Black Hole Collision & Gravitational Waves The Gravitational waves detected by LIGO on 14th September 2015 are attributed to a collision of two black holes, which had been rotating near the speed of light around each other just before the actual collision. The collision happened 1.3 billion years ago, approximately 1.3 billion light-years away and apparently, the energy of the collision exceeded the combined energy of all stars in the observable universe.
LIGO was able to detect the deformation in the fabric of space induced by the gravitational wave caused by the collision, even though the deformation was the magnitude of a fraction of an atomic radius. The reason why the deformation was so "small" by the time the wave had reached planet Earth was due to the relatively large distance of the collision from Earth.
Question: could someone qualified give an estimate of the magnitude of the space-time deformation we would experience on planet Earth, had the collision happened closer to us? I.e. how close would the collision have to happen for the space-time deformation to be millimeters? What about meters? At what magnitude of the deformation would the gravitational wave be dangerous or lethal for humans on planet Earth?
Bryan Greene described the gravitational wave deformation of space-time as a temporary "shrinkage" or "compression" of Earth (and everything on it). Am I right to assume that being compressed by even 1 centimeter could potentially be lethal for all live on Earth?

Part of the answer is easy. The strain measured in that event was about $0.25\times 10^{-21}$. That is an object $1m$ long would be squeezed by $0.25\times 10^{-21} m$ in one direction and stretched by the same amount in the orthogonal direction.
The strain drops off linearly with distance from the black hole, so to achieve a distortion of 1mm in something the size of the Earth (ie about $8\times 10^{-11}$ it would need to be about $5\times 10^{10}$ times closer, so about $0.03$ light years away, or about 2000 AU. Two 30 solar mass plus black holes at that distance would have disrupted the solar system quite a bit before they collided.
To achieve a distortion of 1mm in something the size of a human they would need to be another factor of $6\times 10^6$ closer, so about $\mathrm{30000 km}$, closer than geostationary orbit. In this case we would certainly have bigger problems than the gravity waves.
What I don't know how to calculate is the energy absorbed by the Earth, or a human, in one of these scenarios. I suspect it would not be all that much, at least from the wave.
Added later: this answer gives the total energy passing through the Earth (about 34GJ with the black holes at their current distance) but offers no ideas for how much is absorbed. This would increase according to the inverse square law if the black holes were closer.


Is the influence of gravity instantaneous? When I was in college, I posed to my astronomy professor a thought experiment that had been puzzling my mind for some time: "If all the matter in the Sun magically disappeared instantly, how long would it take its gravity to stop having an effect on us?" His response was that the force of gravity is instant, unlike the speed of light, which appears instant.

My big question is: "Do we know it's instant?" We can't possibly move an object large enough to have a noticeable gravitational influence fast enough to measure if it creates (or doesn't create) a doppler-like phenomenon.

If he was wrong, how do we know it's not?

The first question as stated has a rather trivial answer:

  "If the sun magically disappeared, instantly, along with all its influences, how long would it take its gravity to stop having an effect on us?"

Since the Sun's gravity is among its influences, it would instantly stop having an effect on us. That's just part of the magical situation, and doesn't even involve any physics. A bit more interesting is the question without the bolded part.

In general relativity, changes in the gravitational field propagate at the speed of light. Thus, one might expect that the magical and instant disappearance of the Sun would not affect earth for about eight minutes, since that's how long light from the Sun takes to reach Earth.

However, this is mistaken because the instant disappearance of the Sun itself violates general relativity, as the Einstein field equation enforces a kind of local conservation law on the stress-energy tensor analogous to the non-divergence of the magnetic field in the electromagnetism: in any small neighborhood of spacetime, there are no local sources or sinks of stress-energy; it must come from somewhere and go somewhere. Since the magical instant disappearance of the Sun violates general relativity, it does not make sense to use that theory to predict what happens in such a situation.

Thus, the Sun's gravity instantly ceasing any effect on the Earth is just as consistent with general relativity as having any sort of time-delay. Or to be precise, it's no more inconsistent.

  My big question, now, is: "How do we know it's instant?"

It's not instant, but it can appear that way.

  We can't possibly move an object large enough to have a noticeable gravitational influence fast enough to measure if it creates (or doesn't create) a doppler-like phenomenon.

We don't have to: solar system dynamics are quite fast enough. An simple calculation due to Laplace in the early nineteenth century concluded that if gravity aberrated, Earth's orbit would crash into the Sun on the time-scale of about four centuries. Thus gravity does not aberrate appreciably--more careful analyses concluded that in the Newtonian framework, the speed of gravity must be more than $2\times10^{10}$ the speed of light to be consistent with the observed lack of aberration.

This may seem quite a bit puzzling with how it fits with general relativity's claim that changes in the gravitational field propagate at the speed of light, but it's actually not that peculiar. As an analogy, the electric field of a uniformly moving electric charge is directed toward the instantaneous position of the charge--not where the charge used to be, as one might expect from a speed of light delay. This doesn't mean that electromagnetism propagates instantaneously--if you wiggle the charge, that information will be limited by $c$, as the electromagnetic field changes in response to your action. Instead, it's just something that's true for uniformly moving charges: the electric field "anticipates" where the change will be if no influence acts on it. If the charge velocity changes slowly enough, it will look like electromagnetism is instantaneous, even though it really isn't.

Gravity does this even better: the gravitational field of a uniformly accelerating mass is toward its current position. Thus, gravity "anticipates" where the mass will be based on not just current velocity, but also acceleration. Thus, if conditions are such that the acceleration of gravitating bodies changes slowly (as is the case in the solar system), gravity will look instantaneous. But this is only approximately true if the acceleration changes slowly--it's just a very good approximation under the conditions of the solar system. After all, Newtonian gravity works well.

A detailed analysis of this can be found in Steve Carlip's Aberration and the Speed of Gravity, Phys.Lett.A 267:81-87 (2000) [arXiV:gr-qc/9909087].

  If he was wrong, how do we know it's not?

We have a lot of evidence for general relativity, but the best current evidence that gravitational radiation behaves as GTR says it does is Hulse-Taylor binary. However, there is no direct observation of gravitational radiation yet. The connection between the degree of apparent cancellation of velocity-dependent effects in both electromagnetism and gravity, including its connection with the dipole nature of EM radiation and quadrupole nature of gravitational radiation, can also be found in Carlip's paper.


If a star orbited another star, how would that affect parallax measurements of the other star from the vantage point of the first? Example:

If hypothetically, the vantage point would move 2AU along an orbit around the star being measured, would that make it seem as if the other star moved twice the distance over the back-drop?

The other star would have a significant proper motion.

Over the course of one orbit, it would appear to travel right around the sky once. The variation in position due to the Earth's orbit of the sun would be superimposed on top of this motion.

Except that the proper motion of the star, and its parallax would be much greater than for any real star, this is not really different to the way in which the parallax motion of a star is superimposed on its proper motion.


How does NASA's ASTHROS stratospheric telescope compare to its James Webb space telescope? In Space SE I've asked Would it have been cheaper and faster to put a James Webb-like Space Telescope on a balloon instead of a rocket?
I linked there to a few news items:

CNET: NASA to send stadium-size balloon skyward to study the cosmos
JPL/NASA News: NASA Mission Will Study the Cosmos With a Stratospheric Balloon Even in 2020 balloons are used for space exploration; Q.E.D.
Scitech Daily: NASA ASTHROS: Stratospheric Balloon the Size of a Football Stadium Will Carry a Cutting-Edge Telescope

Question: But here I'd like to ask about the ASTHROS instrument and how it compares in capability and range of instrumentation compared to the JWST. I know that they both have infrared capabilities and cryogenically cooled instrumentation, but I don't know how their instrumentation or spectral ranges compare.  I'm pretty confident that ASTHROS will not have the same aperture as JWST, but I don't know how much smaller it will be
update: The JPL/NASA News article above intriguingly says:

A gondola beneath the balloon will carry the instrument and the lightweight telescope, which consists of an 8.4-foot (2.5-meter) dish antenna as well as a series of mirrors, lenses, and detectors designed and optimized to capture far-infrared light. Thanks to the dish, ASTHROS tied for the largest telescope to ever fly on a high-altitude balloon. During flight, scientists will be able to precisely control the direction that the telescope points and download the data in real-time using satellite links.

I found this link that might seem interesting : https://www.nasa.gov/feature/jpl/nasa-mission-will-study-the-cosmos-with-a-stratospheric-balloon
The article in the link doesn't clearly specify the actual instruments or their functionality, but as this is an official article, I thought it might be useful.
The only info that NASA has officially released about ASTHROS is the cooling systems :

Because far-infrared instruments need to be kept very cold, many missions carry liquid helium to cool them. ASTHROS will instead rely on a cryocooler, which uses electricity (supplied by ASTHROS' solar panels) to keep the superconducting detectors close to minus 451.3 degrees Fahrenheit (minus 268.5 degrees Celsius) — a little above absolute zero, the coldest temperature matter can reach. The cryocooler weighs much less than the large liquid helium container that ASTHROS would need to keep its instrument cold for the entire mission. That means the payload is considerably lighter and the mission's lifetime is no longer limited by how much liquid helium is on board.

Here is a link about the JWST : https://en.wikipedia.org/wiki/James_Webb_Space_Telescope
This link also does not specify the difference between JWST and ASTHROS, but it compares the JWST with the Hubble Space Telescope. Here are some comparions:-

The JWST has an expected mass about half of Hubble Space Telescope's, but its primary mirror, a 6.5 meter diameter gold-coated beryllium reflector will have a collecting area over six times as large, 25.4 square metres (273 sq ft), using 18 hexagon mirrors with 0.9 square metres (9.7 sq ft) obscuration for the secondary support struts.[22]

The JWST is oriented toward near-infrared astronomy, but can also see orange and red visible light, as well as the mid-infrared region, depending on the instrument. The design emphasizes the near to mid-infrared for three main reasons: high-redshift objects have their visible emissions shifted into the infrared, cold objects such as debris disks and planets emit most strongly in the infrared, and this band is difficult to study from the ground or by existing space telescopes such as Hubble. Ground-based telescopes must look through the atmosphere, which is opaque in many infrared bands (see figure of atmospheric absorption). Even where the atmosphere is transparent, many of the target chemical compounds, such as water, carbon dioxide, and methane, also exist in the Earth's atmosphere, vastly complicating analysis. Existing space telescopes such as Hubble cannot study these bands since their mirrors are insufficiently cool (the Hubble mirror is maintained at about 15 °C or 288 K) thus the telescope itself radiates strongly in the infrared bands.

The article goes on to compare the JWST with other telescopes (mainly the cooling systems, aperture and wavelengths) so you can compare the currently being planned JWST telescope with other already launched ones like IRT, ISO and Spitzer.
The above WIKI article is amazingly detailed and may help.
The article linked above contains the wavelength range of ASTHROS as follows :

Managed by NASA's Jet Propulsion Laboratory, ASTHROS observes far-infrared light, or light with wavelengths much longer than what is visible to the human eye. To do that, ASTHROS will need to reach an altitude of about 130,000 feet (24.6 miles, or 40 kilometers) – roughly four times higher than commercial airliners fly. Though still well below the boundary of space (about 62 miles, or 100 kilometers, above Earth's surface), it will be high enough to observe light wavelengths blocked by Earth's atmosphere.

It also defines the targets for ASTHROS, listed as follows :

ASTHROS will make the first detailed 3D maps of the density, speed, and motion of gas in these regions to see how the newborn giants influence their placental material. By doing so, the team hopes to gain insight into how stellar feedback works and to provide new information to refine computer simulations of galaxy evolution.

It will also for the first time detect and map the presence of two specific types of nitrogen ions

A third target for ASTHROS will be the galaxy Messier 83. Observing signs of stellar feedback there will enable the ASTHROS team to gain deeper insight into its effect on different types of galaxies. "I think it's understood that stellar feedback is the main regulator of star formation throughout the universe's history," said JPL scientist Jorge Pineda, principal investigator of ASTHROS. "Computer simulations of galaxy evolution still can't quite replicate the reality that we see out in the cosmos. The nitrogen mapping that we'll do with ASTHROS has never been done before, and it will be exciting to see how that information helps make those models more accurate."

Finally, as its fourth target, ASTHROS will observe TW Hydrae, a young star surrounded by a wide disk of dust and gas where planets may be forming. With its unique capabilities, ASTHROS will measure the total mass of this protoplanetary disk and show how this mass is distributed throughout. These observations could potentially reveal places where the dust is clumping together to form planets. Learning more about protoplanetary disks could help astronomers understand how different types of planets form in young solar systems.

Wavelength Range of JWST explained as :

The JWST will observe in a lower frequency range, from long-wavelength visible light through mid-infrared (0.6 to 28.3 μm), which will allow it to observe high redshift objects that are too old and too distant for the Hubble to observe.[8][9] The telescope must be kept very cold in order to observe in the infrared without interference, so it will be deployed in space near the Earth–Sun L2 Lagrangian point, and a large sunshield made of silicon-coated and aluminium-coated Kapton will keep its mirror and instruments below 50 K (−220 °C; −370 °F).

Also, here are some targets of the JWST : https://www.nasa.gov/feature/goddard/2017/icy-moons-galaxy-clusters-and-distant-worlds-among-selected-targets-for-james-webb-space


Python with image in fits format I'm trying to write a Python program that will do the following: take an image in fits format and a reg file with a list of regions in the sky, and determine which regions in the list are inside the fits image and which ones are outside. This can be done visually with ds9, but I have no idea of how I can access the fits file and determine the coordinates of the boundary of the image.

Any advice? I don't know much about the fits format, but it won't open with a usual text editor like gedit.

Edit: Now I have a more specific problem. I have four points in the sky defined by their declination and right ascension. Is there a simple way to check if these coordinates belong to the image coded in the fits file?

Edit 2: This is what I see as the header of my fits file:

I'm no expert in physics, just a mathematician, so I'm not sure how to proceed from here. Any help would be appreciated...

Edit 3: Something seems to change when I put the terminal in full screen mode. Is there any useful info here?

I personally use Astropy, specifically astropy.io.fits, although I'm not a seasoned user of FITS files and I don't really know their layout.  As an example snippet of code, I often load data from FITS files using

from astropy.io import fits
data = fits.open('data_file.fits')[0].data

You'll find more information in the documentation on the FITS module.


Difference between 3D real space and 3D redshift space? With regards to cosmological simulations (e.g., N-body dark matter only simulations), I've seen people talk about the positions of objects (halos, galaxies) in the simulation in terms of 3D real space and 3D redshift space. The idea is that the positions of objects in 3D real space does not add the contribution of redshift space distortions, whereas 3D redshift space does. But since redshift space distortions are a real physical effect (i.e., the positions/velocities of objects will be affected not only by cosmological expansion but also gravitational interactions), why is 3D real space ever even considered? Is it some kind of highly idealistic cosmology-dependent only scenario, ignoring peculiar velocities?

Difference between 3D real space and 3D redshift space?

  Why is 3D real space ever even considered? Is it some kind of highly idealistic cosmology-dependent only scenario, ignoring peculiar velocities?

Simple explanation:

3D real space is the actual distance, position, velocity, (even spin), etc. of an object; this can be used to measure Earth's distance to our Sun or another planet's distance to its Sun.

3D redshift space is the apparent distance, a distorted view by which one can compare one object to another. The distortion is caused by varying density of the interstellar medium, gravity, motion of Earth and the objects being viewed, even dark matter, etc.

The real distance between two objects can, for example, affect each other by gravity; this alters the trajectory of the objects. The apparent distance has no effect on gravity, only the real distance.

By comparing the real distance, obtained by making calculations, with the apparent distance, obtained by making observations, we can compare what we see with what we calculate; this permits checking the theory, finding new objects (or phenomena, such as suggesting that there is dark matter). This gives us the path lengths for each direction and distance (because distance varies depending on direction and distance due to gravity).

A more complicated explanation is offered in:

"A Spherical Harmonic Analysis of Redshift Space" (Sept 13 1994), by A.F. Heavens and A.N. Taylor

  "1 INTRODUCTION
  An accurate three-dimensional map of the galaxy distribution would be enormously valuable for cosmology, but the lack of an accurate estimator of distance precludes this. Despite best efforts, the errors in the Tully-Fisher and Faber-Jackson distance indicators mean that the best one can do is to use the recession velocity $v$, or redshift, of a galaxy, and to assign its distance $s$ by using the Hubble expansion law $v = H_0s$, where $H_0$ is the Hubble parameter. The resulting `redshift space' map is of course not perfect, because galaxies are not necessarily moving precisely with the idealised expansion of a homogeneous universe. Density inhomogeneities have associated with them peculiar velocities, which introduce a radial distortion between the true (real-space) map and the redshift space map. This distortion is, of course, inconvenient: for example, extracting the power spectrum of density fluctuations from a galaxy redshift survey becomes a non-trivial task. However, the distortion itself can be exploited, as the magnitude of the distortion is dependent on the density parameter of the Universe $\Omega_0$, if fluctuations grow by gravitational instability. Constraining $\Omega_0$ is one of the main aims of this paper.".

"Design and analysis of redshift surveys" (May 27 1997), by A.F. Heavens and A.N. Taylor

  "1 INTRODUCTION
  ...  [This omitted portion: Similar to the above quote, but not identical]
  It is clear that the longest wavelength which can be measured is limited by the size of the survey, so it is attractive to consider surveys which are essentially one- or two-dimensional, to maximise at least one dimension without incurring prohibitive cost in observation time (e.g. Broadhurst et al 1990). The difficulty with such an approach as a method for measuring the power spectrum is that a low-dimensional power measurement at a given wavenumber will have a contribution (which may be dominant) from much smaller scales in three dimensions (e.g. Kaiser & Peacock 1991). The interpretation of the observed power spectrum can therefore be difficult. For surveys which do not correspond to the ‘distant-observer’ approximation (cf. Kaiser 1987), the power spectrum measurement and the redshift distortion become linked, and this further complicates the analysis.

  The ease with which the parameters of interest may be extracted depends on the choice of coordinate system and basis functions in which the density field is expanded. For two reasons the choice of spherical polar coordinates is compelling. Firstly the survey is almost certain to be defined in terms of a fixed areal coverage (independent of depth), and secondly, a flux limited survey will have a selection function φ (or, equivalently, a mean observed density
  $ρ_0(r)$) which is dependent on distance, but not on direction. The mean density of the survey is then separable in spherical coordinates $\overline{ρ}(r) = ρ_0(r) M(θ, ϕ)$, where $M$ is either 1 or 0 depending on whether the direction $(θ, ϕ)$ is in the survey or not.
  The second reason is that, unless $β ≪ 1$, it is impossible to ignore redshift distortion effects, and since the distortion between the real-space map and the redshift-space map is purely radial, it is straightforward to include the distortion in a power-spectrum analysis in spherical coordinates (cf Zaroubi & Hoffman 1996).".

More simply, this webpage describing Halton Arp's image:

Our position (the Earth) is at the bottom point in all cases. Distance (away from the Earth) is measured along the straight edges. In the top left image, we show what a galaxy cluster in Arp's universe would look like without the big bang perspective.  It is a family of galaxies and quasars and gaseous clouds of mixed redshifts (in the top diagrams, the large dots are low- redshift, the medium-sized dots are medium-redshift, and the small dots are high redshift). At the center, there is a dominant galaxy -- it's usually the largest galaxy, and the galaxy with the lowest redshift of the cluster. This galaxy is surrounded by low-to-medium redshift galaxies, and toward the edges of the cluster we find the highest redshift galaxies, HII regions, BL Lac objects and quasars.

The image to the right shows what happens if we try to force the same galaxy cluster into a redshift-equals-distance relationship. The cluster becomes distorted. What was once a sphere becomes an elongated bubble. The central dominant galaxy drops to the front of this bubble, followed by a spike of low-to-medium redshift galaxies stretching away from the earth and "bubble and void" of high redshift objects.

Every cluster in the sky does this, like fingers of god pointed at the earth from every direction. The third image is a 90 degree slice of the sky showing all galaxies arranged according to their redshift-  determined distances. The Fingers of God distortions show clearly, each representing a single galaxy cluster. (The bubbles and voids are not as clear, because this chart cuts off before it gets to high redshift.) Everything points at the Earth.

Without the redshift-equals-distance distortion, a new picture of galaxy clusters and the universe itself is revealed. The age of the universe is no longer known, because we no longer have a constant expansion to backtrack to a bang. The size is also unknown. Most quasars and some galaxies that we see are closer than we thought they were, because they have been distorted by the Fingers of God. But we have no idea how far the universe stretches beyond our telescopes' limits.

Compare the real space in the upper left with the observed image in the upper right.


Graphics packages for publishing What are the most popular packages used to create graphs for astronomy journal papers?
Looking at various journals, the styles of the graphs appear to be quite uniform but I can't identify the package(s) that create them.

The most commonly used packages for generating graphics in astronomy are probably

IDL -- this has long been the most popular, in part because there is a lot of astronomical data reduction and analysis code written in IDL.
SuperMongo
The Python package matplotlib

The apparently uniform style you refer to is probably a historical combination of IDL and SuperMongo.

Matplotlib (and other Python packages that act as wrappers around it) is on a trajectory to displace the others; I strongly suspect it is already much more common than SuperMongo, and may be roughly as common as IDL by now.

You will sometimes see figures produced by the PLplot library as output from programs written
in Fortran, C/C++, etc. Plots produced using R are also starting to appear.


Why did the Comet Shoemaker-Levy-9 fragments cause such large explosions on Jupiter? In July 1994, the comet Shoemaker-Levy 9 (D/1993 F2) tidally fragmented and these fragments collided into Jupiter, as per the image below.

Image source

The question is, what mechanisms resulted in these small fragments causing such large explosions in the Jovian clouds?

Shoemaker Levy 9 was estimated to have released kinetic energy equivalent to 300 gigatons of TNT. That is $1.255 \times 10^{21} {\rm J}$. This release through friction and compression was sufficient to heat the atmosphere to 4000K at first. That in turn should probably be enough to break down the molecular hydrogen and methane, releasing further energy. But that's only my guess. The heating from the impact alone should make a huge fireball.
Sources:
Fragment Size and Mass Estimates
Galileo observations


Is the expansion of the universe greater than the speed of light? If the rate of expansion of the universe is increasing , won't it eventually become greater than c? Also, after inflation, did the rate of expansion slow down and then start to accelerate again?

After inflation, the expansion of the universe did indeed slow down. During the inflationary epoch (lasting roughly $1 \times 10^{-33}$ seconds), the universe expanded by a factor of $10^{26}$. That's incredible! However, the inflationary epoch didn't last long, and that incredible expansion ended pretty soon after it started.

The universe is, as you said, still expanding. In fact (like you also said), that expansion is increasing. However, we have to be careful when we talk about the rate of this expansion. Currently, the rate of expansion between two objects depends on the distance between them, which is encoded in Hubble's law:
$$v=H_0D$$
where $v$ is the recessional velocity, $H_0$ is Hubble's constant, and $D$ is the proper distance between the objects. This relation proves that objects that are farther away are moving away at a greater speed. We can extrapolate from that that, at a sufficiently far distance, two objects would be moving away from each other at the speed of light or greater! However, this is only true for objects very far from each other. But yes, eventually, any two objects sufficiently far from each other will move apart at the speed of light - and then greater.

Source (for length of inflationary epoch): http://www.universe-galaxies-stars.com/Cosmic_inflation.html

Source (for Hubble's law): http://map.gsfc.nasa.gov/universe/uni_expansion.html


Compton scattering of high energy radiation I was reading up on compton radiation, and a question came up which I could not quite answer.

Compton scattering is known to be less efficient at high energies, due to the fact that the Klein-Nishina cross-section falls off at the high energy end. This means that the Universe is more transparent to Compton radiation at high energies.

What other processes could stop high energy photons from propogating through the Universe (i.e., a process that preferentially stops photons at the high-energy end)?

The answer is pair production. Once photon energies exceed 1.02 MeV it is possible to spontaneously create an electron-positron pair in the presence of an atomic nucleus (to conserve momentum). In general for high energy photon interactions with matter you need to consider the photoelectric effect, Compton scattering and pair production. The former is more important at lower energies, the latter at higher energies.

The picture below shows the mass attenuation coefficients for Aluminium and Iron as a function of energy, with the contributions of these three processed identified.


Term for the moment when hydrogen fusion begins in a star I have read of this process many times, but I don't think I know the term specifically for the moment when hydrogen fusion begins. What is this moment called?

Ignition or more fully Stellar ignition is the term you want.


How to calculate the altitude of the Celestial Equator from an observer's latitude? Exam question When observing from a latitude of 50 degrees North on Earth, the Celestial Equator will have a maximum altitude of:
  Answer: 40 degrees

I've looked this up and it says something about the observer's co-latitude. However, I do not understand why this is the case. Could someone explain this please?

Perhaps you have heard that the altitude of the celestial pole (3 in the figure below) is equal to your latitude. In other words, angle 5 is the same as your latitude. Of course, the angle between the celestial pole (3) and the celestial equator (4) is 90 degrees (angle 6). From this, you should be able to calculate the angle of the equator (angle 7).

Item 1 is the horizon, and 2 is the celestial sphere.


How far do we have to go to leave the galaxy? How far is the sun from the edge of the galaxy in the following directions?

Moving along the shortest path parallel to the galactic plane (outward radially)
Moving along the longest path parallel to the galactic plane (radially presumably passing through the center)
Moving along the shortest path perpendicular to the galactic plane ("up")
Moving along the longest path perpendicular to the galactic plane ("down")

I realize these distances may be somewhat fuzzy (edge of galaxy is probably hard to define exactly, galaxy isn't exactly an ellipse, computing distances like this are hard even if the boundaries weren't fuzzy), so ranges and uncertainties are fine. I don't expect precision like computing whether certain points on the edge might be closer than just going straight out from the center and the like.

The sun is within a few parsec (15-25 pc) of the galactic plane, slightly above. The thin disk of the milky way (containing ~85% of the stars and gas) has a density going roughly like $\rho_0 \exp(-|z|/300 pc)$, while the thick disk (older stars, a few percent) has a scale height of 1000 pc instead. So if we want to move up (galactic north) above 90% of the star density we would have to move ~680 parsec, and going down 720 parsec. At this point at least the view would be splendid, but there would still be a fair number of thick disk and halo stars above and below.

The disk has a scale length of 2.5–4.5 kiloparsec (kpc) and the sun is about 8 kpc away from the core, so we are already outside nearly 90% of the stars (not even counting the bulge). The radius is commonly given as 15.5-27.5 kpc, so we are 7.5-19.5 kpc from the nearest edge and 15.5-27.5 kpc from the far edge.

If we count the dark matter halo the distances get even fuzzier. The virial radius (a rough measure of where most mass is inside most of the time) is 200 kpc, so we are basically 200 kpc away from that distance in most directions.


What suggests the cyclic nature of the universe? Proposed by Stephen Hawking In "A Briefer History of Time" by Stephen Hawking he writes that if we were to travel faster than the universe were expanding and for long enough (in a straight line) we would eventually come back to the point we started.

What suggests that the universe is cyclic in nature as this suggests?
Or what led him to come to this conclusion?

There's nothing "cyclic" in the universe Hawking is describing. Rather, Hawking's thought experiment applies to a particular shape of the universe.

The observable universe is, for practical purposes, a sphere 93 billion light years in diameter, with us at the centre. Observations suggest that this observable universe is pretty much isotropic and homogenous. If anything exists beyond this sphere, it's so far away that the light from it hasn't had time (i.e. the age of the universe) to reach us.

It's rational to assume that there is a universe beyond what we can see. This is called the global universe. Since we can't observe it, we can only theorise what its properties might be. There are three broad possibilities for the shape of an isotropic global universe:

  flat (no curvature)
  closed (positively curved)
  open (negativelycurved)

Current observations indicate that the universe is flat, with only a 0.4% margin of error - in other words, if it's a simply-connected universe (e.g. not a torus) then it extends infinitely in all directions. Hawking's thought experiment, on the other hand, takes place in a positively curved universe. This can be thought of as a three-dimensional hypersphere. One way to picture this is as though we're an atom in the surface fabric of a balloon: from where we are, everything looks flat and infinite, but in fact the flatness curves away to form a spherical shape. Importantly, this shape is "closed" - in other words, finite, as is the surface area of a sphere.

What Hawking is suggesting is that if you set out in a straight line on the surface of this balloon, and so long as your movement away from the starting point is faster than the rate the balloon is expanding, then eventually you'll circumnavigate the balloon and end up where you began.

It's purely meant as a demonstration of what a closed (positively curved) universe "looks like". Given that our local, observable universe appears very close to flat, the curvature would have to be so small that the "balloon" would be truly immense; circumnavigating it would therefore take so long (say, a billion billion years) that our Milky Way would be unrecognisable, if it existed at all, by the time you returned to your starting point.

To be fair to Hawking, in 1988 when his ground-breaking A Brief History of Time was published, there was good reason to think that the universe was positively curved, since a truly flat universe (curvature exactly zero) seemed an improbable "special case". However, the discovery in 1998 of the accelerating expansion of the universe, which provided direct evidence of dark energy and firmly installed Lambda-CDM as the preferred model, rewrote the science and was probably one of the reasons Hawking decided to rewrite his book.

Even so, when A Briefer History was published in 2005, only the earliest data from the Wilkinson Microwave Anisotropy Probe (WMAP) was available, putting the total density of the universe at 1.02 (allowing a realistic possibility of a slight positive curvature), whereas by 2012 the WMAP data had reduced this to 1.0027 (very close to flat).


Why is the TESS spacecraft finding fewer exoplanets than expected? Judging from the Wikipedia page, I got the impression that TESS is underperforming, being expected to detect about 20000 candidate exoplanets in its primary two-year mission, but with only a few weeks left, it is now clear that it won't come close to that figure. I am just curious to know why that is.

From Astrobio.net's April 2018 article The Astrobiology Magazine Guide to TESS:

  “The number of Earth-sized and super-earth planets that TESS should find over the course of its two-year primary mission will be in the range of 500 to 1,000 new planets, and overall the number of planets that will be established is likely to be in excess of 20,000 all together,” enthuses MIT’s George Ricker, who is TESS’ Principal Investigator.

That is roughly 10 times greater than the updated total as of March 20, 2020 being in the 1700-1800 range according to NASA's status tracker.

I am not using TESS to find planets, but I'm reasonably sure that the answer is that nobody has looked very carefully at all the data yet.

The TESS data comes in two flavours. There were a subset of about 200,000 stars that were observed with a 2 minute cadence. These targets were chosen to be a combination of bright and small, heavily weighted towards nearby K and M dwarfs - to optimise the chances of finding a few thousand small planets. The vast majority of the reported planet discoveries so far will have come from this list.

https://tess.mit.edu/science/data/

In addition, the most of the sky was mapped repeatedly such that there is "full frame images" of patches taken every 30 minutes over at least 27 days.

In principle, every star in the sky is present in the full frame data. In practice, only stars brighter than about 15th magnitude have reasonable data that might allow the detection of larger planets; the so-called hot Jupiters.

There are expected to be about 20 million stars that are bright enough to facilitate hunting for hot Jupiters. The majority of these will be solar-type stars or more luminous. The occurrence rate of such objects is known to be about 1%, suggesting 200,000 stars will have them. But then only a fraction of about 10% of those happen to transit in front of the star, which is where the estimate of 20,000 comes from.

Extracting and analysing 20 million light curves from the full frame images is not a straightforward task and it simply hasn't been completed yet.

EDIT:

Chapter and verse on this can be found in Barclay et al. (2018). They study the likely numbers of planets to be found by TESS. They split the study into three samples. The 2-minute cadence sample of 200,000 stars, a 3.2 million candidate target list (CTL), which are generally fainter (but still with $V<13$) main sequence stars of solar-type and cooler, where there is a good chance of finding small planets, then a final list of about 20 million main sequence stars with $V<14.7$ around which giant exoplanets might be found; 16 million of these have $T_{\rm eff} >5500$ K and only 4 million have $T_{\rm eff}<5500$ K.

The estimated yields from these three samples are 1250 in the 2 minute cadence sample; about 4400 in the CTL sample and of order 10,000 in the faint full field image sample. Basically in agreement with what I wrote above.

A further important point is that the large full field image sample of giant exolanets will be heavily contaminated by false positives (i.e. not planets). It is understandable therefore that most of the effort so far has been on investigating and verifying the smaller sample of planets found around brighter stars.


What was the field of view of the Ohio State University Radio Observatory of Wow! signal fame? This answer to Did comets 266P/Christensen or P/2008 Y2 (Gibbs) cause the Wow! signal? points out that the comets in question were nowhere near where the radio telescope was pointed.

Wikipedia says that the Ohio State University Radio Observatory (or Big Ear) was a Kraus-type radio telescope but doesn't provide enough information to deduce a field of view.

Questions:

What was the field of view of the Ohio State University Radio Observatory of Wow! signal fame?
What would be the typical rise and fall times of a steady source passing through the fixed telescope's field of view as the Earth rotated?

For a single dish radio telescope we define the primary beam as the telescope's response on the sky as a function of angle. What this means is that half way between the centre and edge of the primary beam, a radio source with a flux of 1 Jy will be observed to have a flux of 0.5 Jy. This response is circular i.e. it is a function of angular separation, and is not dependent on altitude/azimuth. The full-width of this response is typically written as:

where  are the primary beam width in radians, observing wavelength and dish diameter.
As for the big ear telescope, it is obviously not a parabolic reflector or Gregorian offset like the Lovell or Greenbank telescopes (www.naapo.org/W8JK/Images/JDK097l.jpg). Since the secondary reflector is the important one in the determination of resolution, we shall use its dimensions, which are 103m long by 21m high.
The Wow! signal was received at 1420MHz which has a wavelength of 0.21m. Using the above equation, the response would not be circular, but 'fan-shaped'. The response would thereby have approximate dimensions on the sky of 0.12deg by 0.58deg (in azimuth and altitude respectively).
Caveats of this calculation are the non-circular reflectors, which means the actual shape of the telescope's response on the sky would not be Gaussian/symmetrical for that matter. But as for an approximate, angular resolution, 0.12deg by 0.58deg will suffice.
Further to this, if you can find the LST (local sidereal time) of when the Wow! signal was received, and assuming that the big ear telescope is pointing at the zenith (i.e. straight up), the spot the telescope was pointing to would be easy enough to derive based upon telescope latitude and LST. Enjoy!


What is a Barlow lens? I am looking to buy a Celestron 21023 FirstScope 76 Telescope, which is quite inexpensive, and it has good reviews on Amazon.  One thing that many reviewers have said is that the two lenses that it comes with are of low quality, and the suggestion is to toss them and buy a Barlow lens, and perhaps some other more quality lens.

I don't know what a Barlow lens is.

Is this a brand name?  The name of a type of lens?  What distinguishes it from a non-Barlow lens?

I have been an amateur astronomer for over 30 years so I can give you some practical advice on this one.

A Barlow lens is an attachment which fits into the eyepiece holder. It's main purpose is to give increased magnification with your existing eyepieces. They are usually marked as 2x or 3x which indicates how many times they will multiply the magnifying power of an eyepiece. They can be useful for large telescopes which can comfortably handle high powers but for a smaller scope they can be of limited use.

The two problems you would encounter if you used one are, first, that the more you magnify an image the fainter it gets, with a smallish diameter scope like yours this means that you will find it very difficult to see faint objects. The other one is the fact that locating and tracking objects as they move (due to the rotation of the earth) becomes much harder as you increase magnification, the field of view of the eyepiece gets much smaller as you increase the power.

I would personally suggest that you get used to using your new scope for a while as it is, then, see whether you might need one in the future. If your main area of interest turns out to be the moon and planets then a Barlow might be useful at some point, but if you enjoy wide field views of nebulae and star clusters then that is less likely.
Hope this is of some help.


Is there any known asteroid or comet whose path goes through the Earth? Is there any known celestial body of at least 500 ft (150 m) diameter whose Minimum Orbit Intersection Distance (MOID) is within the Earth, meaning it's sure that it can impact the Earth? I know Comet 109P/(Kegler-)Swift-Tuttle has a very close MOID at 130,000 km (81,000 mi) and the Earth probably would be struck by particles from its tail if it came that close. And Apophis can come as close as 47,200 km (29,300 mi) but that's an asteroid (no tail). Are there any large bodies whose MOID is closer?

JPL and ESA provide tools to search for small bodies meeting user-defined criteria.
I tried:

H <= 24
MOID <= 1e-4 au

with each and got these results in common:

(89959) 2002 NT7, an H=16.5 (~1.4 km) asteroid with a 2.29 year period.
MOID≈4000 km but closest approach between 1900 and 2200 is 0.37 au; orbit rather highly inclined (i=42.3°).

(292220) 2006 SU49, an H=19.4 (390-780 m) asteroid with a 1.68 year period. MOID≈10,000 km; 3.2 lunar distance (LD) approach expected in 2029.

2014 DA, an H=22.7 (85-170 m) asteroid with a 1.85 year period and MOID≈4000 km. Discovered after a 9.3 LD approach; other approaches uncertain (JPL condition code 7) due to limited observational data.

2008 BO16, H=22.9 (80-160 m), 3.78 year period, MOID≈15,000 km, condition code 7.

2010 VB1, H=23.2 (70-140 m), 1.21 year period, MOID≈8000 km, 1.5 LD approach expected in 2068.

Each tool also listed a few bodies which the other didn't.
MOID computation methods vary, and I wouldn't assume that it's known very precisely even for numbered asteroids.
The ESA database appears to store MOID at a resolution of 1e-5 AU (1500 km).
JPL Sentry uses different criteria and shows different results including Apophis and Bennu.


No hair and neutron stars I know black holes can be described by only a few parameters. Given the extreme conditions within a neutron star, how much hair does it have, ie. how much of the original star parameters and composition (e.g. metallicity) affects the features of a neutron star?

No complete answer from me, but some obvious examples of "hair" on a neutron star are:

The temperature - both internal and surface temperature can be measured (in principle). These are mainly a function of the age of the neutron star.

The magnetic field - young neutron stars have very strong magnetic fields that are probably an inherited property from the composition and rotation of the progenitor. The field decays with time.

The surface composition may vary from neutron star to neutron star. In principle this can be measured with X-ray spectroscopy. The composition may be connected with the progenitor, but could also reflect accreted material.

Neutron stars have a radius! The radius may or may not be a unique function of mass. It could depend on the rotation, composition and age.

I think though, the gist of your question is could one determine the progenitor of a neutron star from observations of the neutron star? At present the answer to that is no. Even the relationship between neutron star mass and progenitor mass is not understood; it is also unclear why some neutron stars have very high magnetic fields and so on. But ultimately that would be an aim.


What is the actual resolution of Event Horizon Telescope? I am quite impressed with the recently published image of M87* black hole. It appears that this image achieves spatial resolution well above and beyond what was available until today. But how high this resolution is, exactly?

The article "First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole" states that Event Horizon Telescope has theoretical diffraction-limit resolution of ~25 μas.

Another wiki article states that M87* has Swartzschild radius of 5.9×10-4 parsecs. Combined with the distance of 16.4 million parsecs, this gives me angular size of 14.8 microarceconds.

Even with the shadow of the black hole being 2.5 bigger that its radius, the resolution of a widely distributed picture seems to be much higher than 25 microarcseconds stated above. Is the image actually blown up well beyond its original resolution (i.e. becoming more a less an "artistic impression"), or Event Horizon Telescope is actually capable of higher resolutions (10 microarcseconds or less)?

The resolution of an interferometer at a wavelength $\lambda$ is $\theta\sim\lambda/b$, where $b$ is the longest baseline (distance between two telescopes) in the array. According to the first of this week's six papers, with observations at $\lambda=1.3\text{ mm}$, the longest baseline was $b\approx10700\text{ km}$, giving us $\theta\sim25.1\mu\text{as}$. The team expects this limit to be lowered even further with the addition of more observatories.

The picture, of course, seems much finer. The above limit can be lowered a bit by algorithms like CLEAN or regularized maximum likelihood; this brings the resolution down to about $20\mu\text{as}$. This still doesn't explain why the image seems even finer than that figure; that comes from image synthesis techniques that smooth out the data, rather than leaving it in a coarser form.


Declination of the Sun formula I encountered a book discussion that defines the Sun's declination as 23.5 degrees (inclination of Earth's equator to the ecliptic) times the sine of the Sun's longitude. Does this make sense? How do i visualize it?

Yes, it is correct. For better precision:
Declination =23.5*sin(longitude)
This is true only if you don't take into account the eccentricity of Earth's orbit and other movement. It isn't easy to understand why, but I'll try ti explain it.
The different declination of the sun during the year is generated by the different angle of inclination of the Earth (the north pole point always in the same direction, so during the earth revolution the poles don't point always in the sun direction and the protection of the inclination on the sun-earth plane change during the year)
So, what wee see of the sun is the projection of the circular movement of the earth on a line of sight, so an harmonic motion.


What are the prime challenges in search for extraterrestrial intelligence? What have we been able to accomplish so far and what are the prime obstacles that block our sight? My understanding is that Radio Telescopes are the prime tool for the search. I wonder what kind of challenges the astronomers who work on it are facing.

We have no idea how much we’ve been able to accomplish so far in the search for extraterrestrial intelligence.
If there isn’t extraterrestrial intelligence then our progress is zero.  If there is extraterrestrial intelligence and we already found some, then we’ve made 100% progress!
I think the major obstacles for SETI are threefold: funding, stigma, and physics.
Funding:  This article is a couple years old, but it does a nice job of summing up historical low funding for SETI.  Most of the funding is private and on the order of millions to tens of millions of dollars a year.  That might sound like a lot, but ALMA cost $1.3b.  A few million a year isn’t enough to sustain a very robust program or buy, maintain, and staff an observatory.
Stigma: At least when I was working for the NRAO, SETI work wasn’t considered serious astronomy.  There was some smirking in the lunchroom from some of the astronomers towards the folks “looking for little green men.”  I think it’s more useful to try to improve telescopes and data processing techniques, but I don’t think anyone should be stigmatized for pursuing their intellectual curiosity. Stigma usually means less funding, less access to highly sought after observation hours on the best telescopes, and less people choosing to join the field.
Physics: Radio signals decay in power as the distance squared and even the nearest star, Proxima Centauri, is 4.3 light years or about 271,937 AU away from our solar system.  That means they would need an enormously powerful emitter and we would need a very sensitive detector to detect their signal.  See: how far away could we detect that Earth has life?.


Is there a gas giant orbiting TRAPPIST-1? I would like to know if besides these planets, astronomers have discovered a gas planet like Jupiter in this system and if on these planets could exist life without a comet protector like Jupiter does for the Earth.

No such planet has been announced as having been discovered. The paper only shows evidence for the 7 (really 6 because the 7th can't be officially confirmed with only 1 observation) terrestrial planets and does not make the case for any other planets. The paper doesn't indicate that more planets could exist, but does remark that there are large error bars on some of their data, leaving room for uncertainty.

Ultimately, I think we can cross off a gas giant existing in this system for a few reasons.

We don't see transit timing variations due to a gas giant. A gas giant would have noticeable gravitational influences on the inner 7 planets and we would see this influence by the small variations in the orbital periods of the inner planets. The authors of the paper did see transit timing variations, but they were able to explain all of the variations as due to the gravitational influences of the 7 planets only. They never had to invoke an 8th unseen planet to explain what they say.
We don't observe such a (easily-detectable) transit. There are only two reasons we wouldn't see the transit of this planet. Either the gas giant is orbiting in a different plane than the rest of the planets (which are all remarkably close to the same plane, as pointed out by the authors), or else the orbital period is so long, it was never captured by any of the previous observations (which spans a number of years). Neither situation seems likely to occur.
The mass of the central star is only 8% of the Sun's mass. Smaller stars tend to form smaller planets. Its really hard for gas giants to form around small stars, primarily due to lack of material. From what we understand about planet formation, the chances of a gas giant even being able to form around this star is pretty small.

Of course, only continued observation will really be able to convince us that a gas giant doesn't exist.

  On these planets could exist life without a comet protector like Jupiter does for the Earth?

This is a great question. I think the answer is, we can't be sure. Jupiter does do a great job shepherding comets and protecting the Earth. Possibly this system is rife with comets that constantly bombard the planets. However, that's just one small part of the puzzle. Our Moon does a phenomenal job in protecting us as well.

I think, when it comes to these planets, your primary concern for whether life can exist or not is the central star. It is a low-mass, ultra-cool dwarf star. These stars tend to be very volatile, much more so than our generally quiescent Sun. This means these planets are likely to receive much more radiation and be hit by many more solar storms than we are. Furthermore, these planets are so close to TRAPPIST-1 that they're all tidally locked - one face is always towards the star and one is always away. This could make one side inhospitably hot and the other inhospitably cold. The climate/weather on such a planet would likely be unsuitable for life (but who knows for sure). The tidal locking could potentially be good though as it means only the outward-facing side would generally be hit by comets, thus protecting any life on the Sun facing side (assuming its not too hot on that side).


How can there be anything "beyond" the CMB? Two things we take, for this purpose, to be axiomatic:

The CMB is the oldest thing we can observe directly
The cosmological red shift tells us how "old" something we are observing is

Yet we also have a third axiom:

There are some parts of the universe we can never observe because they are receding away from us at a superluminary speed.

But this surely also implies that we can see beyond the CMB if we see anything which has a red shift indicating an expansion speed very close to $c$.

This suggests axiom 2 is incorrect - so what should it be instead?

Yet we also have a third axiom:

  There are some parts of the universe we can never observe because they are receding away from us at a superluminary speed.

This is simply false, so of course it gets you in trouble if you insist on taking it as axiomatic. The average recession velocity goes luminal at redshift $z\approx 1.4$, while there are observed galaxies and objects at $z\sim 8$, e.g., Z8 GND 5296 dwarf galaxy and the GRB 090423 gamma ray burst. Additionally, there are at least some candidates for objects much farther than even that, possibly $z\sim 12$.

That means that other than the CMB itself, the most distant and most ancient object we might have observed hails from when the universe as around $370\,\mathrm{Myr}$ old, which is around a thousand times older than the recombination epoch when the universe first became transparent and hence when the cosmic background radiation was emitted. In terms of redshift, the CMB has $z\gtrsim 1100$ or so.

  But this surely also implies that we can see beyond the CMB if we see anything which has a red shift indicating an expansion speed very close to $c$.

Something at redshift $z\gtrsim 1100$ has a recession velocity of $v\gtrsim 3.2c$.

  This suggests axiom 2 is incorrect - so what should it be instead?

Since (3) says incorrect things, it's best to throw it out instead.


How do scientists differentiate between a total and a partial transit of a planet passing in front of its star? Say there's a star in our local neighborhood with a Jupiter-sized planet orbiting around it. This planet's orbit happens to lie approximately in our line-of-sight – we can only see a quarter of it transit in front of its star.
All scientists do is look at the amount of starlight blocked during a transit and deduce the size of the planet.
So since this planet only partially transits, are scientists able to tell it's a partial transit and the planet is actually Jupiter-sized? OR are they going to naively assume it's just a smaller planet passing in front of its star?

The shape of the transit is different if there is a partial transit, not just the depth.
As a planet passes fully in front of the star, the brightness is almost constant while it is transiting (bar the limb darkening effect). Hence you get a "bucket-shaped" eclipse with a wide, flat bottom.
If the transit is partial then you get a more "U-shaped" and finally a "V-shaped" eclipse because there is a singular minimum point when the maximum area of star is obscured.
In this way you have both the shape and depth of the transit to work with and this can give you both the inclination (or rather the "impact parameter") of the exoplanet orbit and the exoplanet size.


What created the big bang's singularity? I have heard theories for the big bang like: of another universe existing before the Big Bang, or an unstable white hole that blew up, or our universe detaching from our mother universe, or our universe coming out of a black hole. Most of these theories don't make sense, and I want to know the most-likely-to-be-true theory for how the singularity was made.

No one knows what came before the Big Bang if, indeed, anything did.  Theories include:

The Ekpyrotic universe theory where the BB was the result of the
collision of branes.
Various oscillating universe theories where
the expansion of the universe ultimately reverses into a Big Crunch
Quantum fluctuation models where a zero-net-energy universe is a
quantum fluctuation from nothing.
Various multiverse models
where the universe we see is only an infinitesimal bubble in a much,
much, much larger universe.
The Hartle-Hawking idea where
spacetime gets a bit scrambled and there is no before. (Really:
time turns into a space dimension if you go far enough back, and
there is no time.)
Stringy stuff. Very difficult math.

I've only scratched the surface -- making models like this is an avocation to some physicists, while others have discovered that it sells books and generates publicity.  All of the theories have one thing in common: There is no experimental evidence for any of them. Additionally, many of the theories have been shown to contradict currently-understood physical law. (Especially the 2nd Law of Thermodynamics.) The authors generally just shrug and write another paper.

(On the religious side, speculation about what happened before Creation has been around as far back as written history, with roughly equal success. In the 4th century St. Augustine, after being pushed to answer that question retorted that before the Creation, God was creating a Hell for people who ask such questions.
 That didn't stop the speculation either.)


What is the longest observable wavelength of light using an optical telescope? How far outside the visible spectrum could an optical telescope feasibly operate?

I guess it depends what you mean by an optical telescope.

However, if you just mean any telescope that can record images at visible light wavelengths, then it is possible to use these (with the appropriately cooled instruments) to make observation at so-called mid-infrared wavelengths of $\sim 20$ $\mu$m.

See for example on the Gemini telescopes
https://www.gemini.edu/sciops/instruments/midir-resources

The background noise at such wavelengths is extremely high - the telescope and sky look hot at these wavelengths - so these instruments have largely been superseded by space observatories like Spitzer and WISE.

Almost all large "optical" telescopes are routinely used to make observations out to $2.4\ \mu$m (the K band).


Does the sun have a feature like the red spot on Jupiter? Does the sun have a feature or prominence like the red spot on Jupiter? Is there a feature that will remain as long as the red spot?  Maybe beneath the surface?

The Sun has lots of features "like the red spot", but they are dissimilar too.

Similarities: The Sun's photosphere - the bit we can see - is entirely gaseous; the photosphere rotates differentially with solar latitude; the gas is turbulent. There are features that can be seen quite easily - these are the dark magnetic sunspots, typically of size a few thousand km; and the pattern of bright points surrounded by dark lanes, known as granulation, typical sizes of order 100 km.

These features are associated with the convective upwelling of hotter material from below. In sunspots that process is inhibited by magnetic fields so that the surface temperature is lower and that area looks dark in comparison to the rest of the photosphere. Granulation is the visible appearance of the tops of the upwelling convective cells.

However, these phenomena are short-lived compared with the GRS on Jupiter. Sunspots have lifetimes of maybe a month or two and then the magnetic fields are reordered by the Sun's differential rotation and sheared apart. Granulation is ever present but the detailed pattern shifts on timescales of hours as different convective cells rise and fall.


What caused this mysterious stellar occultation on July 10, 2017 from something ~100 km away from 486958 Arrokoth? In 2017 a series of stellar occultations by asteroid 2014 MU69 "Ultima Thule" now officially named 486958 Arrokoth were timed in order to obtain better orbital information before the New Horizons flyby and to look for additional large chunks of debris that might be of scientific interest and pose a danger of collision thereby warranting a more distant flyby.
There was a pleasant surprise in the shape of the asteroid determined from an array of portable telescopes deployed across the occultation paths. The asteroid appeared to be binary, which was puzzling because there were no obvious oscillations in its light curve, but that's a different story.
Below is an assemblage of three such occultation measurements. We can see the asteroid's double circle shape nicely. But what interests me here is the single trace for July 10th. It seems to show an occulting object clearly distinct from yet incredibly close to Arrokoth. A pure coincidence would be more than extremely unlikely as the time window is seconds and the distance less than 100 km at ~45 AU!
Question: But I don't remember reading about a separate secondary body orbiting Arrokoth. So what caused this apparent occultation on July 10, 2017?

From this answer to Will the upcoming observations of occultation by Arrokoth (2014 MU69) be of a single object, or two?

There were three attempts to measure Arrokoth by occultation, and the June 3rd attempt didn't detect anything.  The July 10th attempt had a tiny blip, that appeared to be in the "wrong place", well away from the location that astrometry had predicted. The July 17th occultation was successful, it determined the shape and location well.
Some thought that the July 10th "blip" might have been evidence of a moon.
It was not, it turned out that there was an error in the software that was used to produce the astronometry (the author of the software describes one as "a case of me failing to read my own documentation, another one a sign error") If those bugs are fixed, then the blip on July 10th is moved to the same place as the blips on July 17th.  That blip is Arrokoth.


2017 solar eclipse report I'm writing a report about the solar eclipse happening over north America and was wondering why looking at a solar eclipse is worse than looking at the sun regularly. In addition what alternate materials can be used to make eclipse glasses that are safe to look through.

Normally people don't focus their eyes on the sun; its always in the sky but noone usually has a reason to look at it so you never focus on it, and most know not to. During an eclipse thats exactly where you want to look and focus on, and focussing on it makes it even more dangerous (guessing due to time spent with same area of your retina receiving the focussed energy from it rather than moving around your view and unfocussed spot).

During totality (darkest part of 100% eclipse) your eyes start to adjust for the dark sky and open up, allowing even more light in; as sun comes out of totality it gets very very bright again quite quickly, and your eyes might not be ready for it - use protection as you see the diamond ring start to get bigger/brighter (or only look at the diamond ring on the way into totality for safest view, when its getting darker).

The same effect as totality is almost had by using eclipse glasses or other dark viewers that cover your head/eyes, and switching from that view back to unprotected view of the sun could be equally as dangerous for the same reason.

(I'm not an expert).


Can a photon have a stable orbit around a black hole? Can a black hole free from an accretion disk collect photons in the photon sphere in a prolonged stable orbit?

Could enough photons be in orbit to shade the actual black hole with light?

Would a rogue black hole appear to have an atmosphere made of photons from the light emitted from other distant stars entrapped and released?

For any massive object the gravitational potential energy is given by Newton's law:

$$ V(r) = -\frac{GMm}{r} $$

The gravitational potential energy is due to the attractive gravitational force, but for an orbiting object there is also a (fictitious) centrifugal force pushing it outwards. If we calculate the potential energy due to the centrifugal force and add it to the gravitational potential energy we get an effective potential energy:

$$ V_\mathrm{eff}(r) = -\frac{GMm}{r} + \frac{L^2}{2mr^2} \tag{1} $$

where $L$ is the angular momentum, which is a constant for an orbiting object (because angular momentum is conserved in a central field). If we plot this graph for the Earth-Moon system we get a graph like this:

(this comes from my answer to the question Could we send a man safely to the Moon in a rocket without knowledge of general relativity? on the Physics SE)

Note that there is a minimum in the potential energy curve, and this minimum gives the radius of the stable orbit. Note also that because it's a minimum if we displace the object away from the minimum it will fall back towards the minimum again i.e. this is a stable orbit.

Now, for light we cannot simply use Newtonian mechanics because light is massless, but we can do the calculation using general relativity. The details are a bit intimidating, but we end up with an effective potential just as described above. For light the effective potential turns out to be:

$$ V_\mathrm{eff}(r) = \sqrt{1 - \frac{2GM}{c^2r}}\frac{L}{r} \tag{2} $$

And if we graph this it looks like this:

This looks very different from our first graph, and it's different because light is massless and only ever travels at the same speed of $c$. The graph of $V_\mathrm{eff}$ for light has a maximum not a minimum. The maximum corresponds to the position of a circular orbit, just like the minimum in the first graph, and we find the radius of this circular orbit is given by:

$$ \frac{r}{r_\mathrm s} = 1.5 $$

where $r_\mathrm s$ is the Schwarzschild radius. This radius gives the position of the notorious photon sphere.

But for light $V_\mathrm{eff}$ has a maximum not a minimum. That means if we displace the light by even the tiniest distance from this maximum it will lower its potential energy by moving either inwards or outwards. The orbit at $1.5r_\mathrm s$ is unstable and the tiniest perturbation will cause the light to spiral into the black hole or away from it. This means we cannot accumulate light in the photon sphere as the question asks. Any attempt to put light into this orbit is doomed to failure as even the tiniest perturbation (e.g. from other objects orbiting the black hole, or even from passing gravitational waves) will destabilise the orbit and the light will be lost.


Does Halley's Comet travel past the outer bounds of the Oort Cloud? We know Halley's Comet returns every 75-76 years. We can reasonably compute its elliptical orbit.
We know that the Oort Cloud is a cloud of predominantly icy planetesimals proposed to surround the Sun at distances ranging from 2,000 to 200,000 au. We divide it into  two regions: a disc-shaped inner Oort cloud (or Hills cloud) and a spherical outer Oort cloud.
We know that some comets are thought to have originated from the Oort cloud.
My question is: Does Halley's Comet travel past the outer bounds of the Oort Cloud?

No. Halley's Comet has an aphelion of 35 AU, which is  far less than the believed boundaries of the Oort cloud.
Any object on an elliptical orbit  with a perihelion of 0.6 AU and an aphelion of 2,000 AU has a semimajor axis of about 1,000 AU, and orbital period of about 31,600 years, much longer than Halley's Comet's current orbital period of 75-76 years. To get out to 200,000 AU and back on an elliptical orbit, you'd be looking at an orbital period of more than 31.6 million years.
As mentioned by @NilayGhosh and @planetmaker, 1P/Halley likely started as an Oort Clout object, was perturbed into becoming a long-period comet, and probably  subsequently became the prototypical periodic comet through gravitational interactions with the solar system's gas giants at some point in the last couple hundred thousand years.
As such, though it is possible that Halley's comet may have been in an orbit whose aphelion went beyond the outer boundary of the Oort Cloud in its long-period-comet days, it certainly does not do so now.


What is the underlying nature of the dark spot found on Uranus? What is the nature of bright spots found on Uranus? actually quotes Space.com's Uranus Has a Dark Spot which says:

During the past decade, many bright spots have been seen on Uranus in both red and near-infrared filters. But this is the first dark spot ever seen on the planet.

Question: So I'd like to know if there is any science-based thinking on the underlying nature of the dark spot on Uranus beyond "it looks dark, like the ones on Neptune". Has this all been sorted out or is it still mostly a mystery?
Wikipedia's Climate of Uranus; Uranus Dark Spot gives a lot of descriptive information and relates the spot to similar things seen on Neptune, and describes some speculation, but this article does not seem explain much.

Just as we near the end of the hurricane season in the Atlantic Ocean, winds whirl and clouds churn 2 billion miles away in the atmosphere of Uranus, forming a dark vortex large enough to engulf two-thirds of the United States. (Image credit: NASA, ESA, L. Sromovsky and P. Fry / University of Wisconsin)

There is a science-based approach to explaining the dark spot on Uranus. In 2009 (the image and sighting of the spot in question are from 2006) a paper was published titled: The Dark Spot in the atmosphere of Uranus in 2006: Discovery, description, and dynamical simulations by H.B. Hammel a, L.A. Sromovsky et. al..
In this work they say that the dark spot is a wind vortex. Quoting the paper:

Regardless of how it is computed, the dark features's zonal velocity is higher than all other velocities measured to date near that latitude.

Using computer simulations they are able to predict possible initial velocities, lifespan of the Vortex, center latitude of the initial and center latitude when it reached the end of its lifespan. They go further and state that the mere existence of the vortex shows the dynamic and evolving seasonal nature of Uranus's atmosphere.

So I'd like to know if there is any science-based thinking on the underlying nature of the dark spot on Uranus beyond "it looks dark, like the ones on Neptune".

The abstract explains that the spot has a markedly different spectral character than the one on Neptune:

The dark feature's contrast and extent varied as a function of wavelength, with largest negative contrast occurring at a surprisingly long wavelength when compared with Neptune's dark features: the Uranus feature was detected out to 1.6 μm with a contrast of −0.07, but it was undetectable at 0.467 μm; the Neptune GDS seen by Voyager exhibited its most prominent contrast of −0.12 at 0.48 μm, and was undetectable longward of 0.7 μm. Computational fluid dynamic simulations of the dark feature on Uranus suggest that structure in the zonal wind profile may be a critical factor in the emergence of large sustained


Has optical interferometry been done at radio frequency using heterodyning with a laser in a nonlinear material? If one collects narrow band optical emission from a large telescope with frequency $f_1$ and mixes it in a nonlinear crystal with laser light of a nearby frequency $f_2$, it would produce two new signals at $|f_1+f_2|$ and  $|f_1-f_2|$.
The difference signal $|f_1-f_2|$ could be picked up electromagnetically or perhaps it would be detectable as an AC component in a photodetector somehow, perhaps the photodetector would be the nonlinear element itself.
Once the signal is electrical, it could be recorded for later playback and offline interferometry, or for transmission over large distances for large baseline optical interferometry, or both.
Is this "a thing"? Has anything like this been done or at least tried?

Perhaps I've got it, or them.
These may be what I was thinking of, an optical intensity interferometer based on the Hanbury Brown and Twiss effect effect, but down-converting via heterodyning with lasers.
However: instead of the heterodyne down-conversion process happening in an optical crystal producing radio waves that are electrically amplified, mixing and detection happens in a semiconductor crystal acting as a photodiode and the output signal being photoelectron current. So this is not exactly what was described in the question. Since this is more likely to be the right way to do the measurement, probably I mis-remembered the conversion to radio followed by electronic amplification.

Possibility of Measuring the Width of Narrow Fe II Astrophysical Laser Lines in the Vicinity of Eta Carinae by means of Brown-Twiss-Townes Heterodyne Correlation Interferometry
The paper has a nice explanation of the effect and the measurement they are proposing.
There is light amplification and photons are bosons, etc.

Abstract
We consider the possibility of measuring the true width of the narrow Fe II optical lines observed in spectra of the Weigelt blobs in the vicinity of Eta Carinae. The lines originate as a result of stimulated amplification of spontaneous emission of radiation in quantum transitions between energy levels showing inverted population (Johansson & Letokhov, 2002, 2003, 2004). The lines should have a subDoppler spectral width of 30-100 MHz, depending on the geometry of the lasing volume. To make measurements with a spectral resolution of R > 107 and an angular resolution better than 0.1 arcsec, we suggest the use of the Brown-Twiss-Townes optical heterodyne intensity correlation interferometry. The estimates made of the S/N ratio for the optical heterodyne astrophysical laser experiment imply that it is feasible.

and more importantly from the introduction:

The Brown-Twiss correlation interferometry (Hanbury Brown & Twiss, 1956;
Hanbury Brown, 1974), modified by heterodyne detection using a CO2 laser as
a local oscillator (Johnson et al., 1974) for the 10 µm region, is well suited to achieve very high angular and spectral resolution simultaneously. We will call
this method the Brown-Twiss-Townes (BTT) technique. In the range 0.9-1.0
µm this can be done today by means of two spatially separated telescopes
equipped with two heterodyne photoreceivers, e.g. avalanche diodes, and a
tunable semiconductor laser diode transporting its radiation via an optical
fiber (Sect. 3). A general approach of this method has already been considered and discussed in a non-astronomical journal (Lavrinovich & Letokhov,
1976; Letokhov, 1996). In the present paper, we focus on the use of the BBT
correlation heterodyne interferometry to study the Fe II laser lines in the range
0.9-1.0 µm and the appropriate signal-to-noise (S/N) ratio estimates (Sect. 4).

And from Section 3:

To master new wavelength regions and achieve high spectral resolution levels, the intensity interferometry method was modified to become heterodyne interferometry (Johnson et al., 1974). This technique uses a local monochromatic laser oscillator to produce beats between the light wave of the star of interest and the coherent laser wave of the local oscillator. The method can be considered intermediate between intensity interferometry and direct interferometry. Townes and co-workers made successful observations in the 10-µm infrared window of the atmosphere using a CO2 laser as a local oscillator (Johnsson et al., 1974; Townes, 1977). The baseline used consisted of a pair of auxiliary telescopes spaced a few meters apart at Kitt Peaks solar telescope.

M. A. Johnson, A. L. Betz, and C. H. Townes, 1974 10-μm Heterodyne Stellar Interferometer

A spatial interferometer for 10-μm wavelength which uses two independent telescopes separated by 5.5 m, heterodyne detection of the infrared radiation, and path equalization by a variable-length rf cable, has given interference fringes from radiation of the planet Mercury. Continuous fringe observations during 4000 sec indicate remarkable stability in the optical-path difference through the atmosphere and the two telescopes, fluctuations between 20-sec averages being about 1/6 of the 10-μm wavelength.

D. D. S. Hale et al (2000) The Berkeley Infrared Spatial Interferometer: A Heterodyne Stellar Interferometer for the Mid-Infrared

A detailed description is given of the Infrared Spatial Interferometer (ISI), developed at the Space Sciences Laboratory of the University of California at Berkeley, which is a high spatial resolution interferometer for mid-infrared wavelengths. The instrumentation, its capabilities and performance, data analysis, science program, and future plans are all discussed. The system's use of heterodyne detection, analogous to that of a modern radio interferometer, is also compared with the homodyne or direct methods more commonly encountered in the visible and infrared. The ISI has been operating productively on Mount Wilson for the past 10 years measuring materials immediately surrounding stars and their changes as well as some stellar diameters. The new spectral capabilities described here, a recent increase in baseline length, and the upcoming expansion to a closure-phase imaging array provide important additional types of measurements.

FIG. 1. Conceptual block diagram of the  ISI optics, circuitry, and heterodyne detection system, including laser phase lock and path length compensation systems. Telescope 1 and its trailer, with associated optics and circuitry, is enclosed within the dashed line. Telescope 2 is represented by equipment outside the dashed line. The trailer for telescope 1 is the primary operating location, with the central computer, delay line, correlator, and data acquisition equipment. Telescope 2 and its trailer contains path-length compensation equipment in addition to the necessary optics and detection hardware. When a third telescope is installed, the controls, delay lines, data acquisition, correlators, and other equipment not needed in each single telescope, will be housed in a central station.

See also

Conceptual Design and Applications of HgCdTe Infrared
Photodiodes for Heterodyne Systems, part 2 (big)
Conceptual Design and Applications of HgCdTe Infrared Photodiodes for Heterodyne Systems


Will biological process be disrupted under strong gravitational time dilation? This question is raised by someone I've discussed with, after watching the movie "Interstellar", in which a clip showing Cooper and Amelia landing on Miller's planet near a super-massive blackhole and they experienced quite amount of time dilation due to the gravitational effect. They spent like 20 minutes there and when they backed to the station they found out that 23 years have passed on station (where Romilly waited them for 23 years to return).

It's okay for this conception to be implemented here I believe most people will understand. We will just think that yeah 23 years has passed but they just feel normal, just like a 20-minutes park walking. BUT, no one has ever experienced such a strong time dilation, how could you be sure Cooper "just feel normal"?

I remember reading a book which says if you are rushing directly to center of a blackhole, when you are very very close to the Schwartzchild radius, you may experience a whole lifespan of universe IN A SECOND, in other words, you are rushing to the real end of the world. I really doubt any life could 'feel' that second passing. Anyway, this is an extreme example.

So the question: will biological process behaves normal under certain gravitational condition? If it does, can we feel differently? Does our conscious get used to the normal time flow all life on earth are living with? more crudely, will we die due to the extreme time dilation caused by gravity (provided that gravity affect homogeneously upon us) and if so, how?

An interesting extra: If Romilly could observe Cooper from station and sees a near still 'slow-motion' picture of him, will Cooper conversely see a 'fast-motion Romilly' from the ground of Miller's planet?

Remember this is a theory of "relativity". Now, time dilation due to gravitation effects is rather outside our normal experience. But there are relativistic effects that that you experience all the time.

I'm sitting on a train. Relative to my computer I'm not moving. Relative to the track I'm travelling at 100km/h. Relative to the sun I'm moving about 30 km/s, as the Earth orbits. Relative to a distant galaxy I'm moving close to the speed of light.

But in my frame of reference, I'm not moving at all. So, even though I'm moving at nearly the speed of light, relative to some distant galaxy, I don't notice any slowing down of my watch. My watch is moving with me, in my frame of reference.

It would be the same if you were experiencing intense gravitational time dilation. For example, if you were falling around a black hole. Your watch would be in the same frame of reference as you, so there would not be any observable difference, locally.

If you tried to stop yourself falling, the force required would crush you. Small black holes have such extreme variation in gravity that your head and feet would be pulled apart by the tidal difference, and if you passed the event horizon, you can never come back. So you would be dead if you tried the experiment in practice. However "gravity" itself can't hurt you, only variation in gravity or your own attempts to act against gravity.


Can I see Jupiter, Mars and Saturn through the National Geographic 76/350 Dobsonian Telescope? Is it possible to see Mars, Jupiter and Saturn through the National Geographic 76/350 Dobsonian Telescope? It's the most affordable telescope I can get at the moment. Also, what about the moon? Will it look small?
Specifications

Diameter: 76mm
Focal length: 350mm
Magnification: 18x-117x
Eyepieces: 6mm, 20mm
Barlow lens: 2x
Compass
Moon filter

I see that you have correct data for the magnification. Possible magnifications: 18x, 36x, 58x, 117x. The rule of a thumb is, that for optimal observing of the planets you set the magnification of 20x to 30x for every inch of the aperture. Your aperture in inches: 3. That means, that the optimal magnification is from 60x to 90x. But this rule applies to telescopes with better optics. I don't know how good the mirrors are, but I would recommend the setup with 6 mm eyepiece without a Barlow (= 58x). With this setup, you can observe the disc of the Jupiter, but also the rings of the Saturn. You will be able to see main craters and mare on the Moon.
If you place the Barlow on the scope, the magnification is too high for the small aperture. You should consider it only when observing near double stars. Magnification of 117x won't be useful with planets. Why? Look at the icon in the title bar of this Stack Exchange. When it is small like it is now, you can resolve the big letter A. But if you expand it to the whole screen, you would see only pixels and some form of A. Smaller picture is better, but not too small. Let this rule guide you.

So what is the answer? You will be able to see the Moon and its mare and some craters, but also Saturn with his rings. Jupiter's disc will be seen with ease, but harder will be Mars just on peaceful nights. What about Venus? Maybe better than Mars, but just small Moon like form. Mercury will be visible only as small dot. Neptun and Uranus are too dim to be observable with this telescope, but maybe you will be able to see them with some experience after 1 or 2 months (only like normal stars, maybe blueish). If Pluton is planet for you, it is far beyond the range of your scope. Even I couldn't see it never with my aperture of 250 mm.
But planets aren't everything. If you have budget for buying the solar filter (cheap ones for 10 dollars), you could point the telescope towards the sun, but beware! Don't mimic Galileo Galilei, who was observing the sunspots throught the telescope when the sun was low without solar filter! Check the page https://spaceweather.com/ for sunspots. Also, you could look at the globular clusters with the smallest magnification. Try Andromeda galaxy! It won't have some visible form, but it will be some cloud of brighter region. You could try also nebulae, for example M 57 in Lyra.
You see that you can do a lot with this telescope, but it won't be some spectacular sight and these are the only things you could observe. For more, you have to buy the better telescope. Hope you will have fun with it!


Distance of a planet to the star? QUESTION:
Suppose we discover a planet orbiting a nearby star.
The distance to the star is 3 pc.
We observe the angular radius of the planet’s orbit to be 0.1 arc sec.
How many AU from the star is the planet?

**CONCERN: I am not sure what "The distance to the star is 3 pc" means. The earth's distance to the star? or the sun's distance to the star? or even better, the planet's distance to the star??!!

Any explanation of the question would be greatly appreciated!

My initial approach was some fixed position (say sun/earth's distance) to the star is 3pc,
so I will have    0.1 arc sec = 3pc/distance, and solve for distance as the answer.
(I reckon this is a very simple question for astrophysics, but I need to get basics right)

Use this (http://www.ast.cam.ac.uk/~mjp/calc_parallax.html) but substitute the exoplanet for the Earth, you don't need to involve the Sun in your calculations, just assume the star is 3pc (parsecs) from Earth.

  From Figure 2, the distance between the Sun and the star is :
  d = r / tan P
  If P is 1 second of arc:
  d = 150 000 000 / tan 1" = 30 million million km
  This distance is called one parsec and is a basic unit for measuring astronomical distances.
  Distance in parsecs = 1 / P in seconds of arc


How many generations of stars can be formed in the Stelliferous Era? As in general case, stars are formed from nebula which in some case itself is the result of a supernova.
Also stars need hydrogen to become a star (to do nuclear fusion), but stars consume hydrogen in their lifecycle. Thus, less and less hydrogen is left for the future generation and more heavy elements take that place.
How many generation of stars can be formed until there is no more enough hydrogen left to create new stars?

One can make a theoretical upper bound by considering the most short-lived star possible $\tau_{short}$, and a large supply of initial hydrogen $M_H$. Then one could calculate the fraction hydrogen that is recycled $r$ after the star ends (with a supernova), and get a total number of generations as $ \log (M_{star}/M_H)/\log(r)$. If one uses the solar-mass $r\approx 0.5$ and a galaxy mass of gas $M_H=10^{10}M_\odot$ one could get 33 generations.
One could of course try tweaking this by using heavier stars that recycle better yet are not affected by the growing metallicity of the medium, but it would be rather wasted effort: it is not a realistic model.
The overlap between generations is growing: stars are made today from mixed gas recycled from all previous generations. They also last very different lengths of time depending on mass, so the gas reservoir does not conveniently fill up for the next generation to be created, but rather is topped up while star formation is ongoing. So speaking of generations becomes less and less useful, and instead it makes sense to mainly speak of when a star formed or how much metals it had at the start due to a highly evolved gas reservoir.
One can simulate star formation and recycling by using models of each, but it quickly turns rather complex and worse, dependent on assumptions about how much intra-cluster gas will fall in the future, something that is weakly constrained. Current trends in star formation suggest that we are close to peak star number and that peak star formation was in the past, so relatively few stars will form in the future until the gas levels go below a critical surface density and shuts off (see section D in this paper). But if intra-cluster gas cools and rains down slowly that may prolong things a fair bit. Still, in about $10^{14}$ years normal star formation will have ceased.


If the Sun disappears right now, when the absence of its gravity affects on Earth? Imagine if the Sun disappears right now. When the Earth will be affected by its absence? Does it affect immediately, or it takes almost 8 minutes? (The time that light travels from the Sun to the Earth.)
So if I ask this question in another way, the changes in Space-Time will affect immediately or it will travel by light speed?

As we know by General Relativity, gravity propagates by the speed of light c = 299,792,458 m/s in a vacuuum (like space).
The average distance between the earth and sun is about 149.6 million kilometers, so it takes light about 8.3 minutes from the sun to earth.
This means, if the sun were to disappear right now, we would have to wait 8 minutes and 20 seconds until we would realize. Luckily, by all known laws of physics, this is not possible :)


Date and time system on moons Supposedly, if humans were to establish a colony on one of the moons of a planet (such as gas giants in our own solar system), how could we possibly design date and time system? On Earth, we define date based on rotation about Sun and time on Earth's revolution. But, with a moon of another planet, this will add another factor to date/time system. So, how can we cope with this?

PS: I am not sure about what tags this question should carry. Feel free to correct them.

I really love this question. Were we to establish a colony on our moon, we would probably want a calendar/time system which actually corresponds to physical patterns and cycles on the moon, but also something which is easy to track and keep in sync with Earth, since the two civilizations would certainly be in close contact.

In a way, we already do something this here on Earth with time zones, though time zones are just offsets within the same second/minute/hour/day system, so people throughout the world are in different times, but they stay in sync. But beyond that, our entire calendar system (we currently use the Gregorian Calendar), is mostly based on our own planet's positions relative to the sun. It just wouldn't make sense on the moon. Earth days on the moon would just be arbitrary 24-hour blocks of time; they wouldn't correlate at all to whether it's light or dark outside.

So, if we really wanted to keep some logical synchronization between earth and moon calendars, we would probably want to adjust here on earth to a lunar-based calendar. Most older civilizations did this, using a full lunar cycle to indicate a "month." But here's the (cool) thing: the moon is a little lopsided and way gravity works, the exact same side is always facing us. We never see the back of the moon. So, it's rotating at exactly the same speed as it's revolving around us, meaning a "day" on the moon lasts one full lunar cycle: just over 29 earth days. So even the idea of a day, how long a day is, and what you could accomplish in a day is so far from Earth's that it's hard to even compare the two.

Maybe one idea is to have weeks or months here on Earth which would line up with days on the moon. Earth would still have its 24-hour days and the Moon would have its 709-hour days, but at least we could predict Moon time using our own calendars. One proposal is the The Hermetic Lunar Week Calendar which continually adjusts the length of a week to keep the months in sync with the moon, so that a full month is always one lunar cycle (or lunar day). It would be weird but in a future where humans are legitimately split between Earth and Moon, it would probably make sense for both to keep a calendar like that, which takes into account the length of a day on both bodies.


Estimating galactic dust extinction for medium band filters I have a set of medium-band filters and I would like to compute $A_{\lambda}/E(B-V)$ for each filter which are not reported in the literatures. The magnitudes of the objects in the photometry catalogue should be corrected for the galactic dust extinction using Cardelli et al. 1989 law.

Update

In appendix B of D.J. Schlegel, D.P. Finkbeiner, & M. Davis (1998, ApJ, 500, 525) estimating the $A_{\lambda}/E(B-V)$ for filters is obtained by using this equation
$$
\Delta m_f=-2.5\frac{\int d\lambda W_f(\lambda)F(\lambda)10^{\frac{-A(\lambda)\Delta m_V}{2.5}}}{\int d\lambda W_f(\lambda)F(\lambda)}
$$
$\Delta m_V$ is the reddening magnitude of an elliptical galaxies and $F(\lambda)$ is the flux of source and $W_f(\lambda)$ is the response function of a filter. I am wondering how I can use  Cardelli et al. 1989 law to estimate these quantities for different filters or there is an alternative approach?

The quantity you want is basically the extinction law, and is usually called $k(\lambda)$. An extinction law is a fit to several measurements of the extinction $A_\lambda$ in some direction (or an average of several directions).

Cardelli et al. (1989) provides different functional forms for the mean extinction law, parametrized in their Eq. 1 as
$$
\frac{A_\lambda}{A_V} = a(x) + \frac{b(x)}{R_V},
$$
where $x$ is the inverse wavelength in $\mu\mathrm{m}^{-1}$, and the coefficients are given separately for IR, optical, UV, and FUV in Eqs. 2, 3, 4, and 5, respectively. The total-to-selective extinction $R_V\equiv A_V/E(B-V)$ takes different values for different lines of sight, but usually lies in the range 2.5 to 6, with 3.1 being a typical value in the Milky Way.

To get the quantity you're interested in, simply convert your favorite wavelength to $x$, stick into Eq. 1, and multiply by $R_V$:
$$
k(\lambda) \equiv \frac{A_\lambda}{E(B-V)} = \frac{A_\lambda}{A_V} R_V.
$$


What's the differences between one-dimensional spectrum and two-dimensional spectrum? mostly, we use the one-dimensional spectrum. But sometimes we use two-dimensional spectrum, what's the differences between them?

When you place a spectrograph slit on a source, the spectrum recorded can be thought of as lots of images of the slit at different wavelengths.

Ordinarily, you would sum up this spectrum along the direction of the slit images to give you a one dimensional spectrum. If however, you leave the image as recorded, then you have a two dimensional spectrum - intensity as a function of wavelength along one axis and as a function of position along the slit in the other.

Two dimensional spectra are used when we expect the spectrum to vary with position along the slit. Examples might include a spectrum recorded across a galaxy, or a spectrum of a binary star with the slit placed across both components.

An example is shown below. The inset image shows a broad-band image of V458 Vul - a classical nova that is surrounded by (not visible) shells of ionised material. The authors of this particular study lined up a spectrograph slit as shown in the inset and then obtained the two two-dimensional spectra shown in the main image. What you have to imagine is that each position on the slit produces a horizontal spectrum at a vertical position that corresponds to its position on the slit. Therefore we see a bright spectrum across the middle corresponding to the central source, but there are then "knots" of emission at particular wavelengths that are some distance away from the central star.

Slitless two dimensional spectroscopy is also possible using integral field spectrographs. Fibers record spectra over a two dimensional area. This can also be referred to as two dimensional spectroscopy.