rotation - Would an exoplanet without axial tilt have no seasons?

I considered this as an explanation for George R. R. Martin's books, where several years could go by during each season. If the planet had no axial tilt and very little eccentricity in its orbit, there would be no annual seasons. But if solar energy output would vary sufficiently, you could have seasons, with inconsistent cycle times that measured in decades.

So I thought, "Ha, it is possible."

Then some character in the book noticed "the days were getting shorter" and I had to throw it out. In such a world, day length would always be the same, and it would always match night length.

orbit - What is the optimal escape trajectory from near a black hole?

I'd like to know a little more about the geometry of the ship's trajectory. I would be asking for clarification in comments but I don't know how to put images in comments.

A good distance away the ship is moving nearly a straight line with regard to the large mass. As the ship gets closer the path gradually bends towards the large mass. If you're still a fair distance from the star, the path can be fairly well modeled with Newtonian mechanics and the curving path can be modeled as a hyperbola. The straight line the hyperbola is gradually deviating from is called an asymptote:

This illustration (page 36 of my coloring book) is a hyperbola about the earth, but it could also be a hyperbola about a larger mass.

Escape velocity climbs as you get closer to the mass. The hyperbola's speed is sqrt(Vescape^2 + Vinf^2). I use this right triangle and the Pythagorean theorem as a memory device:

If you did a burn in the opposite direction from your Vinf vector, it could reduce your Vinf and drop you even closer to the mass.

If your burn vector is at right angles to your velocity vector, it would increase your vinf (and thus raise point of closest approach aka periapsis). It would also change the direction of the hyperbola's asymptote.

To better answer your question, I'd need to know more about the geometry of this scenario, what Vesc and Vinf is and how much delta V the ship was capable of. It would be helpful to know at what distance our heroes discover they're in trouble.

If the ship has already fallen close enough that it's traveling an appreciable fraction of c, the above doesn't apply. Conics from Newtonian mechanics is a good approximation until you get too close to the black hole. Then you'd need general relativity to model the trajectory -- and that's above my pay grade.

space - The universe is dying vs the universe is ever expanding

Both are true.

The universe is "dying" in the sense that stars eventually run out of hydrogen, and there aren't infinite amounts of hydrogen in galaxies to replace old stars. This will take a very long time, but eventually all stars will burn out and new stars will stop forming. This is what the study recently in the news is saying.

The universe is ever expanding in the sense that distances between galaxies which are not bound together gravitationally is expanding all the time. If you look at very distant galaxies, they are all receding into the distance.

Combine these two facts and the result is that the universe will become more and more "rarefied" (distances between galaxies will keep expanding), and also all existing stars in galaxies will burn out over trillions of years.

the sun - How to read 5 degree data of green line intensity

The format of the files seems to be described in this file, the content of which I've included below.

The annual files (1939-1993) contain the green coronal emission line
530.3 nm observations.  The coronal intensities are given in millionths
of intensity of the solar disk (coronal units) and converted to the
photometrical scale of Lomnicky Stit Station at a height of 40" above
the solar limb.

Several stations were used in this database with Lomnicky Peak being the
primary station since 1965.

Reference:  Rybansky, et al, 1994, Solar Physics 152, p 153-159.

Data format:

 COLUMN  FORMAT   DESCRITPION
  1-  2    I2     Year, last two digits
  3-  4    I2     Month
  5-  6    I2     Day
  7-  8    2X     Blank
      9    I1     Coronal station code:
                  0 - Interpolated data
                  1 - Lomnicky Stit
                  2 - Sacramento Peak
                  3 - Norikura
                  4 - Kislovodsk
                  5 - Pic Du Midi
                  6 - Wenselstein
                  7 - Arosa
                  8 - Kanzelhohe
 10- 13    I4     Time of the observation in hours (or zero)
 14- 17    I4     Time of the observation in minutes (or zero)
 18-305  72(I4)   Coronal intensities (72 values) from 0 degrees to 355
                  degrees of position angle in increments of 5 degrees.

Using the first row data as an example...

DATE        SC  H   M   1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65  66  67  68  69  70  71  72
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
19390101    0   0   0   0   0   0   0   0   0   0   0   3   3   3   8   15  22  34  41  52  46  40  52  68  59  49  35  17  8   3   3   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   3   3   6   8   12  19  31  40  50  47  43  38  53  73  71  65  56  47  38  24  17  12  6   0   0   0   0   0   0

19390101 is the date (1939-01-01).
The first zero (Marked as SC) is the station code, the second the recorded hour, and the third the recorded minute (H/M). Most of this is 0 due to being interpolated data.

After this information, there are 72 remaining columns (numbered 1-72 above), which represents collected data consolidated in groups of 5 degrees, presumably starting at 0.

Given the amount of interpolation of old data the value may be questionable, but newer data appear to be more complete.

The data format might be a little overwhelming to work with, but you can organize it in excel quite easily - paste it in and each line break will form a row, then use the text-to-column function to break each data into its own column.

galaxy - What does "Normalized to Si 10 to the power 6" mean?

I'm writing a space game that I want to give a more "realistic" feel. When looking for a reference as to distribute elements in planets (for mining, etc) Instead of finding the more usual percentage tables, it seems that all elements are presented in a "normalized to Si 10 to the power 6", and furthermore, it seems that the data is presented as number of atoms, instead of actual mass. I've been searching this for days, and even the "parts per million/billion/trillion" tables sometimes just jump for percentages, where is is again no clear if what is being referred to are masses or number of atoms. Could someone clarify this, or better, point me to a mass percentage table of elements in a solar system/galaxy for reference? Thanks in advance.

Do all planets have a van Allen radiation belt?

Mars does not have a magnetic field of any strength and so does not have a van Allen belt (and this is a serious problem for potential human exploration of the planet). Similarly, neither Venus nor Mercury (nor the Moon, which is arguably part of a two-planet system with the Earth) have a van Allen belt.

The gaseous giants do, however, have radiation belts which are analogous to Earth's van Allen belt.

Spotting aurorae on distant exoplanets would be an indication of a strong magnetic field and thus of the likelihood of a radiation belt. I am not aware that such aurorae have been detected but distant aurorae have been seen around a brown dwarf - a substellar object somewhat bigger than a planet (see http://www.theguardian.com/science/2015/jul/29/astronomers-find-aurora-a-million-times-brighter-than-the-northern-lights).

Alternatively, the radio emissions from high energy electrons trapped in planetary radiation belts might be detectable - this was how Jupiter's radiation belt was discovered around 60 years ago. Work seems to be underway to detect such radiation: https://skaoffice.atlassian.net/wiki/download/attachments/22183971/PoS-exopla-AASKA14.pdf?version=1&modificationDate=1403003959989&api=v2

galactic dynamics - Has the great Andromeda Galaxy ever collided with any galaxies?

Galaxies grow through cosmic time by accretion of the surrounding matter. Some of its mass increase happens through smooth accretion of gas, but much also happens through merging with small clumps of dark matter, gas, and stars, called satellite galaxies. This is called "minor merging".

If merging galaxies are similar in size, it's called major merging. Most large galaxies have gone through of the order of one major merger through its life (Man et la. 2014), but whether or not it happened for Andromeda, we cannot know for certain.

However, if you take a look at Andromeda, you'll see that it has quite a large bulge, i.e. the central, reddish part of the galaxy. This region is dominated by stars with a more "chaotic" velocity patterns. That is, their paths aren't "rotation-dominated" (lie in the disk), but more "dispersion-dominated" (leave the disk). To achieve such velocities, the system has to be disturbed by infalling matter, so a large bulge is probably a signature of a major merger. Investigating the velocity patterns of Andromeda, Dorman et al. (2015) find that it has had a much more violent history than the Milky Way, and in fact models by Davidge et al. (2012) and simulations by Hammer et al. (2010) of the history of Andromeda suggest that 8-9 billion years ago, Andromeda went through a major merger.

Note however that a large bulge can also be explained, at least in cosmological simulations, by a more smooth and "cold" accretion, i.e. gas that doesn't get shock-heated (Dekel et al.)

amateur observing - How to find RA 0

A brief overview of RA is the angular distance measured eastward from the vernal equinox along the celestial equator. Another way to say that refers to where the celestial equator intersects the horizon at a right angle.

If you are able to follow the celestial equator to the point known as the vernal equinox, 0Deg RA is at the intersection point, with RA increasing directly east. The vernal equinox can be found at the first point of Aries, on a celestial sphere it is the point where the Sun crosses the celestial equator from south to north during the March equinox. The point during the March equinox is located in Pisces.

There are methods to determine the vernal equinox at other times, which can be dependent on location and the time. A great way that I personally use, is the same method as 'star hopping'. Using reference points, you can generally determine a line of sight between two or more points, for example if you are aware of a point and it's approximate RA, you can follow the path through another known RA point and evaluate the distance between the points. Following the line of sight you can them determine how far along the line the point of 0 would be, using this method takes much practice and you could even use visual guides such as a thumb as a measuring tool.

Using my thumb, I can say held at .5 meters is equivalent to 2.5 degrees, using stars as reference points I could approximate the line of sight and have a reliant measuring tool to judge distance.

The method you may require, could be entirely dependent on the reason you need to determine the point. If using electronic devices you can follow the celestial equator west along the celestial equator to find the point etc. I can explain other methods in more detail if required, others may have developed their own methods also.

the sun - Could a close passing star be captured by the Sun's gravity?

Unless the stars comes so close that they actually collide, two stars will not be able to catch each other gravitationally. The reason is energy conservation: As they approach each other, their potential energy is converted into kinetic energy, increasing their velocities. When they are closest, their velocities are at their highest, but since there's nothing to take out energy from the system, their kinetic energy will be converted back to potential energy, propelling them far apart again.

If a third star is present, however, this may be able to extract energy from the system, so that one star is slung out while the other two start orbiting each other.

Note however that the probability of two stars encountering each other extremely small, and that of three stars is close to zero.

In the above, I have ignored the presence of planets. In principle, a large planet could help, but since their masses are much smaller than the stars', their effect is quite small.

dust - The name of a particular low extinction region

The Lockman hole?

http://en.wikipedia.org/wiki/Lockman_Hole

It has a column density of neutral hydrogen of $6times10^{19}$ cm$^{-2}$, which will correspond to very little dust.

Two others I've heard of towards the Galactic bulge are known as the Sgr I and Sgr II windows.

Finally, I offer "Stanek's window" towards the bulge, which has been referred to in a number of the Chandra Galactic plane X-ray surveys but appears to have no refereed publication associated with its discovery. I found this on arXiv. http://arxiv.org/abs/astro-ph/9802307 It is at $l=0.25$, $b=-2.15$ and has $E(B-V) sim 0.6$.

optics - Is it possible to steer the sight of a Liquid Mirror Telescope using a plain mirror scheme? If yes, why hasn't it been done?

Designs where the curved primary mirror is fixed, and steering is achieved via a moving flat mirror (siderostat) in front of it (or a set of flats) have been done before. One example is the Pfund telescope. The main design constraint that led to the invention of the Pfund telescope was the need to have a focal point which is fixed in space and easily accessible.

Here's a variation of that design; the need for the fixed focal plane is driven by accessibility concerns here (the user cannot follow a moving focal plane):

Also see the related concept of heliostat - same idea, just applied to sunlight. A moving flat reflects sunlight in a fixed direction. Some solar power plants use heliostats.

So, in principle, fixed curved primary + moving flat is doable, and has been implemented a number of times. However, there are substantial issues with this design.

First off, the size and the quality of the flat mirror are not less than the size and quality of the parabolic primary. Let's say you build a liquid mirror telescope because it's easy. Then you have to make a flat mirror of the same diameter, with the same precision, and all the ease of construction is now lost. Flat mirrors are not easier to make than parabolic. In fact, as a mirror maker, I prefer to work on curved catopters - in some ways they are more predictable during manufacturing than large, high precision flats.

There are further issues down the road for the liquid mirror telescope. You would actually need 2 flats, both very large, both very precise. Both would have to be suspended in the air, above the liquid primary, and supported by complex mirror cells just like curved primaries in any telescope. Overall, it will be more difficult to make such a telescope, not less.

So why is the Pfund design used? Not for ease of manufacturing; as I said above, it's actually more difficult to make it than a regular scope. But in some situations you just need that fixed focal plane for some reason. In that case, you don't have much of a choice. Of course, it's not a design that scales well.

I am assuming a large plain mirror is much cheaper than a parabolic
mirror of the same size.

That was the incorrect assumption. Once that's taken care of, everything else should be clear.

the sun - How often do comets survive passage by the Sun?

I had heard that comet ISON might not survive a close pass by our Sun, and I was curious about the odds of how other comets had fared. So, how often do other comets survive a close pass by our sun? Also, are there any connections between a comet's size or buildup(of material) that makes it more or less likely to not survive?

Connection between Earth, Moon, Theia, and astroid belt?

Let's start answering your question in reverse. Ceres could not be "the missing Theia" (I know you don't say that; I'm addressing a side issue) because of its shape. If an object hit the Earth at an angle (as is currently thought), it would be pretty deformed, if it managed to stay together. If it hit the Earth head on . . . Well, it would almost certainly not survive. So if it did survive the impact, it would be in pretty bad shape. Where would such an object go? Let's investigate the idea that it went into the asteroid belt. That begs a question: Where is it today? Ceres is the largest object in the belt (and we've already ruled it out). If the object was smaller - small enough that it blended in - it would have been captured by the Earth's gravity. So its survival provides a paradox - it would have to be big to get out of Earth's orbit, but nothing that big is known. So chances are, Theia didn't survive the impact. The gravitational pull of the Earth also implies that any fragments surviving the collision would have to be moving pretty fast to escape - so fast that it seems unlikely that they stayed in a stable orbit.

Now for your belt-formation theory. It is, admittedly a very cool idea. The mass of the asteroid belt is about 4% that of the Moon - so it could be the result of the planetary crash. And some theories say that the belt is, in fact, the remains of a planet. There is, of course, one problem - the different composition of the asteroids. There are three types, differentiated by their composition - C, S, and M (their properties can be found online). So it is very unlikely that they came from the same planet.

Finally, your idea about the Earth having an orbit farther out. This one seems to have a good chance of being right. The early protoplanets in the solar system were very - very - unstable in their orbits because of the frequency of collisions. So the Earth could have been in a different orbit, and then migrated inwards or outwards.

I hope this helps.

observation - Why can't we observe the Oort cloud with a telescope?

The angular resolution of the telescope really has no direct bearing on our ability to detect Oort cloud objects beyond how that angular resolution affects the depth to which one can detect the light from faint objects. Any telescope can detect stars, even though their actual discs are way beyond the angular resolution of the telescope.

The detection of Oort cloud objects is simply a question of detecting the (unresolved) reflected light in exactly the same way that one detects a faint (unresolved) star. Confirmation of the Oort cloud nature of the object would then come by observing at intervals over a year or so and obtaining a very large ($>2$ arcseconds) parallax.

The question amounts to how deep do you need to go? We can do this in two ways (i) a back of the envelope calculation assuming the object reflects light from the Sun with some albedo. (ii) Scale the brightness of comets when they are distant from the Sun.

(i) The luminosity of the Sun is $L=3.83times10^{26} W$. Let the distance to the Oort cloud be $D$ and the radius of the (assumed spherical) Oort object be $R$.
The light from the Sun incident on the object is $pi R^2 L/4pi D^2$.
If we now assume that a fraction $f$ of this is reflected uniformly into a $2pi$ solid angle. This latter point is an approximation, the light will not be reflected isotropically, but it will represent some average over any viewing angle.

To a good approximation, as $D gg 1$ au, we can assume that the distance from the Oort object to the Earth is also $D$. Hence the flux of light received at the Earth is
$$F_{E} = f frac{pi R^2 L}{4pi D^2}frac{1}{2pi D^2} = f frac{R^2 L}{8pi D^4}$$

Putting some numbers in, let $R=10$ km and let $D= 10,000$ au. Cometary material has a very low albedo, but let's be generous and assume $f=0.1$.
$$ F_E = 3times10^{-29}left(frac{f}{0.1}right) left(frac{R}{10 km}right)^2 left(frac{D}{10^4 au}right)^{-4} Wm^{-2}$$

To convert this to a magnitude, assume the reflected light has the same spectrum as sunlight. The Sun has an apparent visual magnitude of -26.74, corresponding to a flux at the Earth of $1.4times10^{3} Wm^{-2}$. Converting the flux ratio to a magnitude difference, we find that the apparent magnitude of our fiducial Oort object is 52.4.

(ii) Halley's comet is similar (10 km radius, low albedo) to the fiducial Oort object considered above. Halley's comet was observed by the VLT in 2003 with a magnitude of 28.2 and at a distance of 28 au from the Sun. We can now just scale this magnitude, but it scales as distance to the power of four, because the light must be received and then we see it reflected.
Thus at 10,000 au, Halley would have a magnitude of $28.2 - 2.5 log (28/10^{4})= 53.7$, in reasonable agreement with my other estimate. (Incidentally my crude formula in (i) above suggests a $f=0.1$, $R=10 km$ comet at 28 au would have a magnitude of 26.9. Given that Halley probably has a smaller $f$ this is excellent consistency.)

The observation of Halley by the VLT represents the pinnacle of what is possible with today's telescopes. Even the Hubble deep ultra deep field only reached visual magnitudes of about 29. Thus a big Oort cloud object remains more than 20 magnitudes below this detection threshold!

The most feasible way of detecting Oort objects is when they occult background stars. The possibilities for this are discussed by Ofek & Naker 2010 in the context of the photometric precision provided by Kepler. The rate of occultations (which are of course single events and unrepeatable) was calculated to be between zero and 100 in the whole Kepler mission, dependent on the size and distance distribution of the Oort objects. As far as I am aware, nothing has come of this (yet).

Reason for a correlation between Hot Jupiters and higher metallicity in Kepler data

This is a well known, well researched phenomena. Yes, there certainly is a correlation between metallicity and the likelihood of observing a hot Jupiter.

There are two classes of explanation.

(1) The correlation is real and due to the fact that it is easier to form planetary embryos from metal-rich material in the core-accretion model of giant planet formation.

(2) The observed exoplanets are those that weren't swallowed. The hosts are metal rich because they did swallow others.

Finally, it was thought possible that there could be an observational bias. Planets are easier to find and measure around high metallicity stars. This applied mainly to the Doppler technique, because high metallicity stars have stronger spectral lines. Transit detection should be much less affected.

Most think that some form of (1) is going on. (2) is argued against because the correlation still appears in stars with a wide variety of convection zone depths into which planetary material would have mixed. I'm not sure it is dead though, there have been a number of claims for abundance enhancements that look like the product of planet engulfment.

I'll add some references later. Nice work though to discover the correlation if you knew nothing of it previously.

planet - How would I measure that I'm at a pole?

How would a person measure that he is at a planetary pole? My first inclination is to use a sextant to ensure that the Sun remains at a constant inclination. However, due to the orbit around the Sun and a possible planetary axial tilt, the Sun's inclination may vary over the course of the year and that could affect measurements if the length of the day is a significant portion of the length of the year.

A second inclination is to try to identify a pole star or at least the point about which distant stars rotate during the course of a planetary rotation. The observer could then (at least in theory) measure the inclination of this point assuming that planetary precession takes a long enough time (as on Earth). However, in the most likely chance that there is no bright star near the pole, I don't see how a sextant could measure reliably the inclination of a blank point.

Perhaps the first method could be used, but with other objects in the sky (stars) in place of the Sun. Thus, if a given star's inclination does not change as it (apparently) revolves around the horizon, we are at the pole.

Are there any better methods, assuming a completely self-contained system (i.e. no external satellites)?

Determining Distances in Space - Astronomy

There are a few methods that could be used to measure distances to objects in space. I'm not sure of the ages of these methods, but in many cases, the smaller-scaled methods tend to be older (as we simply didn't know about the larger scale).

The scale of the solar system was initially calculated using the parallax effect - measuring the position of Venus relative to the Sun at different times from several places across the Earth, during a transit. We can use orbital velocities nowadays to calculate average distances from the Sun. In some cases, we can use the light travel time to orbiting satellites to calculate distances very accurately, too.

For nearby stars, the main method is to measure the change in position of the star as the Earth moves across its orbit. This also uses the parallax effect.

For more distant stars, scientists often need to use specific variable stars (such as Cepheids, and RR Lyrae type stars), whose variations are related to their mass. Scientists can then use this data to calculate distance.

Cepheid variables are also used for measuring distances to nearby galaxies.

For more distant galaxies, scientists can use redshift to calculate distance, as more distant galaxies are receding faster than nearer ones, causing a larger doppler effect.

Another method for measuring extremely distant objects is to look for Type 1a supernovae, which, since they always have the same luminosity (their mass is always the Chandrasekhar limit, or about 1.4 solar masses). This was used to calculate that the expansion of the universe was accelerating. However, this method isn't used very often, as these supernovae don't happen very often.

planet - Is the discovery of Alien or Extra Terrestrial Life a function of the science of Astronomy?

The search for extraterrestrial life is usually covered by "exobiology". But astronomy can provide clues of whether a planet or an exoplanet provides some of the conditions, which allow life or indicate life.

The habitable zone - in its various versions - defines, in which distance from a star a planet needs to be to allow for e.g. liquid surface water, a condition regarded as necessary for most life-forms we know from Earth. With the discovery of extremophiles the habitable zone for that kind of life has been extended.

Astronomy can provide information about the central star and the distance of a planet from the central star. From these data a decision is possible, whether the planet fulfills the surface temperature condition for habitability.

Astronomy can provide information about the stability of a star, necessary for life to evolve on its planet.

Astronomy can - in principle - provide information about the chemical composition of a potential atmosphere of a planet. Oxygen and methane at the same time would be regarded as an indicator of possible life on the planet.

Astronomy can determine size and density information about the planet. That way it can be decided, whether it's a rocky planet or a gas planet, and infer the gravitational acceleration at the surface. The gravitational acceleration is relevant, e.g. for constraints of the atmospheric composition, or for possible properties of life, if extant.

space travel - Help plotting a trip to the Moon!

I know this is literally rocket science but, I would like any sources or formulas that would help me plot a trip to the Moon. I'm not sending anything, nor do I ever plan to, I just want to do the next best thing by plotting the trip. So if anyone could give me any info as to how I can plot the trip, that'd be great! :)

P.S. I'm perfectly aware that the moon isn't always the same distance away, that it's like hoping onto a taxi in New York City, and how it's got a lot of work (I wouldn't mind doing it really), I'd just like to plot the trip. And please don't hate on me for asking, let's just be civil adults here. :)

How much of an effect does the moon have on Earth's liquid mantle?

Interesting question. I would say from an energy standpoint, it almost certainly it has no effect.

Of course, the extreme case is Io, one of the Galilean moons whose heat source comes from the gravitational tidal stretching as it orbits very closely to the planet Jupiter. The heat that sustains the core of the Earth, however, is left over from its formation and also comes from radioactive decay of heavy elements.

The differential potential energy (and hence the tidal force) over the planet Io due to Jupiter, which is approximately 1300 times more massive than the Earth, is much larger than that of the Earth due to the moon. The relationship between force and differential potential energy is:
$$ F = - nabla U $$
At a given location on the potential energy curve, the strength of the force is determined by its steepness (derivative) at that same location. Below is a quick plot I've generated for the Earth-Moon system, where the vertical red line represents the average Earth-Moon distance over a one-year period. As you can see it doesn't appear to be very 'steep', though keep the scales of the x- and y-axes in mind.

Admittedly this isn't that exciting of a plot. But, for comparison one could be made for the Jupiter-Io system, and numerical derivatives could be taken for both to calculate the magnitude of the tidal force in each situation.

To answer the question:

If the difference in the gravitational potential energy of object A on B over the scale of B is comparable to the self-gravitational energy of object B, then tidal forces will become important. This self-gravitational energy is the amount required to completely pull apart all massive particles infinitely far away. Formally, this limit is called the Roche Limit.

spectroscopy - Why do we observe spectral lines of specific energy?

The basis of my confusion is that atomic orbitals, even when described accurately by quantum numbers, have definite energies, meaning they represent energy eigenstates of the wave function. They're stationary states, and thus separable solutions to the Schrödinger equation. The general wave function of an electron, however, is a linear combination of such states, so that general solution does not have a definite energy. Still, we observe discrete spectral lines at specific wavelengths (with some broadening).

Why do we observe spectral lines of specific energy when the wave function of the electrons in an atom are linear combinations of energy eigenstates?

It seems like the spectral lines that are observed are just the energy eigenstates, while, according to quantum mechanics, the wave representation of electrons is a linear combination of those states.

galactic dynamics - Python 2D Jean Instability in Spiral Galaxy Simulation

I have ~1000 snapshots of a spiral galaxy simulation (from Molecular cloud perturbations t=0 to t>1Gyr. What I need to do is determine whether any position at any of the snapshot times meets criteria for Jeans instability.

The simulation is 2D, and the snapshot script can read position, velocity and surface density ∑, but not temperature. The simulation also has no gas, instead the simulation was modeled by giving each individual star extra mass which corresponds to gas.
I looked online and several site state the Jeans mass in 2d equal to c$_{s}$$^4$ / G$^2$*∑. But I have no clue how to determine speed of sound c$_{s}$.
Also I am not really interested in Jeans mass, more so whether any position can collapse to make stars, i.e. satisfy Jeans instability.

telescope care - How can I clean my lenses without causing scratching or damages to the lens surface?

Clean your eyepieces in the same way you would clean a camera lens. An air blower, soft (i.e. camel hair) brush, lens tissue or microfibre cloth, and a solvent or alcohol will do the trick.

When I was an undergraduate I did some work with lasers and very expensive dielectric coated mirrors. The techniques here will show you how to carefully clean optics. Never completely wet your lens tissue or cloth. One drop on a lens tissue is usually enough, or a couple of drops on a microfibre cloth.

Essentially, you need to:

1. Use a blower to blow off as much dust as you can.


2. Then use a soft brush.


3. Dampen a small square of lens tissue with pure alcohol or acetone (see warning below). Gently draw or wipe the tissue across the surface once, and then discard. Repeat if necessary.


4. You may need to fog the lens with your breath to help remove water-soluble gunk.

Be insanely careful if you are using a solvent such as acetone. Although a good for cleaning optics, it's not very nice to paint and plastic so it should be a last resort for very stubborn marks well away from the edges of the lens (so you'll never touch the paint with it). Methyl or isopropyl alcohol are safer but less effective, or a generic lens cleaner from a camera store.

pluto - Has New Horizon's data updated Charon's orbital elements?

For years I've been fascinated with the mutually tide-locked bodies Pluto and Charon. In July 2012, The Astronomical Journal published an article The Orbit of Charon Is Circular by Buie, Tholen and Grundy. The authors thought that the eccentricity of Charon's orbit is very close to zero.

It seems to me their opinion is somewhat speculative given the low quality of images from Hubble. Has New Horizons data verified Charon's circular orbit? Is there an online source giving more precise orbital elements from New Horizons data?

I'm also interested in the obliquity of Pluto and Charon.

Are there a lot of collisions between stars in the core of the galaxy?

A high density of stars definitely increases the chances of collisions, however, the high velocity of a halo star orbiting wouldn't increase its chances. Since the halo star is traveling very quickly, the halo star would only spend a small amount of time near the galactic core. Additionally, it would have less time to get deflected, gravitationally, by other stars in the core.