

Since basically all metals come from some stellar process, the question of elemental distribution can vary greatly between different environments depending on when you're observing that particular galaxy, star/galaxy cluster, etc. Galaxy mergers, supernova, and stellar winds can be particularly good at moving metals around a galaxy or galaxy cluster.

Interestingly Wolfram has element data with Universe abundances but I'm not sure where they derive those.


Are there real uses of abstract algebra in astrophysics? It is known that a physicist must have, at least in general, a good level in mathematics in order to research and understand other people's works. Linear algebra is a good example, as ODEs and calculus.

I suppose that some astrophysicists have deep knowledge of abstract mathematics and there are some applications of it (for example, I've been told that there is a connection between topology and cosmology). I wondered if there are some field in Astrophysics in which abstract algebra (i.e. fields, rings, category theory...) has been applied.

There are certainly applications of number theory (as opposed to group theory/algebra - but you do also mention abstract mathematics in general) to astrophysics, though many would suggest these applications are on the boundary between real science and metaphysics.

One such application is the  measure problem - if we assume our universe is one of an infinite number of multiverses how can we draw conclusions about the fundamental physics of the many multiverses, for instance to say that intelligent life is possible in a given proportion.


Can a gas giant have an other gas planet as satellite? Is it possible for a gas giant (A very big one) to have an other smaller gas planet as satellite?

It would seem so.

Think about brown dwarfs. At the lower end of the mass spectrum, they're only a couple dozen times that mass of Jupiter, and only a couple times the mass of Hot Jupiters. Some brown dwarfs have been found to have planets. Taking a look at some examples:

2M1207: Roughly 25 Jupiter masses, this brown dwarf has a planetary-mass object orbiting it, 2M1207b. This object has between 3 and 10 times that mass of Jupiter, and is fairly hot, although it orbits far from the star.
2MASS J04414489+2301513: Roughly 20 Jupiter masses, with a companion on the scale of 5 to 10 Jupiter masses that could be a planet.

Note that these brown dwarfs are very low-mass, only a bit more massive than hot Jupiters. They can have orbiting gas giants - why couldn't high-mass hot Jupiters have the same?


Maximum and minimum gas giant & ice giant densities I'm working on a star system generator for a game; I'd like its results to be plausible but they needn't be super-realistic. I've got the orbital distances and masses of each body in the system, and now want to render them, so I need to determine the radius of each body.

For gas giant and ice giant planets, what's the relationship between mass and density? What are the minimum and maximum densities expected?

Here is a plot I generated in 5 minutes at the site exoplanets.org

To construct this I took planets discovered by the transit method and which had a $M \sin i$ measured using radial velocities. I divided the $M \sin i$ by the sine of the measured inclination angle (this is required to avoid using masses that have been estimated using an assumed mass-radius relation). The y-axis is density, which comes directly (and quite precisely) from transit measurements. Of course transiting planets are the only ones with radii and density measurements.

You have to do this to avoid some very uncertain values that are given for planetary masses that have been simply assumed from a theoretical mass-radius relationship.

As you can see, there is a wide spread (factor of three) in density at a given mass for hot Jupiter's (most of the transiting giant planets are hot Jupiters), but there is a strong correlation. The density is at a minimum for a few tenths of Jupiter mass, but then smaller planets (presumably rocky and icy, rather than gas giants) appear to show higher densities.

Remember, these are all transiting exoplanets, and therefore predominantly orbiting close to their parent stars. There could be biases and selection effects at work! For example although the cores of gas giants are governed by degeneracy pressure and this makes the theoretical mass-radius relationship quite flat, there is the perturbing effect of radiation from the parent star ("insolation") that can make some objects larger. Even beyond this there appears to be scatter that is difficult to understand.

EDIT: For an easy-to-use empirical formulation you could try the relationships proposed by the Planetary Habitability Laboratory.


Using a differential force in the derivation of hydrostatic equilibrium in a star I've been banging my head against this particular derivation of hydrostatic equilibrium in a star for the last few days, from Carroll and Ostlie's Introduction to Modern Astrophysics (2nd ed. p. 286):

The authors consider an infinitesimal cylinder of gas (dimensions $A, dr$) aligned on an r-axis pointing away from the center of the star. Equilibrium demands that acceleration be zero, so we get

$$F_{bottom}  + F_{top} + F_G = 0,$$

Where the first two terms are the forces, taken normal to the surface, due to pressure, and $F_G$ is the gravitational force on the cylinder. The top of the cylinder is away from the center.

Alternative derivations I have found from this point onward make perfect sense- substitute $-\rho A dr$ for the cylinder mass $dm$ in the $F_G$ term, substitute $P_{bottom}$ and $P_{top}$, the rest is straightforward (this is the derivation on Wikipedia).

However, Carroll and Ostlie take an approach I haven't been able to understand. At this point they define
$$F_{top} = -(F_{bottom} + dF_P)$$
where $dF_P$ -I'll write it $dF$ hereafter- is called the differential force caused by the change in pressure due to a change in $r$. Substitution into the first equation and a few other steps here ($dF = A dP$) lead to $dP/{dr} = -\rho g$ as needed.

I have had trouble with the following: $dF$ needs to be negative because otherwise $F_{top}$ is greater in magnitude than $F_{bottom}$ which makes no sense- if $|F_t| > |F_b| $ then pressure isn't acting against gravity, is it? Pressure itself would be pushing the cylinder down in that case. ($b$ is 'bottom', $t$ is 'top'.)

But if $dF$ is negative, then the way the (second) equation is written makes no sense. Wouldn't it make more sense to say $F_t = -F_b + dF$ ?

Partially motivated by this question and partially trying to approach the problem from a slightly different angle, I decided to define $dF = F_b + F_t$ as the net outward force due to the infinitesimal change in pressure between the top and bottom of the cylinder. Then, as $F_{net} = 0,$ we get $dF + F_G = 0$, but this leads to an incorrect equation, namely $$ dF + F_G = 0 \implies dP/dr = \rho g . $$

My main issue is that I do not understand why trying to define a positive $dF$ fails to produce the correct hydrostatic equilibrium equation. Furthermore, if we view $dF$ as an infinitesimal quantity, trying to ensure its sign is consistent with the directions of the forces (outward being positive), we once again get the wrong answer.

Can we only take $dF$ as an inward force? If so, why? If not, how can I establish a positive/outward differential force that will let me derive the correct hydrostatic equilibrium equation?

Edit:

I think I can illustrate my dilemma a bit more succinctly.

Considering the equation $F_t = -(F_b + dF)$, we can try out 2 different possibilities: $dF$ being positive or negative.

If $dF > 0$ then $F_t$ is bigger in magnitude than $F_b$, in which case I don't understand how the pressure gradient creates an outward force because $|F_t|>|F_b|$ implies the downward force is stronger.

If $dF < 0$ then $F_t = -F_b + -dF = -F_b + |dF|$ but as far as I can understand, this form cannot, like any of my attempts to define a positive $dF$, output the correct sign in the final equilibrium equation. So computing the signs (that is, saying $(-dF) = |dF|$) somehow makes the equation incorrect. (Additional edit: For me, this also begs the question, if $dF = A dP$ then is $dP$ negative, and what does that signify?)

The whole exercise illustrates the usefulness of vectors in addressing problems.

$$\vec{F_g} = -\frac{GM(r)\delta m}{r^2}\ \hat{r}$$
$$\vec{F_P} = -\left(\frac{dP}{dr}\right) \delta r \delta A\ \hat{r}$$
$$\vec{F_P} + \vec{F_g} = 0$$
leads to the scalar equation of hydrostatic equilibrium
$$ \frac{dP}{dr}=- \rho g,$$
where $\vec{g}= -g\hat{r}$.


Why do Uranus and Neptune have more methane than Jupiter and Saturn? So the standard theory of the solar nebula is that in the region of the gas planets, ice and rock could condense to form planetesimals, which could then accrete hydrogen and helium to form the gas giants. The giant planets are all mostly hydrogen and helium, but Uranus and Neptune have relatively large amounts of hydrogen compounds like methane (that's what gives them their color).
My question is: why did that happen? How did Uranus and Neptune get their methane? My impression is that all the gas giants were far enough out for methane to condense into ice, so how did Uranus and Neptune end up preferentially with methane?

Why does Uranus and Neptune have more methane than Jupiter and Saturn?

It's a combination of equations of state (EOS), serpentinization, and mixing (rotational and convective) that favors a preference for some reactions (and resulting compounds) over others.

See the references below.

  The giant planets are all mostly hydrogen and helium, but Uranus and Neptune have relatively large amounts of hydrogen compounds like methane (that's what gives them their color).

Jupiter and Saturn are gas giants, Uranus and Neptune are ice giants.

  My question is why did that happen? How did Uranus and Neptune get their methane? My impression is that all the gas giants were far enough out for methane to condense into ice, so how did Uranus and Neptune end up preferentially with methane?

See Wikipedia's "Extraterrestrial Atmosphere":

Graphs of escape velocity against surface temperature of some Solar System objects showing which gases are retained. The objects are drawn to scale, and their data points are at the black dots in the middle. Data is based on "Lecture 5: Overview of the Solar System, Matter in Thermodynamc Equilibrium" and "Stargazer's FAQ - How exactly are atmospheres held?".

Wikipedia says little about the atmosphere of these planets, and the least about Uranus and Neptune:

Atmosphere of Jupiter:

  "There are no methane clouds as the temperatures are too high for it to condense." - Source: "Jupiter's ammonia clouds — localized or ubiquitous?" (April 9 2004), by S.K.Atreya, A.S.Wong, K.H.Baines,  M.H.Wong, and T.C.Owen.

  Quotes from the paper:

  Page 502: "For the production of polycyclic aromatic hydrocarbons (PAHs), chemistry begins with the destruction of methane (CH$_4$) by solar UV photons at $\lambda \le$160 nm, ultimately leading to the formation of benzene ($c$-C$_6$H$_6$, or A$_1$) and other complex hydrocarbons (Fig. 3). In the polar auroral regions where energetic particles also break down methane, ion chemistry becomes dominant in the production of benzene and heavy hydrocarbons (Wong et al., 2003, and Fig. 3).".

Atmosphere of Saturn:

  "Ultraviolet radiation from the Sun causes methane photolysis in the upper atmosphere, leading to a series of hydrocarbon chemical reactions with the resulting products being carried downward by eddies and diffusion. This photochemical cycle is modulated by Saturn's annual seasonal cycle.". - Source: "Ethane, acetylene and propane distribution in Saturn's stratosphere from Cassini/CIRS limb observations" (Nov. 2008), by S. Guerlet, T. Fouchet, and B. Bézard.

  Quotes from the paper:

  Page 406: "3 Method

  We used a line-by-line radiative transfer model to calculate synthetic spectra. It included opacity from CH$_4$, CH$_3$D, C$_2$H$_6$, C$_2$H$_2$, C$_3$H$_8$, C$_3$H$_4, C$_4$H$_2 and collision-induced opacity from H2-He and H2-H2 . The atmospheric grid consisted in [of] 360 layers from 10 bar to 10−8 bar. It was coupled with an iterative inversion algorithm adapted from Conrath et al. (1998), in order to retrieve the atmospheric state (temperature, hydrocarbon vertical profiles) from the measured spectra.

  As a molecular emission intensity depends on both its abundance and temperature, we proceeded in two steps. First, we retrieved the temperature vertical profile from the methane ν4 emission band at 1305 m$^{−1}$ (assuming it is uniformly mixed with a vmr of 4.5 x10$^{−3}$ (Flasar et al. 2005)), providing information in the 1 mbar - 2 $\mu$bar region.

  ...

  Figure 1 shows an example of a comparison between synthetic and observed emission bands of ethane, acetylene and propane at two given pressure levels (all the different pressure levels probed by CIRS have not
  been plotted for the sake of clarity) and Fig. 3 the Corresponding retrieved profiles.".

What that means is that more complex compounds than methane are favored by the conditions, see comments above concerning "equations of state".

Atmosphere of Uranus and Neptune:

  "The  gaseous outer layers of the ice giants have several similarities to those of the gas giants. These include long-lived, high-speed equatorial winds, polar vortices, large-scale circulation patterns, and complex chemical processes driven by ultraviolet radiation from above and mixing with the lower atmosphere.

  Studying the ice giants' atmospheric pattern also gives insights into atmospheric physics. Their compositions promote different chemical processes and they receive far less sunlight in their distant orbits than any other planets in the Solar System (increasing the relevance of internal heating on weather patterns).".

NASA Factsheets - Atmospheric composition (by volume, uncertainty in parentheses):

Jupiter

Major: Molecular hydrogen (H$_2$) - 89.8% (2.0%); Helium (He) - 10.2% (2.0%)
Minor (ppm): Methane (CH$_4$) - 3000 (1000); Ammonia (NH$_3$) - 260 (40); Hydrogen Deuteride (HD) - 28 (10); Ethane (C$_2$H$_6$) - 5.8 (1.5); Water (H$_2$O) - 4 (varies with pressure)
Aerosols: Ammonia ice, water ice, ammonia hydrosulfide

Saturn

Major: Molecular hydrogen (H$_2$) - 96.3% (2.4%); Helium (He) - 3.25% (2.4%)
Minor (ppm): Methane (CH$_4$) - 4500 (2000); Ammonia (NH$_3$) - 125 (75); Hydrogen Deuteride (HD) - 110 (58); Ethane (C$_2$H$_6$) - 7 (1.5)
Aerosols: Ammonia ice, water ice, ammonia hydrosulfide

Uranus

Major: Molecular hydrogen (H$_2$) - 82.5% (3.3%); Helium (He) - 15.2% (3.3%) Methane (CH$_4$) - 2.3%
Minor (ppm): Hydrogen Deuteride (HD) - 148
Aerosols: Ammonia ice, water ice, ammonia hydrosulfide, methane ice(?)

Neptune

Major: Molecular hydrogen (H$_2$) - 80.0% (3.2%); Helium (He) - 19.0% (3.2%); Methane (CH$_4$) 1.5% (0.5%)
Minor (ppm): Hydrogen Deuteride (HD) - 192; Ethane (C$_2$H$_6$) - 1.5
Aerosols: Ammonia ice, water ice, ammonia hydrosulfide, methane ice(?)

Additional references:

"Methane in the Solar System" in English, (Bol. Soc. Geol. Mex [online]. 2015, vol.67, n.3, pp.377-385.), by Andrés Guzmán-Marmolejo and Antígona Segura.

"Abiotic Production of Methane in Terrestrial Planets" (Astrobiology. 2013 Jun; 13(6): 550–559), by Andrés Guzmán-Marmolejo, Antígona Segura, and Elva Escobar-Briones.

"Methane clathrates in the solar system" (Astrobiology. 2015 Apr;15(4):308-26), by Mousis O, Chassefière E, Holm NG, Bouquet A, Waite JH, et al.

NASA - "Scientists Model a Cornucopia of Earth-sized Planets" (Sept. 24 2007).


What is Copernicus referring to when he states that "circles have poles different [from the earth's]" In chapter 4 of "The Revolutions of the Heavenly Spheres" where Copernicus maintains that the objects in our solar system have circular orbits or orbits compounded of several circles, the Edward Rosen translation of the book states this

  It stands to reason, therefore, that their uniform motions appear nonuniform to us.
  The cause may be either that their circles have poles different [from the earth's] or
  that the earth is not at the center of the circles on which they revolve.

To add context: Copernicus believes that features of orbit that are inconsistent to circular motion such as retrograde motion, apogee, perigee, fast/slow movement, etc... Don't actually occur in the orbits of the Sun, Moon, and the planets. Stating that the actual causes of the inconsistencies could either be that "their circles have poles different [from the earth's.]" Or that these objects don't revolve around the Earth.

I'm mainly concerned with what Copernicus is referring to when he states that the orbits of these objects "have poles different [from the earth's,]" and how (if true) it could produce these inconsistencies in orbits.

Remember that Copernicus was espousing a heliocentric Solar System.  What he means by "pole" is the object's axis of revolution and its axis of rotation.  The Earth rotates around its poles: i.e. the North and South pole.  A line between those poles is our axis of rotation.  The axis of revolution would be the axis about which the Earth orbits.  This would correspond to an imaginary line at the Sun.
 Copernicus is presenting the idea that the axis of rotation is not the axis of revolution.


Why does the Tycho-2 catalog not include Hipparcos stars? Both use the same data. But at least, 90k stars are lost in Tycho-2.
Why?

Could you give a source or example: The Tycho-II catalogue paper by Hog et al. (2000) suggests there are about 19,000 stars in Hipparcos or Tycho-I that are not in Tycho-II. This can be because they are too bright (but that is not very many stars) or for other reasons that are not clearly specified (binarity is an issue I think).

Looking at this website, it suggests 4% of stars did not have proper motions and could not be assigned epoch 2000 positions in Tycho II but I don't think these are missing.


Who first hypothesized that the universe is accelerating? I couldn't find this answer anywhere.  Before 1998, was there a notable physicist who conjectured that the universe is accelerating and perhaps even submitted some equations to support it (and the existence of dark energy).  Such a hypothesis would likely have been rejected outright and fallen into oblivion, which is why I have to ask this question to get the answer.  And I don't mean Einstein's cosmological constant since he was trying to make the universe static rather than accelerating.  Someone who actually believed that the universe's expanding rate was increasing even before there was any evidence of it.

Science isn't concerned with belief. The possibility of a dark energy term and therefore an accelerating universe is implicit in GR and in the consequent Friedmann-Lemaitre equations that govern the dynamics of the universe. When the supernova cosmology teams set out to measure the deceleration of the universe, the models that they fitted to their data explicitly allowed for the possibility that the universe might actually be accelerating.

However, such hypothetical universes had certainly been explored before. The De Sitter universe (proposed by Willem de Sitter in 1917) is an accelerating universe consisting only of a cosmological constant. Our own universe appears to be headed asymptotically towards being described as a De Sitter universe.

The idea of $\Lambda$ as a form of "dark energy" that had the potential to cause an accelerating universe was already put forward as an idea by Lemaitre in the late 1920s and early 30s. The picture below shows the evolution of the scale factor for families of solutions and was apparently made by Lemaitre in 1927 (see this science history blog about Lemaitre). The upper 5 curves correspond to a universe that is accelerating today.


How can I find the depth of a portion of the Valles Marineris? How can I find the depth of the low lying part of this image of the western part of Valles Marineris?

I'm interested in the area northeast of Noctis Labyrinthus, southwest of Tithonium Chasma, north of Oudemans, and west of Ius Chasma.

I couldn't find any contour maps of Valles Marineris or Noctis Labyrinthus

You can find MOLA laser altimeter data here:https://pds-geosciences.wustl.edu/missions/mgs/megdr.html.  The files are simple rectangular grids of differences between Martian "sea-level" and measure height at 1/128 degree resolution.  If you have the latitude and longitude, it is quite straightforward to find the height.

To view these files, you probably need the software found here: https://pds.jpl.nasa.gov/tools/about/pds3-tools/nasa-view.shtml

Looks like the software might be a little out-of-date, but you can give it a try.


how to calculate the half-mass radius and tidal radius of a (simulated) globular cluster I am exploring a dataset of a direct N-body simulation of a star cluster, such that all particles have the same mass and

  G = M = −4E = 1

for the whole cluster. The data available is the positions and velocities of all stars (at certain snapshots of the simulation).

I'd like to be able to calculate some basic characteristics of the cluster. First I did the center of mass (which is just the mean of all coordinates since all masses are equal), but I am not sure how to proceed for these two:

The half mass radius - I can't seem to find an established (i.e. most efficient) way to calculate this. My first idea is to use a bisection method with the center of mass and the total radius as starting points, and do window queries with a spherical envelope until it contains half the stars. Is there something more efficient than that?
The tidal radius - what I've found so far always involves variables drawn from the galaxy the cluster is in (like the total mass of the galaxy and so on). However, this being a simulation, there is no such data. Yet the dataset states that some stars escape the cluster over the length of the simulation... I must be missing something here

Your first question is about computing, not astronomy. You find a cumulative histogram of distance from the centre of mass and where that reaches 50% of the stars.
As to your second point, there is no tidal radius; you need two bodies in order to have a defined tidal radius. The tidal radius of a cluster is directly related to the gravitational potential external to it.
Stars can escape from a cluster because sometimes they can accumulate enough kinetic energy in weak interactions with each other, that their speed exceeds the escape speed of the cluster. It is a classic result that the "evaporation" timescale is of order 100 times the cluster relaxation timescale, even in the absence of an external gravitational field (e.g. Gerhard 2000).


Impact on the rest of the solar system if Mercury or Venus were disassembled? I've watched a few theoretical videos about Dyson spheres where they mention that the most practical way to do that would be to disassemble a planet - preferably one already close to the sun - Mercury or Venus.
Question: Would the solar system become completely unstable if one (or both) of those planets got disassembled? As a follow up question: what if one or more of the gas giants somehow were taken out of the solar system?

Not really. The mass of Mercury and Venus together are just 0.0027 of Jupiter's mass. So the effect is really small.
Now, in principle, there are resonances where the regular tug from planets affect the long-term evolution of the orbits of other planets. The exact details get very messy, but in some cases the presence of a planet stabilizes certain orbits - or destabilises them (this is very visible in the asteroid belt). But the planetary orbits look largely non-resonant. So if two planets went missing there would not be much of an effect.
It is likely that this is true for Jupiter too. What would happen is that the Trojan and Greek asteroids would drift out of their 1:1 resonance and end up in a loose belt, and the asteroid belt would also reorganise.
Overall, you don't need much mass for a Dyson sphere if you want to just collect energy. My paper on using one to settle the universe disassembled Mercury mostly as a conservative estimate to get more than enough material - I currently think you need a few largish asteroid masses, maybe Ceres (assuming it has the right elements, an important if). Conversely, Dyson element orbits will be subject to gravitational interactions from remaining planets that will cause precession and other possibly unwanted shifts one need to compensate for. But a Dyson sphere is mass-wise a microscopic thing compared to planets.


Astronomy Olympiad Gravitation Qn Question:
Approximately once in 5 years people on Earth can observe bright comets whose nuclei have radius about 1km. The orbits of such comets are close to parabolic. Assuming that these nuclei are uniformly filling the volume of spherical Oort cloud with radius 10000 AU, estimate the number of large comet nuclei and mass of Oort cloud.

I'm not sure how to even start this question because I don't get how the comets uniformly fill Oort cloud yet on Earth we can only observe comets once every 5 years (unless there are some things blocking our views of these comets?). Would appreciate any help.

P.S. Relativity should not be needed in this question...

Presumably you're supposed to start by calculating the minimum orbital period a comet can have for a 10,000 AU aphelion distance.

Then divide that period (number of years) by five, assuming we see on average one of these every five years.

That will give you an estimate for how many there are out there.

(I would also tell the person setting the question that there are some pretty wild assumptions implied in the question!)


Critical density of the universe (no, not that one)? I seem to recall reading something that said if the density of the universe was off by as little as one atom per cubic meter, the universe, as we know it, would not exist; one less and there wouldn't have been enough gravity to form galaxies and stars, one more and there would have been too much matter. (I don't know (or remember) what would have happened in the case of too much matter.)If I Google the title of this question, all I get is stuff about the expansion of the universe, nothing about whether or not it would exist. I've tried other variations but can't seem to find anything.Did I grossly misinterpret this? If not, does anyone know of any articles that can confirm or refute this?

You're basically asking about the Flatness Problem. As quoted from Wikipedia:

  If the initial density of the universe could take any value, it would seem extremely surprising to find it so 'finely tuned' to the critical value $\rho_c$. Indeed, a very small departure of $\Omega$ from 1 in the early universe would have been magnified during billions of years of expansion to create a current density very far from critical. In the case of an overdensity ($\rho > \rho_c$) this would lead to a universe so dense it would cease expanding and collapse into a Big Crunch (an opposite to the Big Bang in which all matter and energy falls back into an extremely dense state) in a few years or less; in the case of an underdensity ($\rho < \rho_c$) it would expand so quickly and become so sparse it would soon seem essentially empty, and gravity would not be strong enough by comparison to cause matter to collapse and form galaxies. In either case the universe would contain no complex structures such as galaxies, stars, planets and any form of life.

This is more or less what Phiteros says in his comment above. As he states, the distinction here is not that the universe wouldn't exist at all, as you state, but rather it wouldn't exist as we know it, with galaxies, stars, planets, or life of any form.

To explain a bit more, the basic idea is that the universe will have started out with a more-or-less homogeneous and isotropic distribution of matter with some density $\rho$ (this is a pretty strong assumption in its own right, and worth addressing in a completely different answer). Note that the overall curvature of the universe is directly tied to this density so you may see some sources talk about this in terms of curvature instead of density. The main point, as described in the quote above is that the evolution of the universe, i.e., the ability for galaxies, stars, planets, life, etc. to form, is dictated by a critical density, $\rho_c$. If $\rho = \rho_c$ (or as close to equal as to be insignificantly different), our universe can form as it is now. The flatness problem comes into play because the Big Bang Theory implies that if the universe did not start out with (almost) exactly $\rho = \rho_c$, it would have veered far off course from our current universe and resulted in either a Big Crunch or a Big Rip.

This idea poses a really big problem for the Big Bang Theory because it requires such a precise setup for our universe, where any betting person would've said there's no way the universe could've started out with $\rho=\rho_c$. The main resolution to this problem is by introducing inflation into the model. The main idea here is that the Universe may or may not have started out with $\rho = \rho_c$, but so long as it was close enough, the hyper inflation at the beginning of the universe would have forced the difference to be so small as to be effectively zero, negating the effects described in the quote above. Another potential, and not necessary mutually exclusive answer is found in the Anthropic Principle, which I won't delve into here.


How to calculate the limiting magnitude of Hubble? I've found various sources on the web stating that the limiting apparent magnitude of the Hubble Space Telescope is about 31 or 31.5. Wikipedia lists that here and it has a cite to a pdf about it.

What I want to know is how is that calculated?

I'm aware of two methods found at the bottom of a table here, but they seems to be general calculations for ground-based telescopes, because if I plug in Hubble's numbers, I get something around 21. The difference between an apparent magnitude of 21 and 31 is actually something like ten thousands times (in terms of brightness).

Also, one key factor missing in their formulas is exposure time. I'm pretty sure the limiting magnitude has something to do with exposure time. Hubble Ultra Deep Field, for example, had an exposure time of about 1 million seconds.

So to sum up, how would we calculate the limiting magnitude of a space-based telescope, in visible light?

The table you linked to gives limiting magnitudes for direct observations through a telescope with the human eye, so it's definitely not what you want to use.

The quoted number for HST is an empirical one, determined from the actual "Extreme Deep Field" data (total exposure time ~ 2 million seconds) after the fact; the Illingworth et al. PDF you linked to explains how it was done. Briefly, they decided the limit would be defined by a signal-to-noise ratio of 5, and then figured out what the noise level in the final combined images was by integrating the total flux in many circular apertures of diameter 0.35 arc seconds placed in regions of blank sky background, and then computing the standard deviation ($\sigma$) of these measurements. Five times $\sigma$ was then the limiting flux. Knowing the photometric calibration (the conversion between observed counts and apparent magnitude; see the paper for specific details), they converted this $S/N = 5$ limit into an apparent magnitude.

If, instead, you want try to estimate in advance what the limiting magnitude should be, then you have to consider several factors. Simplifying a bit, the equation for long-exposure, background-limited $S/N$ is
$$
S/N \approx \frac{s t}{ \sqrt{ s t + n_{\rm pix}(b t)} }
$$
where $s$ = detected flux from the source (star, galaxy, etc.) in electrons (i.e., detected photons) per second, $t$ is the integration time in seconds , $b$ is the flux from the background in electrons per pixel, and $n_{\rm pix}$ is the number of pixels you integrate over for the measurement. $s$ can be computed from the combination of the object's apparent magnitude, the diameter of the telescope's mirror and the overall efficiency of the telescope + detector system. $b$ can be determined in a similar fashion, using the estimated background brightness (which, for a telescope like HST, is mostly sunlight reflected from dust in the inner solar system). $n_{\rm pix}$ is a number chosen as a compromise between maximizing the amount of light from the source (higher $n_{\rm pix}$) and minimizing the noise from the background (lower $n_{\rm pix}$). This depends on the telescope's resolution (better resolution = smaller images of stars and other point-like sources = fewer pixels needed); the empirical calculations by Illingworth et al. used an aperture size amounting to about 100 pixels.


Why does the Event Horizon Telescope (EHT) not include telescopes from Africa, Asia or Australia? The Event Horizon Telescope seems to include these radio telescopes currently:

Image by European Southern Observatory (ESO)/O. Furtak; CC-BY 4.0-licensed, see the source on Wikipedia Commons and the original image link.

See also the map and list on their official website.

It is also said, that it has a “effective diameter of the entire planet”.
But it's striking, it does not include half-of the earth… It has no telescopes in Africa, Asia or Australia.

So:

Why were not they included?
Would it increase the diameter if they would include some from there? If so, again why did not they? ()
Or, similarly asked: How can it be the diameter of the earth if only half-the-earth is included in the network?

Please try to explain it in a simple way first. I am no astronomer.

What I've noticed so far when skimming their official pages is that they write here:

  As more telescopes are added to the EHT, we will be able to produce images of the emission around black holes. In general, the fidelity of images produced by an interferometric array increases as additional telescopes are added to the array.

This seems to support my question of why they did not use possibilities in Asia or so…
I guess, it would also make sense to have a more or less uniform distribution across the planet (or does not this matter?), that's why a "dot" in Africa might make sense too…

Would it increase the diameter if they would include some from there?

No. Not by much, at least. The telescopes are already ~20,000 km apart, so you can't create a longer baseline that still has a simultaneous view of the target.

Don't forget: Earth is a sphere. Only one half of that sphere can observe M87 at the same time.

Telescopes in the Eastern hemisphere would enable more observations, but I don't know if that would bring any improvement over what they already had.


What does Stephen Hawking mean by 'an infinite universe'? In the recent $100m search for extra terrestrial life project project, Stephen Hawking is quoted in the following way:

  "We believe that life arose spontaneously on Earth," Hawking said at Monday's news conference, "So in an infinite universe, there must be other occurrences of life."

My understanding is that scientists believe that the universe isn't infinite - there there is a finite number of stars, it's continuously expanding but has a finite size at a given time.

What's Stephen Hawking refering to here?

Due to the finite speed of light, and the finite age of the Universe, only a portion of it is observable. When people talk about "the size of the Universe", "the number of stars in the Universe", etc., they usually refer to the observable Universe, i.e. the sphere in which we are centered, and which has a radius given by the distance light has been able to travel in the 13.8 billion years since the Big Bang. Note that since the Universe is expanding, this radius is more than 13.8 billion light-years. In fact it's 46.3 billion light-years.

Observations indicate that, on large scales (i.e. above roughly half a billion light-years), the Universe is homogeneous (the same everywhere) and isotropic (the same in all directions). Assuming that this is indeed true is known as the cosmological principle. If the rest of the Universe follows this principle, then there are three possible overall "versions" of universes that we can live in. We call these versions "flat", "closed", and "open". Whereas a globally closed universe would have a finite extent, globally flat or open universes must be infinitely large.

The observable Universe is, within measuring uncertainties but too a very high precision, flat (e.g. Planck Collaboration et al. 2016). Hence, we might think that the whole Universe is, in fact, infinite. But sort of like standing in a large forest with limited visibility doesn't tell you whether the forest is just larger than you can see, or if it's infinitely large, we can't with our current theories and observations know whether the Universe is finite or infinite.


How does the amount of dark matter in measured galaxies vary? I have recently viewed two news articles announcing a galaxy composed almost entirely of dark matter and one with hardly any. This made me wonder if there is a "continuum" of percentages of dark matter in galaxies, where it has been measured, or if there is a "preferred" range.

tl;dr: In general, smaller galaxies have relatively more dark matter than larger galaxies. The atypical galaxies that you refer to are discussed in the last paragraph.

Mass fractions in the Universe

Matter in the Universe is dominated by two components; baryons (i.e. atoms in various forms) and dark matter (DM). The baryons predominantly exist in two forms: gas (including plasma) and stars (some gas condenses to form dust, planets, etc., but that's a minor part).

The fraction of the Universe's total energy in the form of matter is $\Omega_\mathrm{M}\simeq0.31$ (most of the rest is dark energy). The baryons and DM have fractions $\Omega_\mathrm{b}=0.05$ and $\Omega_\mathrm{DM}=0.26$, respectively (numbers from Planck Collaboration et al. 2016).

Hence, the baryons and DM comprise fractions
$f_\mathrm{b}  = \Omega_\mathrm{b}  / \Omega_\mathrm{M} = 16$% and
$f_\mathrm{DM} = \Omega_\mathrm{DM} / \Omega_\mathrm{M} = 84$% of the total mass, respectively.

Galaxies have more dark matter than the average Universe

Galaxies formed when DM+gas overdensities decoupled from the Hubble flow and started collapsing, and so were "born" with the "cosmic" fractions. However, observationally it is found that the baryon fraction in galaxies is much smaller; for instance, a "typical" Milky Way-sized galaxy roughly has $f_\mathrm{b}$ only half of the cosmic average, and the DM fraction is correspondingly larger, >$90$% (e.g. Werk et al. 2014).

Gas and dark matter dynamics

The reason is the different mechanisms that affect the dynamics of the particles.
Whereas the DM is collisionless, the gas particles collide and dissipate their energy, making it easier to cool and contract. Thus, the part of the galaxies that we can observe is much smaller than "whole" galaxy; the  typical "half-light radius" is but a few percent of the emcompassing DM halo (Kravtsov 2013, Somerville et al. 2017). The half-light radius is the radius within which half of the light is emitted; when you see an image of a galaxy, it typically looks perhaps 4-5 times larger than this. So, something like this:

A significant fraction of the baryons reside in the halo as well. This is the hot gas of millions of Kelvin, and the high temperature and low density makes it difficult to detect, as it glows only in faint X-rays.

Feedback blows out gas, but dark matter stays

But various physical processes act so as to try to blow the baryons — but not the DM — out of the galaxies. These processes are known as feedback, and are due to energy being "injected" in the baryons.
For massive galaxies with halo masses $M_\mathrm{h}\gtrsim10^{12}\,M_\odot$ this feedback is dominated by their central black hole accreting gas, resulting in extreme luminosities manifesting itself as a quasar, or active galactic nucleus (Silk & Rees 1998; Croton et al. 2006). For smaller galaxies with $M_\mathrm{h}\lesssim10^{12}\,M_\odot$, the feedback is mostly due to stellar winds and exploding stars depositing thermal and kinetic energy in the surrounding gas (Dekel & Silk 1986; Hopkins et al. 2012). At even lower masses, the galaxies are so small that a significant fraction of their gas may be ejected altogether during early epochs of star formation (e.g. Bullock et al. 2000), resulting in galaxies that consist virtually only of DM and a few stars.

The smaller a galaxy is, the shallower its gravitational potential, and thus the easier it is for the gas to escape the galaxy.

Hence, in general the smaller a galaxy is, the larger its amount of dark matter is.

Conversely, the larger a halo is, the more its mass fractions converge toward the cosmic fractions. These are only reached for halos of masses $M_\mathrm{h} \gtrsim 10^{15}\,M_\odot$, which are no longer individual galaxies, but rather groups and clusters. This is seen in the figure below (from a paper from last week by Henden et al. 2018), which shows the stellar mass fraction (left) and gas mass fraction (right) as a function of halo mass:

The baryon fraction is $f_\mathrm{b} = f_\mathrm{stars}+f_\mathrm{gas}$, and the DM fraction — which is what you're asking for — is then given by $f_\mathrm{DM} = 1 - f_\mathrm{stars} - f_\mathrm{gas}$. The stellar fraction is seen to decrease with halo mass, due to the AGN feedback discussed above, but the total star+gas fraction increases.

Note though that although the DM — being collisionless — is not exactly blown out of the galaxy like the baryons, the gravitational attraction between the two components still affects the DM and alters the density profile of the halo (Duffy et al. 2010).

Galaxies with more gas than dark matter (?)

Thus, a galaxy without baryons is not a huge mystery, as long as it's small. Even larger galaxies are apparently able to rid themselves of most the baryons; van Dokkum et al. (2016) reported a MW-sized halo with 98% DM.

A galaxy with baryons, but without DM is more spectacular, but was reported recently by van Dokkum et al. (2018) (yes, the same guy).
In another answer about DF2 I discuss various processes that might lead to such a galaxy, including misinterpretation of the data.


What conditions would lead to this event around the black hole in the Pictor A galaxy? This is a picture of a jet of particles exiting the supermassive black hole in the center of Pictor A galaxy at nearly the speed of light. Source

This event is supposedly created from a black hole of 40 million solar masses. The full quote here:

  The newly released picture shows the terrifying power of an actual
  supermassive black hole located in the galaxy Pictor A, some 500
  million light years distant.  This black hole is about 40 million
  times the mass of the Sun (that’s about 10 times larger than the black
  hole at the center of our own galaxy), and if it were to replace the
  Sun within our Solar System, its event horizon would swallow the
  orbits of both Mercury and Venus.

Now a quick search to Wikipedia would show a abundance of supermassive black holes many, many times larger than that supermassive black hole as well as a few that are around the same mass as that.

To my question: What set of special conditions that surround this particular supermassive black hole such that it is capable of creating this spectacular event?

Edit for clarity: By this I meant the jet and the hotspot.

This is a clear example of an astrophysical jet, in this case, most likely a relativistic jet. In short, an accretion disk forms around a black hole (supermassive or otherwise). Matter is pulled towards the black hole and further energized, before being accelerated into a jet emanating from the black hole's poles. Two different mechanisms have been proposed for the formation of jets:

The Blandford-Znajek process requires that a magnetic field forms (from the accretion disk) that is centered around the black hole. Charged particles then move along the field lines, into jets. I recently wrote an answer about the details (see How does an accreting black hole acquire magnetic fields?). For this process to work, you need an accretion disk. It is generally considered the most likely explanation for black hole jets.
The Penrose process takes rotational kinetic energy from the ergosphere outside the event horizon and gives it to particles moving in jets. Note that this does not rely as heavily on the accretion disk as the Blandford-Znajek process does. For this process to work, you need a rotating black hole surrounded by some matter, likely in a disk.

The hotspot is, to me, much more interesting. It reminds me of structures seen around young stars: bipolar outflows (streams of gas that can form shock waves) and Herbig-Haro objects (the results of shock waves from relativistic jets. Obviously, the mechanisms are different, so no clear analogy can be drawn. But what is interesting about bipolar outflows and Herbig-Haro objects is that the shock waves produced therein result from collisions with the interstellar medium.

If a similar mechanism were to cause the shock waves by the hotspot, then we could conclude that the jets have hit the intergalactic medium. But I don't think this is necessarily the case, in part because of just how long these jets are prior to the formation of the hotspot. One would think that if the hotspot and shock waves are because of collisions with the intergalactic medium, the jets would be much shorter, because they would likely have reached higher density regions of it sooner. So that's why I find it interesting, and why I can't give you a good reason as to why the hotspot formed where it did, or the precise reason for it being there at all.


Are these parallel lines I'm seeing in this image a real pattern on the Moon? In this question I mention the GIF in EarthSky.org's Moon Phases update Lengths of lunar months in 2017. After watching it a while, I've noticed a pattern of parallel nearly vertical lines on the Moon image that's used to generate this simulation. I've shown it below. However, if I look at the moon image in Wikipedia, which is much larger, higher resolution, and has perhaps higher contrast, I don't see it.

It could be there, but less noticable due to the enhanced level of detail i the large image, but I am wondering - is it real, or not. If not, how did it get into this image?

above: Animation used in EarthSky.org.

above: Frame 29 from the GIF Animation used in EarthSky.org.

above: A casual analysis of the cropped ROI. The traces are color: top, middle, and bottom third, column averages, black: entire column average. Short vertical lines are drawn by hand to try to point out the pattern that I'm seeing.

above: "Full Moon photograph taken 10-22-2010 from Madison, Alabama, USA. Photographed with a Celestron 9.25 Schmidt-Cassegrain telescope..." from here.

They are not real.

The images used in the animation use a mosaic of photographs taken by an orbiting satellite, the Clementine orbiter. This satellite has a polar orbit, and so returns images in strips that run roughly north-south. Due to variations in lighting between orbits, when the strips are joined together, there are artefacts at the joins.

The whole moon image from a ground-based telescope doesn't have such artefacts. The lunar orbiter view was used as it covers the whole moon, including the far-side. As the moon orbits Earth, it appears to wobble (an effect known as libration.) By starting with a whole moon map, and then projecting it to a sphere, this libration can be simulated. You couldn't do that with a single ground-based image.


Are there radio white dwarfs? We have discovered about 2500 radio pulsars. Part of them show pulsations in other bands like X-ray and gamma ray. The radiation mechanism remains unclear now.

I wonder whether there are radio pulsations caused by the spins of white dwarfs. It is the best to give reference papers.

AR Scorpii1 appears to be an example. It is a binary system, consisting of a white dwarf and an M-type red dwarf. It was apparently originally classified as a $\delta$ Scuti variable star, but it was later discovered to be a true close binary, with a period of 3.56 hours.

The white dwarf emits pulses, as discovered by Marsh et al. (2016), with a period of about two minutes. These are visible in wavelengths from ultraviolet to radio (see Fig. 2):

The most noticeable patterns are in the ultraviolet, and the weakest are in the radio band, but the signals are certainly detectable.

The rational for determining that the compact object is a white dwarf follows from its luminosity, its relatively long spin period (longer than any neutron star pulsar yet discovered), and the fact that the pairing with a red dwarf is "more natural" than the odd alternative involving a low-mass neutron star and high-mass red dwarf.

The system may form what is known as an intermediate polar, involving accretion onto a white dwarf influenced by the object's strong magnetic field. The other notable example is AE Aquarii, as Rob Jeffries mentioned. However, its radio emissions do not involve pulsations. Why it doesn't emit pulsating signals at radio wavelengths is another question entirely, and not one I can answer right now.

More recent results (Buckley et al. (2017)) indicate that the radio emissions from the system are polarized, similar to those of neutron stars. It seems that AR Sco shares even more characteristics with pulsars than was previously thought.

1 The Wikipedia page, I just discovered, is terrible.


Does this black hole magnetohydrodynamics equation even superficially make sense? My question is about the journal paper mentioned in an Academia Stack Exchange post. Please understand that this paper has never been posted on arXiv, and I can provide only a link whose content is behind a paywall.

Summary of my question: it boils down to "whether a spatial coordinate of a fiducial observer can have a nonzero partial derivative with respect to the coordinate time."

I am interested in the validity of the central result of this paper. It is Eq. 4.24, which reads
\begin{equation}
\begin{split}
&\nabla\cdot\left[\frac{\alpha}{\varpi^{2}}\left\{1-\left(\frac{\omega-\Omega^{F}}{\alpha}\varpi\right)^{2}\right\}\nabla\Psi\right]
- \frac{\omega-\Omega_{F}}{\alpha}\nabla\Omega^{F}\cdot\nabla\Psi\\
&+ \frac{4\pi\dot{\varpi}}{\alpha^{2}\varpi}\left(1-\frac{\dot{\Phi}}{4\pi}\right)\frac{\partial \Omega^{F}}{\partial z} + 4\pi \frac{\partial}{\partial z}\left[\frac{\dot{\varpi}}{\alpha\varpi}\frac{\omega-\Omega^{F}}{\alpha}\left(1-\frac{\dot{\Phi}}{4\pi}\right)\right]\\
&+\frac{1}{\alpha\varpi^{2}}\left[\left(\frac{\dot{\alpha}}{\alpha}+\frac{\dot{\varpi}}{\varpi}\right)\dot{\Psi}-\ddot{\Psi}\right] + \frac{\dot{\varphi}}{\varpi}\frac{\omega-\Omega^{F}}{\alpha}\frac{\partial\Psi}{\partial\varpi}\\
&-\frac{16\pi^{2}\xi}{\varpi^{2}}\left(1-\frac{\dot{\Phi}}{4\pi}\right) = 0,
\end{split}
\end{equation}
where a dot on top of a symbol denotes a partial derivative with respect to the coordinate time $t$.

The above partial differential equation is supposed to describe the magnetosphere of a Kerr black hole. The authors use the spherical coordinates $(r,\theta,\varphi)$ and define $\varpi$ as follows:
\begin{equation}
\varpi \equiv \frac{\Sigma}{\rho}\sin\theta,
\end{equation}
where
\begin{equation}
\rho^{2} \equiv r^{2} + a^{2}\cos^{2}\theta,
\end{equation}
\begin{equation}
\Sigma^{2} \equiv (r^{2}+a^{2})^{2}- a^{2}\Delta\sin^{2}\theta,
\end{equation}
and
\begin{equation}
\Delta \equiv r^{2} + a^{2} - 2Mr.
\end{equation}
Note also that $\alpha$ is the lapse function defined as
\begin{equation}
\alpha\equiv \frac{\rho}{\Sigma}\sqrt{\Delta}.
\end{equation}

The functions $\Psi(t,\textbf{r})$ and $\Phi(t,\textbf{r})$ denote the magnetic and electric fluxes through an $\textbf{m}$-loop passing through $\textbf{r}$, where $\textbf{m} \equiv \varpi\hat{e}_{\varphi}$ is the Killing vector associated with axisymmetry.

What confuses me is the following: $\varpi$, $\varphi$, and $\alpha$ are simply spatial coordinates or combinations thereof, and their (partial) time derivatives should all be identically equal to zero because space and time coordinates are independent variables. This would render many parts of Eq. 4.24 nothing but convoluted ways to express the number zero.

I have also tried to follow the derivation of Eq. 4.24, and figured out that the authors implicitly assumed the following relations:
\begin{equation}
\dot{\Phi} = \dot{\varpi}\frac{\partial\Phi}{\partial \varpi}
\end{equation}
and
\begin{equation}
\dot{\Psi} = \dot{\varpi}\frac{\partial\Psi}{\partial \varpi}.
\end{equation}
Recall that a dot means a partial derivative with respect to time. As $\dot{\varpi}$ is identically zero, the above relations seem to be wrong.

However, what makes me somewhat unsure about my conclusion is that this paper is published in The Astrophysical Journal, a renowned peer-reviewed journal in astrophysics. (I have little expertise in astrophysics.)

Could someone verify whether my suspicion is well founded or correct me where I am wrong? Thanks in advance!

I believe your assumption of the partial derivatives with respect to time being identically zero is incorrect.  When you are talking about working in phase space, i.e., Liouville's theorem with functions of positions and velocities, then you are correct that the partial derivatives of one phase space variable with respect to the others is zero.  But here (I presume), they're looking at the temporal dynamics of the black hole magnetosphere.

It is a little dense (but if you're working through Equation 4.24 above then you'll have no trouble with this), but you might find the stuff in this paper as filling in a lot of the background equations.


Why does the Supernova 2006cm give a very different value for the Hubble constant? Why doesn't it increase error bars for the Hubble constant? The Supernova 2006cm has a redshift of 0.0153 which translates into a recession speed of 4600 km/s.

It has a distance modulus of 34.71 which translates into a luminosity distance of 87 Mpc.

This gives a value of 53 km/s/Mpc for the Hubble constant.

Why doesn't this anomalous observation create sufficient doubt in the value of the Hubble constant?

At a distance of $d = 87\,\mathrm{Mpc}$, with a Hubble constant of roughly $H_0 = 70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ cosmological expansion should make the host galaxy UGC 11723 recede at $v=H_0 \,d\simeq6100 \,\mathrm{km}\,\mathrm{s}^{-1}$.

However, galaxies also move through space, at typical velocities from several
$100\,\mathrm{km}\,\mathrm{s}^{-1}$ in galaxy groups (e.g Carlberg et al. 2000) to some $1000\,\mathrm{km}\,\mathrm{s}^{-1}$ in rich clusters (e.g Girardi et al. 1993; Karachentsev et al. 2006).

The observed velocity of $4900\,\mathrm{km}\,\mathrm{s}^{-1}$ (Falco et al. 2006) is hence $\sim1200\,\mathrm{km}\,\mathrm{s}^{-1}$ smaller than the Hubble flow, but quite consistent with what may be expected.

This is why supernovae at such small distances cannot be used to deduce the Hubble constant, unless a very large number is observed such that statistical errors cancel out.


What is the percent flattening in Haumea? I've recently noticed that in Wikipedia articles such as Pluto (Link), there's this number that says how much flattened it is (Definition Here). In Pluto, it's >1%.

Haumea, which is a very flattened dwarf planet, actually doesn't have this information on Wikipedia, and I haven't been able to find it online.

It would be great if someone could find this info (and it's source as well), because I can't seem to find it anywhere.

Thanks in advance!

That would be because Haumea is a Triaxial ellipsoid. It's dimensions are different in every cardinal direction. The term 'flattening' only makes sense for the biaxial ellipsoids, because two of the axes are the same and one is different (in the case of Pluto, the equatorial axis is 1% larger, hence 1% flattened). The concept of 'flattened' doesn't make terribly much sense when all three axes are different.

Haumea's axis ratios are approximately 1 : 0.75 : 0.5, if that's the information you're after.


Why 225088 Gonggong is not a dwarf Planet yet? Per definition a dwarf planet is:

  a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape1, (c) has not cleared the neighbourhood around its orbit, and (d) is not a satellite.

The Wikipedia page for 225088 Gonggong, former 2007 OR10 states three possibilities for its dimensions:

  1535+75−225 km
  1280+210−210 km
  1200+300−200 km

Which is all minimum 1000km in diameter. So how can you still doubt the hydrostatic equilibrium for such a large body?

As the comments already say, an object being a dwarf planet is a matter of convention. If the IAU says it's a dwarf planet, it's a dwarf planet. Otherwise, it's not. The requirements you are listing from Wikipedia are the IAU criteria for pronouncing objects as dwarf planets, but that does not mean that all objects fulfilling these criteria are dwarf planets. (don't ask me for the reasonings of the IAU, i'm not an expert on astronomer's brain twists)

There are a lot more examples of objects that could be dwarf planets, and are considered as being that by many researchers, despite these objects not having the status of dwarf planet. Wikipedia's List of possible dwarf planets has about 200 objects facing the same issue as 2007 OR10.

edit: as someone in the comments mentioned, not all objects on this list are actual candidates for dwarf planets (which is not what I meant, but I might indeed have implied this)


How can we calculate velocity of an object given the distance from an object in parsecs? If you had the distance from a celestial object, in parsecs, how would you calculate the velocity of the said object?

Edit: I'm sorry I don't have more context, the specific questions is: "A galaxy that is 10 million parsecs away will be moving at what velocity?"

You can't, not very well anyway. That's simply because the velocity of an object isn't calculable from the Hubble constant until the so-called Hubble flow starts to dominate (which in turn only happens at cosmological distances, i.e. very far away).

That said, if you are in the regime where Hubble flow dominates, you can do this easily. The Hubble constant is approximately $70 km/s/Mpc$. Just convert your distance into megaparsecs, and multiply. You end up with a velocity, which is the one you're looking for (this neglects peculiar velocity, which will affect everything in the sky).


Why do black holes have jets and accretion disks? If supermassive black holes possess the gravity required to prevent the escape of photons and other mass particles, why do jets and accretion disks form?

They seem to indicate that something is coming out of the black hole, while mathematics and physics seem to tell us that this is impossible.

It would seem that supermassive black holes only exert gravity towards themselves.

When it comes to accretion disks, nothing is coming out of the black hole. That's just orbiting matter, though it is swirled around a bit by frame dragging. Even at high gravity, the ability to orbit around a massive body still exists. The gravitational force is already being "used up" to cause the orbiting (it accounts for the centripetal force), so there is no need for the gas to fall in.

As for jets, as far as I can tell there is no single explanation (I am not sure of this). One candidate explanation is the Blandford-Znajek process1

The following image is from Black Holes and Time Warps: Einstein's Outrageous Legacy, by Kip S. Thorne:

Basically, most black holes rotate, and sometimes the intense rotation can cause forces that overcome gravity, even by a few orders of magnitude.

When a black hole spins, magnetic field lines anchored to it2 spin along with it. Plasma (from the accretion disk) is then flung out along these lines, similar to what happens when you put a marble in a conical cup and rotate it. This is depicted in the first image.

In the second image, current passes through the field lines (I do not understand this one as well as the first, however this post has a reasonable explanation), accelerates plasma with a mechanism similar to an electromagnetic railgun. This is another way of creating jets.

Note that the energy here comes from the rotational energy of the BH, not the mass-energy of the "contents" of the BH (which is lost to the universe unless we consider Hawking radiation)

(I shall have a closer look at the paper when I have time and update the answer accordingly. Comments appreciated)

1. Blandford, R. D., & Znajek, R. L. (1977). Electromagnetic extraction of energy from Kerr black holes. Monthly Notices of the Royal Astronomical Society, 179, 433-456.

2. While the no-hair theorem forbids a naked black hole from posessing magnetic field lines, one with an accretion disk may have them as the field lines cannot "escape" through the disk.


Starlight: are the rays that we see here on Earth parallel? Are the rays of light emitted from stars that are perceived by an eye here on Earth parallel?
Do they travel in a straight line from the star to the eye, never crossing, and equidistant?
Do they wiggle around and cross as they move through space?
Do the rays meet at a point on the retina of the eye?
Assuming that a star is pretty far away, it seems reasonable to think that they've traveled zillions of miles without being parallel.

Light rays travel along things called geodesics in spacetime (specifically they travel along a certain class of geodesics called 'null geodesics').
If spacetime is flat, which will be the case in the absence of gravity, then those geodesics are just straight lines as we normally think of them, and so yes, light rays travel along straight lines in that case.
But there is gravity and spacetime is therefore not flat.  This means there there is really no definition of 'straight line' any more: geodesics are the best thing we have (that's why they're called geodesics rather than straight lines).
But in very many cases the deviation caused by spacetime not being flat is pretty small: for instance it's possible to see the difference in apparent position of stars if the light from them passes close to the Sun, but it's a small deviation.
In some cases – if the light passes close to very massive objects, the deviation can be very large (and in fact if the object is massive enough, it can be as large as you like).
The general effect of light travelling along geodesics which are not well-approximated by straight lines is called 'gravitational lensing' and it's now a well-confirmed thing which is used in practice to detect things like exoplanets (amazingly, in this case it's the lensing of the light from stars by the planet which is observed, which is just astonishing.)
So a brief answer is yes, almost always, but occasionally not at all!


Temperature of the Sun's rays What is the temperature of the light that leaves the Sun towards the Earth and does it cool down during it's journey here ? If it doesn't cool down then how come it isn't frying the Earth ? Is it our atmosphere that is preventing it from doing so or does it cool down during it's trip here in space ?

The Sun's radiation spectrum is close to thermal at $T_\odot = 5778\,\mathrm{K}$. That means that that power output, given by the Stefan–Boltzmann law, is around $L = \sigma A T^4$, where $\sigma = 5.6704\times 10^{-8} \,{\mathrm{W}}/{\mathrm{m}^2\mathrm{K}^4}$ is the Stefan–Boltzmann constant and $A$ is its surface area:
$$L_\odot = \sigma(4\pi R_\odot^2)T_\odot^4 = 3.85\times10^{26}\,\mathrm{W}\text{.}$$
However, at the Earth's orbital radius $r = 1\,\mathrm{AU}$, this radiation is spread across a surface area of $4\pi r^2$, so the power incident on an Earth-sized sphere would be just
$$P = L_\odot\frac{\pi R_\oplus^2}{4\pi r^2}\text{,}$$
so approximating the Earth as a spherical blackbody, the equilibrium temperature is determined by its own thermal radiation balanced by this incident radiation:
$$\sigma(4\pi R_\oplus^2)T^4 = P\text{,}$$
which gives a surface temperature of
$$T =  T_\odot\sqrt{\frac{R_\odot}{2 r}} = 279\,\mathrm{K}\text{.}$$
Therefore, no special mechanisms are necessary to prevent the Earth from frying.

In reality, the Earth is not a blackbody because of its albedo and atmosphere, but its actual global temperature is not too far off from this estimate. The average surface temperature is close to $288\,\mathrm{K}$. Earth's atmosphere actually raises the average temperature, not lowers it.


What is the bright object above the moon in Sudbury, Ontario? There is a bright object above the moon in Sudbury, highly visible to the eye, nothing else as bright in the sky except for the moon. I'm looking around 6 and 7am.  What is it ?

It's probably the planet Venus. You can use an online planetarium (or one of the many mobile apps) to identify objects. This link shows the sky this morning at 6:45am at your location:


If one galaxy were to collide with another, what would it look like to an immortal inhabitant of one of their planets? I was reading this article posted on /r/space about photographing black holes, and they showed a picture of what's believed to be two black holes formed from two galaxies colliding.

I didn't realize the collision of galaxies could result in black holes, but it got me wondering. If you lived in one of those galaxies, what would happen to you? Would your planet be destroyed in the blink of an eye at some point? If so, when?

Would the sky gradually fill with more and more stars? If your galaxy became a black hole, how would you experience that? All at once or very gradually?

In the vast, vast majority of cases, not much happens. Galaxies are a whole lot of empty space.

If the Sun was a soccer ball in a field in California, the nearest star of similar size, Alpha Centauri, would be another soccer ball all the way across the continent, in Greenland. This is a scaled view, where everything is proportional. Think of all that empty space in between.

So the galaxies would merge, or keep swirling around each other, but for the most part stars and their systems would just continue as they were. It is extremely unlikely that any given star would collide. That's true for most of the volume of the galaxies.

In the center, however, things are a little different. Most galaxies already have very massive black holes at the center. These may collide and merge, or orbit each other a very long time, or continue separately.

The formation of new black holes as a result of galactic collisions must be a very rare event. Even then, the entire galaxy would not "become a black hole"; rather, a small fraction of it would be added to an existing black hole or, in very rare cases, produce a new black hole.

For most observers in such galaxies, there would not be dramatic changes, even over very long time intervals. This is because, again, galaxies are mostly empty space, and because the stars you see with the naked eye are very close to you, within a few dozen to a few hundred light years, which is a small portion of the whole galaxy.

EDIT: As shown in the comments, it's more accurate to think of Alpha Centauri as not a single soccer ball, but instead a larger soccer ball and a volleyball separated by a few hundred meters - it's a double star. Then Proxima Centauri would be a pingpong ball hovering 100 km away from Alpha.


First visibility of the moon I am new here, and hope to state the question well.

In Islam, it's known that the Lunar Month starts if the Moon is sighted after the sunset of the 29th day of that month.

If someone claimed that he sighted the moon before the conjunction or if the moon sets before the sun, then this claim is certainly false.

My question is, what is the least conditions on the possible visibility of the moon?

There are many criteria that confirm the impossibility of sighting the Moon, but many people still claim the sighting. Which one is wrong?

Here is 13 hours 48 minutes.
That's a mighty early sighying:
https://www.universetoday.com/107700/ultra-thin-young-crescent-moon-sighted-from-u-s-southwest/
11 hours 40 minutes was the world record as of 2014.


Snowball Earth brightness The Earth likely froze over almost completely about 700 million years ago. This increased its albedo significantly, and I wonder if that would have a considerable effect on its apparent magnitude from other planets. (The Sun was like 4% fainter, though.)

If so, would the Earth be naked-eye visible from farther away 700 mya than it is now? Maybe from Uranus's moons?

Earth is already pretty bright due to cloud cover, with a typical albedo of .3-.35 -- that is, it reflects about a third of the visible light that hits it.

That means it couldn't get more than about three times as bright even if it were perfectly reflective (albedo 1.0), which means about 1.2 magnitudes brighter.

Spotting Earth from a great distance with the naked eye is less an issue of brightness, more an issue of separation from the Sun. I can't run numbers at the moment to get actual magnitudes or angular separations.


Where are the two recently confirmed unusual brown dwarfs? The News report of two confirmed unusual T-type brown dwarfs but they don't tell where in space or on the night sky they were found or how far they are from the Earth/Sun. The brown dwarfs are WISE 0414 and WISE 1810. Does anyone know where they are located?

The relevant research paper is Schneider et al. (2020) "WISEA J041451.67-585456.7 and WISEA J181006.18-101000.5: The First Extreme T-type Subdwarfs?".
This gives the full designations, of which WISE 0414 and WISE 1810 are abbreviated forms. The designations contain the J2000 coordinates (J041451.67-585456.7 refers to right ascension 04h14m51.67s, declination -58°54′56.7″). It turns out that WISE 0414 is in Reticulum and WISE 1810 is in Serpens (Cauda).
The distances are highly uncertain, from the paper:

If we proceed with absolute magnitude–spectral type relations for field brown
dwarfs (Dupuy, & Liu 2012) and designate the spectral
type of WISEA 1810−1010 to be T0, wildly discrepant
distances are found for different passbands. We find a
distance of ∼14 pc using WISEA 1810−1010’s W2 magnitude, but a distance of ∼67 pc using the K−band
magnitude. Combined with our measured proper motion (Table 1), these distance estimates lead to a $V_\mathrm{tan}$
range of 77–360 km s−1. For WISEA 0414−5854, a similarly large distance range is found (52–94 pc), corresponding to a $V_\mathrm{tan}$ range of 170–307 km s−1. Parallax
measurements for these objects will be necessary to determine accurate $V_\mathrm{tan}$ values. Nevertheless, it is clear
that both sources are high velocity objects consistent
with membership in the metal-poor Galactic thick disk
or halo.

(emphasis mine)


Using SkyChoord to read in multiple coordinates. so I recently wrote a basic code to analyze the distance between two points which are stored in two separate excel files. Now that I have that code working its time to apply the legitimate use and use this code to analyze not just 2 dimensions (x,y) but three (ra,dec,z). In the data sheets now I have stored the coordinates of two separate galaxies.  Heres the amended code below:

import math
import pandas
file1 = pandas.read_excel('Book1.xlsx')
file2 = pandas.read_excel('Book2.xlsx')
file1['RA_diff'] = file2['RA'] - file1['RA']
file1['DEC_diff'] = file2['DEC'] - file1['DEC']
file1['Z_diff'] = file2['Z'] - file1['Z']
dist = file1.apply(lambda row: math.hypot(row['RA_diff'], row['DEC_diff', row['Z_diff']]),   axis=1)
if dist.values >= .5:
    print 'no match'
elif dist.values <= .5:
    print True, dist

This code works great with just the RA and DEC but not no much with the Z added in.

My hope is that somebody please give me some pointers on how to shorten this whole process by using the method:

from astropy.coordinates import SkyCoord

Basically: How do I use this tool to my advantage in reading in (from two separate excel documents) two separate coordinates of (ra, dec, z) to determine if the objects have any proximity to one another?

My research has turned up rather fruitless to analyze the points in this way specifically as I mostly simply don't understand the help pages. This is my first ever coding project so please be gentle in your advice, recommendations, help, feedback or ANYTHING else you might be able to offer. Thanks in advance.

From the documentation

>>> c1 = SkyCoord(ra=10*u.degree, dec=9*u.degree, distance=10*u.pc, frame='icrs')
>>> c2 = SkyCoord(ra=11*u.degree, dec=10*u.degree, distance=11.5*u.pc, frame='icrs')
>>> c1.separation_3d(c2)
<Distance 1.5228602415117989 pc>

The rest of the code is just reading the excel files and printing the results. What you have now is incorrect, even without the "z" coordinate. You can't calculate the separation of two points in spherical coordinates by Pythagoras' theorem: eg (30*, 0*) and (30*, 359*) should be very close. You need to convert to cartesian coordinates first, which is what the astropy module does.