Why does the moon appear on cloudy night sky? Now, I was looking the sky when I saw the Moon showing up in a sky completely cloudy, like this:

But a little different. The clouds were doing an eye shape. What does explain that phenomenon? Looks as if moonbeams drilled through the clouds!

Clouds are obviously not completely opaque, and what you are seeing is a break in the clouds. It is of course possible for the clouds to cover the moon, however, often the moon can shine brightly through the clouds and illuminate the clouds in some nice way.

This video might help in a visual way: https://www.youtube.com/watch?v=aLd_yhIWE48


How well can we in principle determine $T_{\textrm{eff}}$ of a star? This is a question about the basics of astronomy, which I have never happened to see a good discussion for. It is about how well would we be able to measure effective temperature of a star, if we had any arbitrarily perfect measurement devices.

Here is some context. Canonical definition of $T_{\textrm{eff}}$ of a star is based on its bolometric luminosity $L$ (total electromagnetic energy radiated by the star per unit time) and its photospheric radius R (radius, at which the optical depth at a given wavelength is equal to unity). This way, the definition specifies  $T_{\textrm{eff}}$ through $L=4\pi \sigma R^2 T_{\textrm{eff}}^4$, where $\sigma$ is Stefan-Boltzmann constant.

The definition clearly alludes to black-body law. Many stars, including our own Sun, have a spectrum that does not follow it. For this reason, one often talks about another effective temperature, which is the temperature of stellar material at photospheric radius, and which can be determined by examining stellar spectrum. There are a few more complications to that, but let's put them aside.

Determining  $T_{\textrm{eff}}$ is extremely important in characterising stars, therefore there exists a variety of methods of measuring it, and naturally researchers strive for obtaining the best possible precision.

Hence, the question: How well can one in principle measure $T_{\textrm{eff}}$, if one could have arbitrarily perfect instruments?

Edit: I would like to see a quantitative estimate in your answer. Is the best possible precision for $T_{\textrm{eff}}$ of order $10\textrm{K}$, or is it $1\textrm{K}$, or some $10^{-4}\textrm{K}$, or can we measure it arbitrarily well?

Here are just a few sources of uncertainty/arbitrariness: convection in stars, dependence of photospheric radius on wavelength, limb darkening, stellar variability, to name a few.

I would encourage the answers to be in the format "Source of uncertainty" - "Simple derivation" - "Estimate of the effect". If there are more than a few estimates, I will add a summary of them in the question or in a separate reply. Please, also feel free to edit the question if you might like to.

The question is compromised by saying that you allow arbitrarily perfect measurements.

If we have a bolometer that can measure the amount of flux from a star, at a distance that is known to arbitrary accuracy, with arbitrarily good spatial resolution, then what we do is measure the bolometric luminosity from a 1 m$^2$ area at the centre of the stellar disk. This flux is $\sigma T_{eff}^4$.

Now of course, stars do not have homogeneous atmospheres (spots, granulation, meridional flows, non-sphericity due to rotation...), so the result you would get would depend on exactly what 1 m$^2$ bit of atmosphere you were looking at. So, with my arbitrarily accurate instruments I would have to measure the luminosity from every 1 m$^2$ patch over the entire surface of the star. Each one would give me another estimate of $T_{eff}^4$; each would be somewhat different. That would be difficult, but the form of your question allows me to ignore those problems.

At this level of precision, the utility of a single $T_{eff}$ for the whole star is questionable, but if you wanted one then it would be the flux-weighted mean of all the above measurements, and as far as I can see one can instantaneously determine it to whatever accuracy you desire. Of course it will then vary if you have a variable star, and it will vary from point to point with time due to granulation; so the accuracy of the $T_{eff}$ could depend on how quickly and by how much it varies compared with how long it takes you to do your arbitrarily accurate measurements.

I think to get a better answer, you do need to specify some realistic observational constraints - such as (a) you cannot resolve the star at all, or (b) that you can resolve it, but observations can only take place from an earth-bound observatory (thus not allowing you to take flux measurements from the whole surface at once).

One thing occurs, is that in unresolved observations, even with an absolutely accurately measured luminosity (assuming isotropic radiation) there is still the issue of what radius to use. The radius at which the radiation escapes the star (at optical depth $\sim 2/3$) is ill-defined and wavelength dependent. An error bar of maybe tens of km is appropriate here, since atmospheres are 100-200 km "thick". For a solar-type star this would limit $T_{eff}$ accuracy to $\sim 0.1 K$ !


Sun's spectrum red shift Does Sun's spectrum expose any red shift at all? Namely, the center of it's visible area (not due to limb effect). If it does, how much is it and does it comply with relativity theory or is it higher/lower than theoretically predicted?

I red about it an article dated 1960 (http://adsabs.harvard.edu/full/1960MNRAS.121..421H) and not sure if new studies show different results. Thanks.

Light from the solar photosphere is observed to have a gravitational redshift. The expected value, based on General Relativity is equivalent to a doppler redshift of 633 m/s. It is difficult to measure the exact value because it is obscured and blurred by the turbulent motions in the Sun's atmosphere.

As far as I am aware, the estimated values are entirely consistent with General Relativistic predictions, though the precision is not high enough to make this an especially sensitive test (e.g. $698\pm 113$ m/s Takeda & Ueno 2012).


Has someone looked the other way? I learned that gravity always pulls, it is always attractive. There is no antigravity, no "negative"  mass. I also learned that most matter is dark, invisible. We know that because we see visible matter moving towards invisible bundles of dark matter and other effects like accelaration or gravity lenses.

What I ask myself is: Couldn't there be "negative" bundles of mass just the other way that pushes matter away instead of invisible dark matter that pulls it? Has someone tried to find something like that?
What is the proof for the fact "Gravity is always attractive" beside that fact that it seems to be?

Granted, it may be a stupid question, but I lack a bit in physics education that is not very related to chemistry.

What I ask myself is: Couldn't there be "negative" bundles of mass just the other way that pushes matter away instead of invisible dark matter that pulls it?

The galaxy rotation curve indicates a (positively massed) dark matter distribution that is close to spherically symmetric; cf. dark matter halo. I take it that you are asking whether instead of modeling it as a positive-mass distribution around the galaxy, we can model it instead as a negative-mass distribution surrounding the galaxy pushing the stars inward.

No, that's not possible. Since the effect is spherically symmetric, the hypothetical negative-mass distribution would need to be spherically symmetric as well. However, Newton's shell theorem guarantees that everywhere inside a void surrounded by such a distribution with this symmetry, whatever the sign of the mass is, the gravitational force vanishes. So a negatively-massed dark matter distribution outside the galaxy would do nothing at all.

In general relativity, the analogous statement is guaranteed by Birkhoff's theorem, and although GTR is nonlinear (and there are stars in the way), in our galaxy gravity is weak enough to be handled by the linearized theory.

  What is the proof for the fact "Gravity is always attractive" beside that fact that it seems to be?

In general relativity, gravity doesn't have to be attractive. For example, inside a perfect fluid with density energy $\rho$ and pressure $p$, $\rho+3p<0$ would imply that gravity is locally repulsive in the sense that a ball of test particles initially at rest expands rather than contracts under gravitational freefall. More generally, the strong energy condition characterizes whether or not gravity is attractive in this sense.

However, there is no known material that violates the strong energy condition, besides possibly dark energy, which is a cosmological constant in the standard ΛCDM model, as Gerald says.

  Has someone tried to find something like that?

There are many studies and simulations that consider dark matter with a nonzero pressure component, sometimes even anisotropic pressure components. For example, "hot" dark matter would have $p\sim\rho/3$, while "cold" dark matter would have $p\sim 0$, "warm" dark matter somewhere inbetween. The CDM in the ΛCDM model stands for "cold dark matter", naturally.

There are more exotic possibilities with anisotropic pressure components, etc. But I don't know of any paper that looked specifically for $\rho<0$ dark matter, and for the above reasons I'd be surprised if one existed.


How do I build a stargazing aficionado's Sun funnel to observe our nearest star safely? How do I observe the Sun safely, with tools I could build myself and without breaking the bank? If I wanted to build a Sun funnel on my own and use it on my enthusiast grade telescope, how would I do that?

What supplies and tools would I need, how do I attach it to my telescope so it can be applied to it at will, and are there any other, simpler yet safe ways to observe the Sun and its activity with my telescope? This is approximately what I had in mind:

How do I build something like that? I'm primarily interested in observing sunspots, but would also like to know, if there is any way for me to safely observe Sun's coronal activity to any appreciable detail with an enthusiast grade newtonian/dobsonian telescope?

Additionally, could I project the telescope's image directly on some screen behind it, without having to use any intermediary digital equipment, like a recording camera and a digital light projector?

As for projecting the Sun onto a screen at a low cost, I would recommend starting with a ~50-200$ sunspotter box, which is basically a lens mounted on a wooden box, that projects the sun onto a white piece of card. The advantage of using a telescope is that it can be programmed to track the Sun, so that if you want to trace sunspots, for instance, you can do so at leisure, instead of having to race to finish before the Sun moves off of the page.

As for observing coronal features- this is a very difficult task. A H-alpha filter (expensive) can be purchased for a home telescope outfitted for solar observing. This would allow you to see filaments/prominences, which is low T (10^4 K) chromospheric material that extends into the corona, suspended by magnetic field and buoyancy forces.

To observe coronal material from Earth, you would need a coronagraph, which blocks out light from the central disk of the Sun. This is because coronal features are extremely dim, as compared with the photosphere. From Earth, coronal features are best observed with during a total eclipse. Using a telescope mounted coronagraph at home is not ideal (and probably not feasible) because a lot of light from the Sun would leak into your field-of-view, due to both diffraction, as well as sky brightness. The University of Hawaii takes these sorts of observations, but even with all of their expensive equipment, the space-based LASCO instrument is able to do far better.


Are there home-brew photometers for amateur observing of variable stars and are they widely used? Comments on Why do these photometric observations of Betelgeuse look “quantized” in 0.1 magnitude steps? suggest that these are visual estimates, mostly (but not all) to 0.1 magnitude resolution.

Are there any designs for simple photodiode-based amateur photometers for stellar brightness measurements?

Just as an illustration of the kind of thing I'm asking about, I'm imagining a pair of binoculars with a 1 mm photodiode suspended by its wires the focal plane of one eyepiece, and a Raspberry Pi recording the photocurrent (with a small amplifier) and audio simultaneously ("I'm now measuring xxx... mark!") The data would be jumpy but presumably would reach a plateau whenever the star fell on the active area of the diode.

Or is this too impractical and not backwards-compatible with existing data?

It should be doable with a standard photographic setup, a star catalog with distances and measurements for a some standard stars and a bit of software.

With the usual "ritual" for obtaining images from the sky with a given setup, chip and temperature (obtain dark frames, flat field frames and ground noise frames for division and subtraction) one can calibrate the brightness of an area (subframe around a star) in a photography by comparing it to known stars. The capture software or one of the many post processing packages for amateur astronomy can calculate the brightness of a region, if it is not totally saturated, i would guess if it is well away from any saturation.

A more detailed description: http://www.bellatrixobservatory.org/cvaaI/17/

Edit: An add-on script for one of the amateur software packages for doing photometry: https://pixinsight.com/doc/scripts/AperturePhotometry/AperturePhotometry.html.


How would a retrograde satellite experiencing tidal deceleration affect the rotation of the primary? There are two common scenarios like this one, where an orbiting body orbits its primary slower than the primary rotates, resulting in the orbiting body moving away and the primary experiencing a slowdown in rotation. Whereas in the opposite, an orbiting body that orbits faster than the primary's rotation spirals in while the primary's rotation spins faster.
I know that a retrograde satellite will experience tidal deceleration and spiral in toward its primary body, but how will it affect the rotation of the primary?

For a retrograde satellite, you are right that the satellite will migrate inwards towards the planet. Contrary to a prograde orbit, the rotation of the primary will slow down.
Think about it in terms of angular momentum. Let the primary have a positive angular momentum and the satellite a negative one (since they rotate/orbit in opposite directions). Since the satellite is being pulled inwards, its angular momentum is being lowered in magnitude (becoming less negative). In that case the primary's spin angular momentum needs to become less positive to conserve the total angular momentum. This means the primary's rotation will slow down.
An example with numbers (unitless):
Primary(initial) = 10 // Satellite(initial) = -5 ///
Primary(final) = 7 //   Satellite(final) = -2 ///
Thus a transfer of 3 angular momentum units has occurred.
Eventually the satellite will slow down the primary until the primary is no longer rotating (assuming the satellite is not lost by this point). Then it will cause the primary to start rotating in the same direction as the satellite is orbiting.
Hope this helps!
EDIT:
In this paper, see equation (7), the torque on the primary due to the satellite. If we only care about the sign, we can note that $N_m \textit{~}\, (n_m -\Omega_p)$ where $n_m$ is the orbital frequency of the satellite and $\Omega_p$ is the rotational frequency of the primary. Let's take our previous example of the $\Omega_p$ positive and $n_m$ negative. This would make the torque $N_m$ negative, no matter what the magnitudes of the frequencies are. Consequently, the positive $\Omega_p$ would be reduced, signifying the slowing of the primary's rotation.

$$N_m = 3 k_2 \tau (n_m - \Omega_p) \frac{GM_m^2 R_p^2}{a_m^6} \tag{7}$$

where the subscripts $m$ and $p$ refer to the moon and planet respectively, $k2$ is the Love number of the planet that depends on its rigidity and $\tau$ is the tidal time lag of the planet.


What increases or decreases the mass and density of a fixed radius star? Assuming a relatively even proportion of mass and radius, a 0.25 solar masses and radii star would have a density of 22.5003 g/cm³, or about 16 times our Sun's density.
Keeping the radius of 0.25 solar radii, what influences would cause different 0.25 solar radii stars in the main sequence to have higher or lower masses/densities than the "normal" 0.25 solar masses?

Stars are broadly divided into 3 types. These 3 types are divided on the basis of their composition of gases and elements other than H and He. So even if these stars are of same radius, their composition is different.
I am not sure but I think that as different stars have different composition and their rate of fusion is different, their density is different and so is their mass. Also while some stars are just forming and are at that radius, their gas composition is different than what a dying star of that radius is and so their masses is different.
I don't know if my version of the answer is right, but I hope this helped.


Is the Dwarf Planet class really necessary? Another way of asking this is, what is the difference between dwarf planets and asteroids? Aren't they the same things? It's just that some asteroids are spherical and others aren't...or is there something else?

I can understand why Pluto was demoted. Same thing happened to Ceres (after 50 years of being called a planet?) when we found out it was in an asteroid belt. It would be more helpful to laymen, I think, if the Kuiper Belt was renamed to the Second Asteroid Belt or maybe the Icy Asteroid Belt.

But why not stick to the original classes where we only had planet and asteroid? (and moon i guess.) Why add a new class called dwarf planets? Was it just to temper the protests?

EDIT: I forgot to add, we never needed a dwarf planet class before, despite knowing that Ceres was spherical for a long time. So where has this need, if it really exists, come from?

A lot of the naming conventions were originally "because they remind us of things we already called this", or simply "tradition".  How we name things has slowly but surely adjusted with time as more objects were found, and a more robust classification system was needed.

Imagine it like having bins to sort your toys into.  If you have a small number of balls, perhaps you'd stick them all into a single bin called "balls".  But as you get more and more balls, you find they no longer fit into that bin.  Looking at them, you notice they are all either quite small, or quite large.  So you make two bins: small balls and large balls.  Or maybe you notice they are all either very soft (stuffed or Nerf versions, perhaps), or very hard (baseballs, for example).  So you could have a "soft balls" and "hard balls" bins.  Keep collecting ever more balls, and you may need three, four, etc. boxes to fit them all in.  And each time you will naturally try to order them so that each box contains balls that are similar to each other: these are all soft and green, these are all hard and white, these are all big and bouncy, etc.  This applies equally well to all sorts of collections: baseball cards may start all together, but then get sorted into teams and years or even individual players as a collection gets very large, and so on.

This is basically what's happened as we've classified and reclassified objects we've found in our solar system.  We started with a small number of objects, but as we found more and more of them it became too unwieldy to stick them all together, so we started to separate them more and more.

Ceres was labeled a planet because it seemed like a tiny version of, but otherwise very similar object to, existing planets.  Then we eventually discovered there are a lot of things in the same general orbital region as Ceres, and if those were to also be planets then we'd soon have a gigantic list of planets.  Since all these objects seemed pretty similar, and came from the same general region, they were given their own class of objects: asteroids.

Pluto was labeled a planet due in part to some initial errors in the data that suggested it was larger than it actually is.  Despite a growing number of oddities about it that made it look increasingly un-planet-like, tradition left it as a "planet"; it wasn't particularly problematic for this one little odd-ball to be lumped with the others.  Finding a host of new, similar, and sometimes—in the case of Eris, at least—bigger objects forced a reconsideration.

Incidentally, there are also comets, which are not the same as asteroids.  Asteroids are rocky objects in the inner regions of the solar system.  Comets are icy objects from the outskirts of the solar system: the Kuiper belt and Oort cloud, in particular.  They are vaguely similar to each other: generally very small, lumpy, potato-like objects, but we noticed that asteroids were mostly rocks and metals between Jupiter and Mars, and comets were mostly ices beyond Neptune.  So we separated them into their own groups.

Pluto is more comet than asteroid, and likely originated from either the Kuiper belt or Oort cloud.  In this case, it likely got knocked into a closer orbit via gravitational interactions with the gas giants, or possibly a star that got close enough to the Oort cloud.


Is Planet Nine shepherding the Kuiper Belt? Is it possible Planet Nine is shepherding the Kuiper Belt similar to the way Jupiter shepherds the asteroid belt?

I understand that very little is actually known about Planet Nine at this point, but has it been postulated that it has control over the Kuiper Belt? I don't exactly intend to read any theoretical papers on the existence of Planet Nine because I am sure it will be way over my head, but I understand that it is from the position of several Trans-Neptunian objects that its existence has any merit at all.  So, I am wondering if part of that theory includes the Kuiper belt as a whole?

Estimates of Planet 9's orbit currently suggest that it doesn't have any major effect on the Kuiper Belt, because its orbit is too far away and on a different plane than the Kuiper belt, and from the inner Oort cloud, at 200 and 1200 aphelion and perihelion, However it does have an effect on Trans-Neptunian objects that transit through the Kuiper belt. It doesn't get closer than 4 times the distance of Pluto and it transits at a different plane to the Kuiper belt.
Shepherding is the act of actually creating and directing the asteroid belt by providing many objects with a semi stable orbit with too violent collisions to make a planet (biggest is Ceres at ${\rm 500 km}$ diameter), and having a massive effect on the unstable collection of asteroids, like making large stable groups around Jupiter's Lagrangian points at 60 degrees to Jupiter, and making fast resonant orbits that are not round like stable asteroids but periodically go close to Jupiter and then go straight through the inner asteroid belt and back to towards Jupiter actually in a triangle.

Neptune's orbit averages 30AU, and the Kuiper belt is generally held to be between Neptune and Pluto's orbits, Pluto orbits at 31-48AU.
In that sense, Pluto and Neptune are the two objects which have the biggest effect on the Kuiper belt.
The Trans-Neptunian objects all traverse the Kuiper belt, with their Perihelions ranging from 17 to 50 AU, and if Trans-Neptunian objects swing out towards Planet 9, it's a less stable orbit for them, than if they swing out away from planet 9, so all the large Kuiper belt objects swing away from the alledged direction of planet 9, where they can have a stable course without a transiting planet to interfere with them. Trans Neptunians tend to not align themselves with Planet 9's orbit and tend to find a balance away from Planet 9 and away from Jupiter and the majority of them don't get closer than Neptune, about 7/8ths of them are further than Neptune. https://en.wikipedia.org/wiki/List_of_trans-Neptunian_objects
The Trans-Neptunian objects are often referred to as Kuiper belt objects, and they didn't start their course to 100ds of AU's distance because of Planet 9, but now they are affected by planet 9 because they are in its vicinity over millions of years. In a million years, they have about 500 chances to approach planet 9, and 500,000 chances in a billion years.
The shepherding effect is complex, Jupiter accelerates objects very fast in stable orbits that resonate with it, it prevents planets from forming from the asteroid belt, and it disrupts the otherwise stable asteroid belt, sending objects fast through the asteroid belt and wherever, towards and away from the Sun. Jupiter created and maintains the asteroid belt which is unstable space debris, and it protects Earth from comets that want orbits that through its path.
Planet 9's inclination is about 30 degrees, so it can't interact with the inner Oort cloud, and the outer Oort cloud is too far away.


What is a hard spectral state vs. a soft spectral state? In X-ray astronomy, the source is considered to be in the hard or soft spectral state. So what is the meaning of the hard spectral state? What are the soft state and hard state in spectroscopy?

Active galaxies are known to change state as seen by a change in slope of their X-ray and gamma-ray spectra.  We say that a spectrum has become harder (or changed to its hard state) when the slope changes so that there are relatively more high energy photons, and it becomes softer when the ratio of low energy photons to high energy photons increases.  The physics of why they change state is not yet understood.
If the high energy spectrum is in a thermally dominated state, ie a Planck-like spectrum, then it is certainly soft.  If it is in a steep powerlaw dominated state with low  $\alpha < 1, I_\nu = f^{-\alpha}$, then it is still usually considered soft. But if $\alpha$ is higher, then it is hard.   But, it is also a relative term, so a system cycling between any two different values of $\alpha$ will be going between its hard state and its low state.


Open data for satellites positions Is there a site / service where I can get the data for the positions of satellites (I mean artificial satellite, ISS, etc.)?

I know that some sites provide a visualization of these positions, but I'm only interested in the data.

Thanks.

Edit, for clarifications: What I want is only the data. My final goal is to create my own site that displays the position of the satellite (I do that just for fun). That's why I just need the data, and not a service that displays the position on a map.

There are many such online services, most of them free and a Google search away, so I won't make this a list answer, and since you didn't specify what data in particular you're hoping to find, here's one of my favorite satellite trackers with fairly complete position data, ground track display, map options and so on: NASA iSAT (Interactive Satellite Viewer). You might want to allow it to use your location for more convenient display, but it isn't necessary to enable that.

That's for a desktop computer, but if you're hoping to spot satellites (a.k.a. tracking) on the go, then I'd personally suggest installing Sky Map + on your smartphone / tablet (it is free, but there are of course others), because it includes a lot more useful information and has both compass / gyroscope / GPS positioning for easier identification of spotted satellites (it pans automatically) as well as manual panning mode. You can tap on screen to display the toolbar and select objects that you want displayed, or switch to ruby & black monochromatic night mode, if default display is too bright. Satellite information can be updated in settings via an additional download, and all of it is free.

For downloadable data alone (to perhaps include in your own software or import into your database), one of such sites is CelesTrak that includes TLE (Two-Line Element) sets and a Space Track TLE Retriever 3 tool to download Space Track data sets.


Dark matter inertial mass We know the existence of dark matter because we can test its gravitational mass (e.g. in gravitational lens) but, since we cannot see this matter, how we can be sure that it has an inertial mass, and it is the same as the gravitational mass? In other words, does the principle of equivalence apply also to dark matter?

If the inertial mass is not equal to the gravitational mass, it would be equivalent to the gravitational constant, G, being different, or perhaps non-constant, for dark matter. If that were so, the manner in which dark matter would orbit the milky way would be different, leading to a different distribution of dark matter

We know from the rotation curve of the milky way roughly how dark matter is distributed in the milky way. Our models are consistent with the inertial mass of dark matter being equal to the gravitational mass.

This is, of course, far from "proof". As we don't even know what dark matter is, it is impossible to be certain of any of its properties. And the equivalence of inertial and graviational mass is not "proved" even for normal matter (but no experiment has ever detected a difference) But it would be exceedingly surprising if gravity affected dark matter differently, and there would need to be strong evidence for that. As it stands, there is none.


Can lunar occultation of Venus occur during solar eclipse? Moon can occult Venus. Venus can transit across the solar disc. Moon can elipse Sun. Can all three celestial events occur at the same time - Moon is at front of Sun (partial eclipse is fine) and Venus is behind Moon (ideally part of the planets is seen at lunar limb)? Observer is at Earth.

Yes, but such an event would be very rare. Venusian transits last only about 7 hours, and there are only two in 113 years, So Venus is in transit for about 0.0015% of the time.

So as a back-of-the-envelope calculation, you would need to see about 70000 eclipses before you had a combined transit/eclipse.  There are about 2 solar eclipses a year, so you might hope to get this unusual syzygy once every 35000 years or so.

None are forecast.


What exactly is a fortney grid transmission spectra modeling I am trying to model some exoplanets and I don't understand how this model works. Below is a link of the model. What I don’t understand is how does graphing the transit depth  vs wavelength provide information. I am trying to determine the atmospheric chemistry/atmosphere/properties of planets.
https://exoctk.stsci.edu/fortney

Planets with atmospheres are not discs with hard edges, when viewed in transit across the star. The atmosphere allows light to pass through the limb of the planetary disc.
The radius within which the planet is effectively opaque to light from the star will depend on the density and composition of the atmosphere as a function of height and also the wavelength of light that it is illuminated by. This is because the opacity of the atmosphere will be much greater at wavelengths where some molecule or atom that is present has an absorption feature.
Therefore if you observe a transit at different wavelengths, you will see different transit depths, because the planet has a different effective area at different wavelengths.
For example, if the atmosphere contains lots of atomic sodium, then because sodium strongly absorbs light at 589nm, the planet is opaque to a greater radius at 589nm, and the transit depth will be bigger at 589nm than at wavelengths either side of this.
Ps. (Jonathan) Fortney is the name of the scientist who developed the grid of models.


Impact of inclined orbit satellite on a planet If a satellite in an inclined orbit breaks up in orbit and multiple fragments hit a planet, do the individual fragments follow
1 a sinusoidal path
2 a geodesic ( or great circle curve)
3 a straight line
I'm having real problems trying to visualise this!
I realise the ground track of an inclined orbit follows a sinusoidal path but what happens when impacting a rotating planet?

Yes, yes and yes.

Your main misconception is that satellites follow a sinusoidal path. That is just a distortion of the map.

The path of the satellite is in a single plane. When that plane meets the Earth produces a great circle (which is effectively straight, there are no straight lines on the curved surface of the Earth, great circles are the closest that you get to straight)

When you project that great circle onto a map you may get a sinusoidal path, it depends on the projection. Your statement "The ground track of a satellite follows a sinusoidal path" is not correct, that is just an effect of the transformation from a globe to a plane, not "real".

The path of the fragments is, compared to the size of the Earth is very short, it is on the same great circle that the satellite was orbiting in (except as the fragments get closer to the ground they start to move with the atmosphere). If projected they would be on the same track as the satellite. But a great circle is the closest thing to straight on the surface of the Earth.  The rotation of the Earth is much slower than the orbital speed. By the time the fragments have slowed to terminal velocity then they fall roughly in a parabolic curve to Earth, the same as if you threw a ball off a building.


Why did astronomers believe most or all stellar black holes had masses no greater than 15 solar masses? The so-called 'mass gaps' for black holes, according to theoretical models, are between 2-5 solar masses and 50 to 150 solar masses.  (Actually, I have read that there is no good theoretical reason for the lower, 2 to 5 solar-mass gap....)
But, I have also read that astrophysicists were surprised to find black holes larger than 15 solar masses using the LIGO gravitational-wave Observatory....
For instance, from New Scientist:

Then there are stellar black holes. These are created in the gigantic explosions that end the life cycles of massive stars, and the closest to Earth is around 1,000 light years away. They tend to weigh in at between five to 15 solar masses, and they were the black holes that most astronomers had assumed LIGO would pick up. But the 2015 discovery only made sense if one of the colliding black holes was roughly 35 times the mass of the sun, while the other was around 30 times this mass.
Subsequent detections threw up more seemingly inexplicable black hole masses. The GW190814 signal involved one black hole that was too heavy, at around 23 solar masses, and one that was too light, at about 2.6 solar masses. Then there was GW190521, from a collision between black holes of 85 and 66 solar masses. “These observations are very hard to explain with astrophysical scenarios and they are quite easily explained with primordial black holes,” says Sébastien Clesse, a cosmologist at the University of Brussels in Belgium.

Read more: https://www.newscientist.com/article/mg24933280-100-is-there-an-ancient-black-hole-at-the-edge-of-the-solar-system/#ixzz6sOzdIpJW
But, WHY are they 'very hard to explain' in terms of conventional astrophysics?
I read elsewhere that, before LIGO, no stellar-black-holes had been detected above about 15.65 solar masses, but that reference did not say that none were expected above that mass....

The so-called 'mass gaps' for black holes, according to theoretical models, are between 2-5 solar masses and 50 to 150 solar masses. (Actually, I have read that there is no good theoretical reason for the lower, 2 to 5 solar-mass gap....)

The lower mass-gap is suspected observationally because we have yet to observe a neutron star with mass greater than about 2 M$_{\odot}$ (the error bars on such measurements vary greatly depending on the method of observation, and its controversial currently as to what neutron star is the most massive currently known), and because we've also not discovered a black hole in an X-ray binary whose mass is lower than about 6 M$_{\odot}$. However, a binary neutron-star merger can produce a binary black-hole (BBH) which is likely to be in this lower mass-gap. Thus, in reality, the gap will probably be populated by high mass neutron stars (if they rotate very fast and have inclination, etc...) and by low mass black holes that result from binary neutron star mergers.
The current nomenclature for the masses of observed black holes reflects the uncertainty inherent in the field. Right now, although the limits are arbitrary:
stellar mass means $\lesssim 100$ M$_\odot$, intermediate mass means $\sim 1000 - 10^5$ M$_\odot$, supermassive means $\gtrsim 10^6$ M$_\odot$. There is no upper limit on the mass of the black hole from general relativity, but astrophysical and cosmological considerations, though model dependent, can yield an upper limit of about $10^{11}$, but it could be larger. These have been called "stupendously big" and "ultramassive."
Theoretically, the bounds on this lower mass-gap are motivated from below by stellar evolution, e.g. neutron stars are expected to only form up to a certain mass (depending on the metallicity), and astrophysical processes such as accretion. Very importantly, the bounds depend on the equation of state of nuclear material, which is uncertain and one of the "holy grails" that gravitational-wave (GW) astronomers are after.
So people often just write a range of $2 - 5$ for simplicity when writing in pop sci articles. The upper mass-gap attributed to pair-instability supernova is generally thought to be around $50 - 150$ M$_{\odot}$ (this is the black hole mass), but these limits are uncertain because they depend on the uncertainties of stellar evolution models and supernova physics. Just like with the lower mass-gap, this gap could, in practice, be populated by black holes that form from hierarchical mergers in dense stellar clusters (dynamical channel), or from isolated binary-star evolution that can in principle produce high stellar-mass binaries like GW190521 that survive failed supernova, although it is uncertain because this depends on stellar winds and core mass calculations.
EDIT: As Rob explains below, the history of stellar wind mass-loss theories is an active field. The progenitors of stellar-mass black holes are high mass stars (i.e. $m_{\rm ZAMS} \gtrsim 30$ M$_{\odot}$). For example, Wolf-Rayet stars have been viewed as the end-point of stellar nuclear evolution of high-mass stars since the 1980s. WR stars have strong winds for their size, which are line-driven, similar to the O-type stars that they likely evolve from. The mass-loss rate from the stellar surface is typically modeled as a power law of the star's luminosity and metallicity, i.e. higher mass and higher metallicity both imply more mass loss. So an initially high-mass star will experience strong winds, even more so if it has high metallicity (as Rob points out, low-metallicity environments might be loci of black holes near/in our galaxy). However, as you might hear/read in pop-sci and scientific articles, this does not preclude the existence of high-mass black holes! The most massive stars that we have observed to date are WR stars, implying they might have evolved from even more massive stars, and in the extreme case, supermassive stars are thought to be the "seeds" of supermassive black holes.

But, I have also read that astrophysicists were surprised to find black holes larger than 15 solar masses using the LIGO gravitational-wave Observatory....

I suspect you've read this from pop science articles, which often do not properly characterize the sentiment of a scientific article, but it's a difficult thing to do. The reason that anybody would be "surprised" to find black holes with masses greater than 15 M$_{\odot}$, is that before the discovery of BBHs (from the direct detections of gravitational waves) we only had suggestive evidence for the existence of stellar-mass black holes from observations of X-ray binaries. See here and here for reviews of known stellar-mass black holes in X-ray binaries.

“These observations are very hard to explain with astrophysical scenarios and they are quite easily explained with primordial black holes,” says Sébastien Clesse, a cosmologist at the University of Brussels in Belgium."

Again, this just depends on who you are asking. Everyone wants to say that their work is the most relevant formation channel for what LIGO/Virgo are seeing, and this is okay because the number of known sources is still too small to make rigorous claims about formation of BBH sources from GW detections. Also, since the signal-to-noise that the current detectors can achieve is so low (e.g. rarely above ~20), it is very hard to constrain the possible formation of even a single event. So many events that are on the edge of the current theoretical uncertainties are called "difficult to explain." This quote that you provided is perfect demonstration of this, since there actually is no evidence that priomordial black holes even exist to begin with!!!
For the event that you specifically asked about, GW190814, it is difficult mainly because of the very low mass of the secondary. But, this could be explained by, for example, isolated evolution of a binary star with an initial very low mass ratio, where the less massive component could evolve into a neutron star or a black hole. There are people who study isolated binary evolution and they claim that all LIGO sources can be explained by their channel, but they tune their simulations to produce the LIGO results. There are people who study dynamical channel evolution and claim that there is strong evidence for this or that source to be from this channel. People have to write papers and fund their students, and they do a lot of the ground-work that will make more rigorous investigations plausible once we do have larger samples of known sources. In the coming decades, it is expected that the third generation of GW detectors will provide on the order of MILLIONS of detections and then population-level constraints on formation will be much more convincing, and these detectors will have very high signal-to-noise system and constraining formation of individual events will also be more convincing.

I read elsewhere that, before LIGO, no stellar-black-holes had been detected above about 15.65 solar masses, but that reference did not say that none were expected above that mass....

I hope I've clarified this by now! If you read papers leading up to 2015 from the GW community, for example this review, they were certainly expecting to see binary black holes with masses greater than 15 M$_\odot$.


Does 2 merging black holes necessarily make a quasar? 2 black holes are about to merge to become a larger black hole. Does this mean it'll become a quasar?

From what I know, quasars are supermassive black holes or a collective amount of them. So, if it merges and becomes a supermassive black hole, does this mean that it is a quasar? If the size is smaller than what would be considered as a supermassive black hole would it not be a quasar?

Does 2 merging black holes necessarily make a quasar?

Basically no.  While the merging of 2 black holes is a very interesting event, a quasar is what you get when 1 very large black hole eats a whole bunch of matter and the light from the quasar comes from the intense heat and interactions from that tightly bound, rapidly spiraling and very excited matter.

Quasar's were probably most common when galaxies are young but there are a few more recent ones (see examples in comments).  Quasar

Related Stack Exchange Question

  If the size is smaller than what would be considered as a supermassive
  black hole would it not be a quasar?

Almost all large galaxies have a super-massive black hole in their center.  Source.  The sizes vary with the size of the galaxy.   Quasars are much more rare, only in a few galaxies.

As for the specific size of black hole that can form a quasar, credit to Rob Jeffries below.


Universe Sandbox 2 accurate representation of gravity I've been playing Universe Sandbox for a while now and I have never been able to make a near Earth asteroid collide with it. By "make" I mean, simulating billions of years of known, near Earth objects until one of their orbits intersect. In this explanation Sir Cumference describes that Universe Sandbox 2 uses Newtonian physics to in its simulations. But wouldn't that calculate enough pull from Earth to slightly change the trajectory of the NEO to eventually impact?

We know, with almost 100% certainty that a LARGE NEO will impact Earth (probably sooner than later), otherwise why would we be investing so heavily on the Jet Propulsion Lab's Asteroid Watch program.

Can the game not accurately simulate gravitational pull on those large scales or is there something else (probably a lot) I'm missing? Are all known NEOs not projected to have a relevant collision intersection with Earth?

A NEO only impacts Earth if both bodies are in the orbit intersection zone at the same time, closely enough for gravity $(F \propto 1/r^2)$ to bring them in contact.
In a simulation, the timestep should also be short enough to detect a collision.
An object at a moderate relative speed of 10 km/s crosses Earth's diameter in about 20 minutes; a longer timestep could turn a hit into a miss.

If you're already modeling real asteroids, try some which have hit Earth:
2008 TC3,
2014 AA,
2018 LA.
The short observation arcs make their pre-impact orbits highly uncertain, so a few small bodies spread within $\pm\sigma$ of each orbital element value may improve your chances.
Alternatively you could set an object up for immediate collision with Earth at a relative speed of 12 to 20 km/s in any direction, and run the simulator backward to see how it would get there.

The asteroid risk is real, but we should not overstate it.
If you visit JPL CNEOS Sentry and use unconstrained settings, it shows only a few objects with more than 1 chance in 1000 to hit Earth in the next 100 years, and most of those are small.
Few NEO orbits are known precisely enough to make meaningful predictions beyond that.
The Palermo scale quantifies a given object's threat to Earth in the foreseeable future.


Mathematically calculate if a Planet is in Retrograde I am trying to find out if a planet is in an apparent retrograde motion with respect to the earth at any given point in time. Given the time in Julian days.

I already have the geocentric and heliocentric coordinates and velocities of the planet using the JPL ephemeris, but not sure of what mathematical formula to use to identify the retrograde motion.

I read this article "https://physics.stackexchange.com/questions/249493/mathematically-calculate-if-a-planet-is-in-retrograde" which had a similar question but I am not sure of:

Is the answer correct as it has not been marked as correct?
How to represent earth in the XY plane only when it has XYZ planes and why do we even need to do that? Can't we just use the heliocentric equatorial plane which I think is the same as the one used by NASA JPL ephemeris.

Here is a quick answer. Apparent retrograde motion of a planet as seen from Earth means that its ecliptic longitude is decreasing. (Thanks to @barrycarter for correcting my previous statement.) You have to calculate the apparent angular position of the planet from the Earth in ecliptic coordinates (as explained here and here) and find places where the ecliptic longitude is decreasing.

You can subtract the positions of Earth from the position of the planet in either coordinates. Then you express that vector in spherical coordinates. It doesn't matter if it's heliocentric or geocentric. What matters is the direction that the axes of the coordinate system is pointing, not where the center is.

If you want RA and dec, use ICRF coordinates, and these can be transformed to ecliptic coordinates as well. An easy way to do this is to use the python package Skyfield.

Here's a sample script and a plot. This is Mars from 2010.0 to 2020.0 and the thick red line represents retrograde motion.

import numpy as np
import matplotlib.pyplot as plt

from skyfield.api import load

planets = load('de421.bsp')

earth   = planets['earth']
mars    = planets['mars']

year_zero = 2010
days = np.linspace(1, 3650, 10000)
years = year_zero + days / 365.2564
ts = load.timescale()
t = ts.utc(year_zero, 1, days)

# thanks to @barrycarter's comment, do it the right way!
eclat, eclon, ecd = earth.at(t).observe(mars).ecliptic_latlon()

eclondgs      = (180./np.pi) * eclon.radians
eclondel      = eclondgs[1:] - eclondgs[:-1]

eclondel[eclondel < -300] += 360. # this is a fudge for now
eclondel[eclondel > +300] -= 360. # this is a fudge for now

prograde   = eclondel > 0.

eclon_prograde   = eclondgs.copy()[:-1]
eclon_retrograde = eclondgs.copy()[:-1]

eclon_prograde[-prograde]  = np.nan
eclon_retrograde[prograde] = np.nan

plt.figure()
plt.plot(years[:-1], eclon_prograde,   '-g', linewidth=1)
plt.plot(years[:-1], eclon_retrograde, '-r', linewidth=3)
plt.ylim(0, 360)
plt.title('Mars Ecliptic longitude (degrees) AD 2010.0 to 2020.0',
          fontsize=16)
plt.show()


Is there a relationship between stars' absolute magnitude, spectral class and relative location in a cluster? I am interested to know whether a pattern has been observed with regard to the characteristics of a star (in particular, its absolute magnitude and spectral class) and its location relative to others in the same cluster. For example, do older, cooler stars tend to occupy the centre or edges of a cluster with greater frequency than younger, hotter stars? And do stars of a certain class and magnitude tend to appear together?

I have found no specific mention of it, but the question surely relates with theories of the formation and evolution of galaxies.

Stars born together in clusters have more-or-less the same age. As a rule of thumb, any spread in age, measured in millions of years, is smaller than the extent of the cluster in parsecs.

For most stellar clusters, smaller than a few pc, the only chance of measuring age differences occurs in the first 10 million years of life. There is no evidence for age spreads in clusters beyond 30 million years old and therefore no chance of identifying any trend of age with position.

In young star forming regions, the picture is very complex. Estimating the ages of individual stars is difficult. Generally speaking, newborn stars are closely grouped together, whereas slightly older stars are a bit more dispersed. In gravitationally bound clusters, such differences tend to be eliminated in dynamical timescales of less than a few million years.

Mass segregation can occur in clusters. Some argue thus might be primordial, but it certainly can happen dynamically. The net effect is that more massive objects tend to be more centrally concentrated in a cluster.

There is evidence for multiple populations in some old globular clusters. The picture here is very complicated, still being researched, and not something that is easily summarised.


How to read Babylonians' tablet that were used to track Jupiter's movements? There is a science news article on how Babylonians used geometry to track Jupiter’s movements.

Here is an image of cuneiform tablet which shows Jupiter's movements.

From a layman's point of view, it looks like someone engraved gibberish on a tablet. How do we even know it was used to track Jupiter's movements.

Can anyone translate this? Thanks.

This news story is based on an article from Science The image is also taken from the same Science magazine article. The text here is a procedural text, it describes the process of using a trapezium to make distance-speed-time calculations, for approximation of the motion of Jupiter along the ecliptic.

You should look at the original article in science and the author's website


How can you determine the initial volume of a planet's atmosphere? Since the surface pressure of a planet is determined by the mass of the column of gasses above it one would surmise that to determine the pressure you must know the volume and mass of the atmosphere.

Knowing the composition and volume of the gasses in the atmosphere would allow you to calculate their mass but how do we determine what that volume is?

Assuming we are only concerned with initial conditions when the primary atmosphere (created through accretion) was formed would the volume be arbitrary?

I hope this isn't too broad of a question. I'm trying to pin down a possible initial state that would be created when a new planet is formed and the conditions stabilize.

In the Q on Earth Sciences SE What is the mass of our planet's atmosphere, hydrosphere, and cryosphere combined? this formula was derived: $$ M_{\mathrm{atm}_\bigoplus} \approx \frac{4\pi R^2_{\scriptscriptstyle \bigoplus} P_{\mathrm{sea\,level}}}{g_{_\bigoplus}} $$ which can be rearranged to derive pressure from the total mass of the atmosphere. $$  P_{\mathrm{sea\,level}} \approx \frac{g_{_\bigoplus}M_{\mathrm{atm}_\bigoplus}}{4\pi R^2_{\scriptscriptstyle \bigoplus}} $$


How to compute for Distance Modulus' uncertainty/ies? This is rather a short question. As we know of;
Distance Modulus (DM) $\mu = 5 \log d - 5$
If $d = 168_{-14.9}^{+27.5}$ pc ($3\sigma$ value), how can I possibly compute for $\mu$'s uncertainty?
P.S. Perhaps I need to multiply those $\pm$ values to a 'some constant'(?)
Thanks a lot and clear skies.

You can just use these upper and lower bounds to create an upper/lower bound for the distance modulus. The lower bound is $168-14.9 = 153.1$, and the upper bound is $168+27.5 = 195.5.$ You can calculate the distance moduli for these values to get upper and lower bounds:
$$5\log(153.1) - 5 = 5.924876 \\ 5\log(195.5) - 5 = 6.455734$$
Then we calculate the distance modulus of the base value: $$5\log(168) - 5 = 6.126546$$
To get the deviations, we just subtract the distance moduli from the original. Therefore, your distance modulus is equal to $6.126546_{- 0.20167}^{+0.329188} \text{ pc.}$ I hope this helps. If there are any issues with my answer, please notify me.


Closest stable orbit about the sun of an asteroid? What is the closest perihelion an asteroid in stable orbit could have? Is there a limit defined by orbital mechanics or could an object be in stable orbit, only too close that melting or sublimation would prevent the object from surviving?

There's no limit defined by orbital mechanics.  Newton's law of gravitation allows for any perihelion that isn't actually inside the sun.
The Parker Solar probe is in a stable orbit (discounting planned interactions with Venus) with a perhelion of 6.2 million km (at a temperature of 1400⁰C)  But there is no reason that an object couldn't go closer. There is an asteroid 2006HC4 with a perihelion of just 10.2 million km. Its aphelion is beyond the orbit of Mars
Gravitational effects are not the only consideration for stability. E.g. the Yarkovsky effect will tend to deplete the vulcanoid region (Vokrouhlický et al. 2000), YORP effect can spin up asteroids to breakup velocity, radiation pressure removes dust.
However getting into such an orbit is difficult.  If you are a main-belt asteroid, you would need a huge push to get you into a sungrazing orbit.  Comets from the Oort cloud don't need so much of change in velocity (as they are already moving slowly) and so most bodies that we see falling close to the sun are made largely of ice, and are disrupted by the sun's heat.


Why do objects burn when they enter earth's atmosphere? Why do all objects burn when they enter our atmosphere? is this because of our atmosphere composition? and does this happen on other planets as well?

You'll often hear that it's because of friction, but that's often not the main factor. For larger objects it's more likely the pressure they create.

In both cases the reason is the enormous speed, often tens of kilometers per second. When a larger object enters the atmosphere at these speed the air in front of it gets compressed so much that it becomes extremely hot. (Think of pumping up a tire; you're also compressing air and you can feel the valve becoming hot.) The compressed air will often disintegrate the object in the air, and then the debris may burn because of the heat. This is exactly what happened to the asteroid above Russia last year: it exploded with an enormous flash in the air, and left little traces on the ground.

This happens on other planets as well, if they have a sufficiently dense atmosphere. In 1994 the comet Shoemaker-Levy crashed into Jupiter. It disintegrated before entering Jupiter's atmosphere due to the strong gravitation, but when the fragments entered the atmosphere they could easily be seen lighting up as they burned up.

edit
Remember the Space Shuttle? It had heat resistant tiles on the bottom of the craft to protect it from burning when it entered the atmosphere, even though its speed is only a fraction of a meteorite's speed when that enters the atmosphere.
During the last launch of the Space Shuttle Columbia some material from the external fuel tank damaged this heat shield, and upon re-entry the heat and the highly pressurized air under the craft could enter it, causing the craft to disintegrate and kill all crew.


Semi-major axis vs. apogee and perigee of orbit This article on Wikipedia about Sedna states that its aphelion is 937 AU, its perihelion is 76 AU and its semi-major axis is 484 AU.
I would have expected the SMA to be half of the sum of the aphelion and perihelion. Is the article in error, or is there a difference that I'm not aware of?
I know apoapsis and periapsis are sometimes given relative the surface of the object being orbited, see this thread, but the effect should be negligible in this case and would anyway work in the opposite direction. Anything else I'm not seeing?

That's Wikipedia for you. The linked page demonstrates that Wikipedia is not a reliable source. Here are some of the problems:

The values for aphelion, perihelion, semi-major axis, and eccentricity are inconsistent with one other.
The values for perihelion, semi-major axis, and eccentricity are unsourced.
The values for perihelion, semi-major axis, and eccentricity have far too much precision. Sedna was discovered 17 years ago, corresponding to about 0.15% of Sedna's orbital period. That's far too short of an arc length to justify five or six places of accuracy.
The value for semi-major axis is inconsistent with other sources.
The value for aphelion is poorly conducted original research. Footnote 5 (the reference for the aphelion value) states that the source is from osculating orbital elements about the solar system barycenter as retrieved from JPL Horizons.
There are two key things wrong with this. One is the use of osculating elements, which can be deceiving. The other is using orbital elements about the solar system barycenter rather than about the Sun. This is just wrong.


Eagle Nebula (Pillar of Creation) destroyed? How do they know that the pillars have been destroyed if the light will reach us in 1000 years time?

  The "Pillars of Creation" from the Eagle Nebula. Evidence from the
  Spitzer Telescope suggests that the pillars may already have been
  destroyed by a supernova explosion, but the light showing us the
  destruction will not reach the Earth for another millennium.

Article explaining that we won't see the effects in another 1000 years

It's a bit hard to say for sure as the article isn't terribly clear, but what I think they're saying is that there is a dust cloud to the upper right side of the Pillars (as viewed in the photo.) They further say that the dust cloud shows evidence of a supernova shock wave passing through it, presumably from the upper right and presumably from a supernova.  (Note that the supernova was not observed, and they don't report on a remnant being visible.) Then they say that when that shockwave reaches the Pillars, the Pillars will be destroyed.  They estimate that that will be observed from Earth in the next thousand years or so.  (Note that they don't report measuring of the speed of the shockwave -- I'm guessing they assume it's moving as typical speeds.) Since the Pillars are about 7000 light years away, than means that this destruction "already" has happened.

There's nothing impossible about all this, but it looks like speculation based on limited actual facts.  It's also worth mentioning that what you see on the web went through a press office, and press offices are paid for doing publicity, not for doing science.  The quality of what a press office posts (already undermined by being a popularization, which is hard to do well even when you're trying to be accurate) is frequently biased by a publicity-at-any-cost attitude. Always read press releases and the like with your sceptometer turned up to High.

Personally, I'd like to see stronger evidence for the existence of the shockwave, and evidence that the shockwave will actually disrupt the Pillars. (The Pillars are considerably denser than the medium around them, and so may be resistant.)


How long does lunar opposition surge last? Are there measurements of the full Moon getting suddenly brighter? Wikipedia's opposition surge is a short article and forwards shadow hiding and coherent backscattering as proposed mechanisms, but it doesn't really explain how much the brightness of the Moon actually "surges" and how quickly it happens.
I was reminded of this by this interesting answer.
Question: Are there measurements and good quality plots of lunar opposition surge? How fast is it? How long does it last?

I don't think the coherent backscattering is the predominant mechanism for visible light; it's primarily seen in radar1. I'll be happy to be proven wrong, but the shadow-hiding seems to be pretty easy to embrace in photographs.
Images from https://space.stackexchange.com/q/20071/12102 and answers there. First is taken by the Yutu rover on the Moon (Chang'e 3 mission) second is a famous image (it's cropped, a reflection in a visor of the photographer, first lunar selfie!) and the third is from What causes Hyabusa-2's close-up images of Ryugu to be dark in the corners?
See also

Are there ANY verified satellite images of visible light coherent backscattering from Earth?
Now what do we think? Is this purple dot really caused by Cassegrain optics and coherent backscattering?
What's the story behind this Apollo-era image?
Lot 345 of Christie's “Voyage To Another World” auction supposedly has the only photo of Armstrong on the Moon, but isn't this one also? this was interesting...
1Clementine Bistatic Radar Experiment "coherent backscatter opposition effect"

The lunar opposition surge has been well studied, likely because we can study it in detail, we have surface samples, and so it serves as a baseline for other bodies in the solar system (as it does for many other kinds of surface studies).  It is quite substantial in visible light.
Probably Clementine data are the oldest-modern reference, and among others, Buratti et al. showed that from a baseline normalized reflectance of ~0.6 at a phase angle of 10°, it increased to 1.0 at a phase angle near 0° (hence, normalized reflectance).  Their Fig. 6 shows that this increase happens over just the last few degrees, which is typical of opposition surges.  Shkuratov et al. (1999) also published based on Clementine data and their Fig. 5 again shows a ~10s% increase over the last ~10° of phase angle.
What you really want is an expanded plot of just the last few degrees of phase angle, which they include in their Fig. 10 (I'm not reproducing the images here due to © concerns).  They show that the Buratti et al. (1996) results increase by ~20% in brightness when going from just a phase angle of 0.5° to 0°.  The paper compares this to numerous other materials.  That's all in UV to visible light.
Velikodsky et al. (2016) also looked at this from LROC-WAC data.  For the UV (415 nm) and red (689 nm) bands, they show (Fig. 6) that from a phase angle of 1° to 0°, the increase can be around 50%.  Going from 5° to 0° in a different part of their paper (Fig. 9), the increase can be a factor of ~35–45%.  This is again wavelength- and material-dependent.  I would say that that paper is probably going to be the best quality plots, or at least a paper that uses LROC-WAC data.
As the Shkuratov et al. (1999) paper notes: "Below about 10° the brightness of the Moon grows more sharply than at large phase angles. The lunar opposition effect is about 1.25 at 1°–10°."  So it could be considered that the "effect" starts <10°.
Those all seem to tell a reasonably consistent story that, within those last few degrees, the phase function increases the visible light returned by up to about 50%.


Would blocking sunlight on Venus help make it habitable? Lets say we had the technology to create a mini-Dyson structure, like a shutter style curtain between the Sun and Venus, blocking the sunlight in a controllable manner to cool down it's temperature.
Could it be the first step to reverse the greenhouse effect and make Venus more "terraformable"? Or at least more explorable like Mars? Would there be any unintended consequences?
Would this be useful on other hot extra-solar earth-like planets?

The fundamental problem is the heat capacity of the planet. If you keep it out of sunlight long enough it will eventually cool to the temperature of the background ratiation, bit it will take a long time. If we just treat it as a blackbody surrounded by a 0 K universe the cooling time will roughly be $t_{cool}\approx 2.5\cdot 10^{11}$ seconds if we want to reach 300 K. That is about 7900 years. Wait for about 29,000 years and you can start scooping up frozen carbon dioxide. And this assumes good heat conduction and that the interior is not hotter - I think there will be bad geological issues when trying to change the crust temperature.

Another issue is of course the total lack of sunlight. Martyn Fogg describes a neat solution in his book Terraforming: orbit a reflector in a polar orbit, angled at 45 degrees so it reflects sunlight to the planet. This would for the right orbit give a daily cycle despite Venus rotation issues and the shade shield.

Whether this is a sensible start for terraforming or just evidence that the technology does not help very much depends on your level of optimism and timescales. For exploration you may want a method that does not transform your exploration target as much.


Calculate angle of inclination for a certain angle in a planet's orbit? The background is that I'm trying to write a computer program to show at what angles each planet would be able to be seen transiting in front of the sun from an observer outside our solar system.  My endgame is to calculate the relative percentages of the sky that could see any group of planets transiting together.  For instance in the direction the Earth is from the sun in June and December, an alien observer that could see Earth transit could also see Venus transit, but from the angle where the Earth is in September or March they would not ever be able to see Venus transit.

I wrote a program using basic stats and circular orbits to test out the idea, but I would like to make it more robust using actual elliptical orbits and I'm having trouble.  For circular orbits with the sun at the center I was able to just take the inclination of Earth's orbit times the sin of the viewing longitude relative to the longitude of ascention.

double viewingLongitude = longitudeRadians - LongitudeOfAscent;
double planetAngle = Inclination * Math.Sin(viewingLongitude);

For instance Earth's orbit has an inclination of 1.57 degrees and longitude of ascent at 348.74 degrees.  At 348.74 degrees and 168.74 degrees Earth will have an actual inclination of 0 degrees.  At 78.74 degrees and 158.74 degrees Earth will have an actual inclination of 1.57 and -1.57 degrees from the plane.

Is there a similar easy way I could calculate that inclination for the elliptical orbit of the Earth or will I have to solve Kepler's equations?

In short, no, you don't have to solve Kepler's equation. If you define a viewing longitude and you know the full set of Keplerian orbital elements, you can calculate if a planet will show a transit.

Let me first clear up some of the jargon, though. The term inclination is traditionally reserved for the angle between the orbital plane and the reference plane. So unless the entire orbit is wobbling (for instance due to precession) the inclination will be constant for all positions of the planet.

The angle that varies as the planet moves through the reference plane is the latitude. However, in this particular problem calculating the latitude isn't particularly useful. The more practical coordinate to look at is the height of the planet away from the plane, I'll call this $r_z$. If along your observers line of sight you find $r_z$ to be smaller than the solar radius, the planet will show a transit.

Working out a fully general elliptical orbit in 3 dimensions is somewhat tricky, so I'll start out with a simple Cartesian coordinate system aligned with the orbital plane. In subsequent steps I work my way back using a number of coordinate transformations.

First a list of the Kepler parameters and their meaning:

$\nu$ - true anomaly - The anglular position with respect to perigee in the orbital plane.
$\omega$ - argument of periapsis - The angular position of perigee with respect to the ascending node in the orbital plane.
$\lambda_{asc}$ - the longitude of ascending node in the invariable plane ($\Omega$ in the picture).
$i$ - inclination - the angle between the orbital plane and the invariable plane, such that $\lambda_{asc}$ gives the rotation axis.

Now, in the orbital plane, the radius of the planet orbit is given as
$$
r(\nu) = \frac{a(1-e^2)}{1+e\cos(\nu)}
$$
If I define the x-axis to align with the ascending node, I can write the position vector as
$$
\vec{r}_{orb} = r(\nu)
\begin{bmatrix}
\cos(\omega+\nu) \\
\sin(\omega+\nu) \\
0
\end{bmatrix}
$$

To move to a Cartesian coordinate system aligned with the invariable plane I have to apply a rotation of angle $i$ about the x-axis, so
$$
\vec{r} = R_x(i)\vec{r}_{orb}= r(\nu)
\begin{bmatrix}
\cos(\omega+\nu) \\
\sin(\omega+\nu)\cos(i) \\
\sin(\omega+\nu)\sin(i)
\end{bmatrix}
$$
So now I have an expression for $r_z$, I just need to know how $\nu$ relates to the planet longitude in the invariable plane, $\lambda_{planet}$.

I can find the longitude of the planet relative to $\lambda_{asc}$ as
$$
\lambda'_{planet} = \arctan( \frac{r_y}{r_x} )
$$
such that the actual longitude is
$$
\lambda_{planet} = \lambda_{asc} + \lambda'_{planet}
$$
Inverting this last expression gives
$$
\nu(\lambda) = \arctan( \frac{\tan(\lambda - \lambda_{asc})}{\cos(i)} ) - \omega
$$

Now I have all the equations to answer the question:
If the planet is along the observer's line of sight, then is has a true anomaly
of $\nu(\lambda_{obs})$, which gives a height above the plane
$$
r_z(\nu) = r(\nu)\sin(\omega+\nu)\sin(i)
$$
If $|r_{z}| < R_{sun}$ the planet can be seen in transit.


Has a near earth object in heliocentric orbit ever been bright enough to be visible to the unaided eye? The question Can we see asteroid 1998 OR2 with unaided eye? got me thinking. Space.com's Vesta: Facts About the Brightest Asteroid says:

  Vesta is the second most massive body in the asteroid belt, surpassed only by Ceres, which is classified as a dwarf planet. The brightest asteroid in the sky, Vesta is occasionally visible from Earth with the naked eye. It is the first of the four largest asteroids (Ceres, Vesta, Pallas and Hygiea) to be visited by a spacecraft. The Dawn mission orbited Vesta in 2011, providing new insights into this rocky world.

The brightness of an object seen from Earth is proportional to (among other things) $1/r^2$ so an object which occasionally passes very close to Earth will occasionally be far brighter than normal; an object normally of order 200 million km away that comes to within 200 thousand km will be a million times brighter, and at 2.5 magnitudes per power of ten that means that for a brief time it could be 15 magnitudes brighter than average.

Questions:

Has a near earth object in heliocentric orbit ever been bright enough to be visible to the unaided eye?
Are there any predictions of events in the foreseeable future when this will happen?

Please exclude comets which are themselves invisible and it's the giant clouds of dust and gas they produce that we see and planets (and dwarf planets) who's heliocentric orbits make them regularly visible.

The following may provide some helpful definitions:

Is there a distinction between NEOs and near-Earth asteroids? Is there a difference?
What (actually) defines an Aten-class near-earth asteroid?
Has Hubble ever been used to try to image a near Earth asteroid?
Is the passage of three asteroids near Earth today just coincidental?
https://space.meta.stackexchange.com/q/1459/12102

The Near-Earth close approches website shows close approaches to the Earth by near-Earth objects (NEOs). The table showing all close encounters indicates the absolute magnitude.

The data can be exported to a CSV file to estimate the apparent magnitude for each object, using the following equation.

$$
m = H + 5 \log_{10} \bigg( \frac{d_{BS}d_{BO}}{d_0^2} \bigg) - q(\alpha)
$$
where $H$ is the absolute magnitude, $m$ is the apparent magnitude, d_{*} are the distances between the objects and $a(\alpha)$ is the reflected light. $q(\alpha)$ is a number between 0 and 1.

I only want to know what happens when the object is closest to the Earth, so I use the approximation that the distance from the Sun to the NEO is 1AU.

$q(\alpha)$ is complicated to compute, so I just compute $m$ using $q=0$ and $q=1$. This leads to

min value $ = H + 5 \log (d_{BO}) - 1 < m < H + 5 \log (d_{BO}) = $ max value

with $d_{BO}$ the distance between the Earth and the NEO expressed in astronomical units (AU).

The server is unhappy when I try to get the entire database, so I limited my export to the objects that come reasonably close to Earth (d<0.05 AU), with no time limit.

Among these 24588 objects, 4 have a maximal magnitude less than 6, and 16 have a minimal magnitude less than 6. So between 1900 and 2200, no more than 16 NEOs are visible by the naked eye.

In particular, 99942 Apophis (2004 MN4) has an apparent magnitude between 1.7 and 2.7 based on these estimates. Its close approach date is April 13 2029.

But this doesn't say anything on NEOs from before 1900 or after 2200.


Pulsars with accreting disk in binary system Following this line, I am wondering about the following question.

Accreting pulsars in binary systems are usually thought to accrete from a prograde disk, so increasing their spin in the process.

But why is the disk supposed to be prograde?

As far as I know all accretion disks are prograde. When the pulsar starts accreting mass from it's companion this mass is pulled to follow the pulsar's rotation.


Knowing time any where and any when My question is if I put you down somewhere in the Milky Way galaxy in any given period of time, is there a way for you to tell when and where you are based on stars or constellations? Or some known astronomical event like a supernova? How accurate would that be?

This question is someone open-ended since you don't provide many constraints, so I'll impose the following two conditions of my own to help me give an answer:

I'll assume that after you're randomly placed in space and time, that you can make any observation one could make here on Earth - that is, you have whatever equipment is necessary to observe anything about the Universe we can currently observe.
I'll assume that you have access to all current astronomical knowledge (in a digital library or some such thing) such as star catalogs, physics books, published papers, etc.

How do we know our location?

In determining location, because we exist in three dimensional space, we have to specify position with three coordinates. The simplest coordinate system in my mind, in terms of what we can measure, are the three coordinates below:

our radial distance from the center of the galaxy,
our height above or below the galactic plane,
and our azimuthal angle from some reference point.

Yes I know these coordinates aren't orthogonal, but they relate well to measurements one could make and simple coordinate transformations could make them orthogonal.

The first one is pretty easy. We can currently measure the distance to Sag A*, the black hole at the center of the galaxy. It's not particularly easy and measurements have fluctuated over the years with respect to our position on Earth (see e.g., Eisenhauer et al. 2003 or Boehle et al. 2016), but it is a measurement which could allow you to define #1.

The second coordinate could be achieved by simply mapping the local star field. A survey akin to SDSS could accomplish this. This is precisely what was done in this Humphreys & Larson 1995. It would take time and a lot of work, but you could make this measurement pretty easily.

So far so good. Now we come to coordinate #3 and suddenly we hit a problem. We need to know our azimuthal position with respect to some reference point. That is, if you look down on the galaxy and consider our angle from some line, what would that line be and what would that angle be? Since the clear intent is to relate our new position to where the Earth is, the most logical reference line is the line connecting the Earth to the center of the galaxy. But how do we know where that line is with respect to our new position? I'm afraid I don't have a good answer here. Others suggested using pulsars but that isn't foolproof. First, you don't know when you're being deposited so it could be billions of years in the past or future when all current knowledge of pulsars is no longer relevant. Second, you might be on the other side of the milky way where we can't actually see anything currently and thus have no knowledge of pulsars over there.

Your best bet might be to map out the star distribution of as wide a swath of the galaxy as you can see to try and understand what the spiral arms look like near you. We've already done this for our current position in the galaxy. Galactic arms move and change slowly, taking hundreds of millions if not billions of years to change significantly. If you can recognize the general structure of the arms, that would give you a decent reference to your azimuthal position.

How do we know the time?

I'm going to break this down into two possible answers. The first assumes you've been placed in a time not too distant from our current time (think less than a million years) and you're still pretty near to our current position.

In the case above, pulsars are the way to go. Pulsars pulse with extreme regularity, so that they're great time keepers. But if your goal is to know how much time has passed, you need to look at the time rate of change of the pulses. As it turns out, the pulsars don't pulse with perfect regularity. The time between pulses decays very slowly over time due to the pulsars losing angular momentum very slowly. The general step to calculating a reasonably precise time is as follows.

Find a pulsar that is currently known and has current measurements of the pulse rate and decay in pulse rate. To make sure you've identified a given pulsar as the correct one, you'll have to map its relation to other stars via a wide survey (the star fields will have changed, but if you're not too far away from our time you can predict with reasonable accuracy where most stars will be or have been in the past).
Measure the pulse rate (and decay rate if you wish, but that may take years or even decades).
Compare your currently measured pulse rate to the present day measured rate and decay rate and do some calculations. You should be able to figure out your current time with respect to the time now fairly precisely. I can't say how precise, but I wouldn't be surprised if you could get within a decade or so of the current time (depending on how accurate your pulsar models are).

The only caveat to the above approach is that pulsars can "glitch". Normally the pulse rate decays smoothly, but every once in a while a pulsar might just glitch and quickly change pulse rates. It is unclear exactly why these glitches occur and they're unpredictable so you have to make the assumption that your pulsar hasn't glitched between now and whatever time you're in. If it has, your time may be off wildly. To mitigate this, you should of course use as many pulsars as you can find. If one pulsar gives a different number than the rest, you can assume it glitched and throw it out.

The second case is more tricky. Now I'm going to assume you're in a time really distant from our own. Millions or possibly billions of years away from now. In that case, any hope in finding a precise time (or even a precise year) is wildly presumptuous. At best, you can figure out your general time within the universe by measuring the current age of the universe. We currently know the age to be $13.799\pm 0.021\ \mathrm{billion\ years}$ based on the latest and greatest measurements. You can see our uncertainty is down to 21 million years. If you make similar measurements of the Universe's age in your time, then the best you'll be able to do is define your time with respect ours with an accuracy of ~20 million years. But if you're a billion years in the future, that's a pretty good measurement in my opinion.


What is the term for a star swallowing another star? A star A goes through the body of another star B, or is swallowed by B. There is no tidal disruption.

It sounds like kerzan. Does anybody recognise this pronunciation?

The term you're searching for is probably accretion (I guess it might sound similar to a kerzan if the speaker had a cold or the listener couldn't hear it well enough for other reasons). This term is not limited to close binary stars (accreting binaries) cannibalizing each other because they orbit each other at such proximity that the L1 Lagrange point between them extends into their own Roche lobe, they form accretion disks connected through an accretion stream, and they feed off each other (thus why this is often referred to as cannibalism):

   Artist's conception shows an accreting binary at the center of the globular cluster NGC 6624 (Source: U. of Tennessee AstroWiki)

Some examples of accreting binaries are symbiotic novae, X-ray binaries, microquasars, X-ray pulsars, and so on. See links for more examples and explanations. Other examples of accretion include stellar accretion of planetary materials of a planet in a low altitude orbit around its parent star, formation of planets via accretion of materials of the protoplanetary disk, active galactic nucleus (AGN) like quasars (could also sound similar), novae, and e.g. the Earth still accretes on average ~ 110 metric tons of new materials per day, too.


How do I get started in astronomy data analysis? I am learning some machine learning (I have previous background in statistics) on my own, and I am interested in getting some hands-on practice by doing some ML analysis in R and Python.

Given how mad I am about astronomy, I would love to get my hands dirty on doing some ML using open data. I am aware that organisations like NASA have lots of open datasets. What I am less clear about is the kind of analysis that needs to be done.

So, I'd like to know if there is any website where I can get a repository of space data (images, signals, whatever) and which asks what analysis is required; kind of like Kaggle where one gets the dataset and has the required question which one can attempt.

A possibility might be a course at a university, youtube, or a self-study-course via a book.

What we've used in our astrostatistics class was "Wall & Jenkins: Practical Statistics for Astronomers" which presents theoretical sections with exercises as follow-ups. No answer sections exist, as you need to do some programing for some of them.

But you can maybe lend this or similar books at a local university library, without the need to spend money.


What powered the Big Bang? According to the first law of thermodynamics, law of conservation of energy states,

The total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.

Question is where was the energy that triggered the big bang at the first place? What are the popular hypotheses?

This is a difficult question to answer. Physics really starts after the big bang. Scientist don't know about the laws, if any, before the first instance after the big bang. The time before and during the big bang is really the province of philosophy.


What is a hypernova and have we observed any? Inspired by the question "What does it mean for a star to go nova or supernova? Can I safely observe these?", I am curious about what hypernovas are?

Have we observed any occurring, or the at least the after-effects?

Is there an upper limit of how large a stellar explosion can be?

A hypernova is just a really, really big supernova.  UMass has a (tacky designed) web page that explains it.

  A hypernova explosion typically has a mechanical energy output of ~ 10^53 ergs, or about a factor of 100 greater than a supernova.

Regarding aftereffect, the page says this:

  The age of the hypernova remnant NGC5471B is about 30 thousand years, while the age of MF83 is about 1 million years.

As best as I am able to determine, we have not had a chance to observe any hypernova candidates in the modern era, although APOD featured the same one as mentioned by UMass:

According to New Scientist, research suggest the upper limit to a star is about 150 solar masses. These are the stars that create the infamous supernovas.his is as derived from the Eddington Limit.  Although R136a1 is an example of a star at nearly double that.  It is believed that these monsters are what are responsible for hypernovas. There is much to be learned from these stellar monsters!