natural satellites - Why does Jupiter have so many moons?

Bigger is better.

Most moons, especially those of gas giants, are not "formed", they are just "captured" (unlike our Moon, which could have been captured, but probably was formed in a much more exciting way).

Jupiter is the most massive planet in the solar system. It stands to reason that it has a larger region of gravitational influence (where its influence outweighs the force due to the other planets and the sun). So, it's easy for it to capture rocky masses.

If you have a look at the contours on the following image (Ignore the Lagrange points marked on it, I only want the contours)

the circular area around the Earth is more or less the area (there's a velocity dependence here which I'm not getting into) in which a moon-like body can form a reasonably stable orbit. The size of the small "well" will increase as the planet moves farther from the sun, and also when the planet is more massive.

Jupiter is both pretty far away from the Sun, and is very massive. This leads to a huge sphere of influence.

The asteroid belt may have something to do with this too, but I doubt it (it's pretty far away). However, if we assume the "half-baked planet formation" theory for the formation of the belt, Jupiter may have leeched off much of the mass that would have otherwise become part of that planet during the formative period.

orbit - Are there ever any simultaneous transits of both Mercury and Venus as seen from the Earth?

EDIT: As it turns out, I'm not the first or even the second person to run calculations like this:

Meeus' work (second link) mentions the 13425 CE event in "Table 1. Simultaneous and near-simultaneous transits of Mercury and Venus, years 1 to 300,000"

Within the limits of DE431 (7 May 13201 BCE to 7 May 17091 CE), there is no
time at which both Mercury and Venus transit the Sun.

The closest we get to this:

• On 16 Sep 13425 CE at 11:57pm UTC, Venus starts transiting the Sun. This
  transit ends the next morning (17 Sep 13425 CE) at 7:30am.




• Less than 9 hours later, at 4:27pm, Mercury starts transiting the
  Sun. This transit ends at 10:26pm.

The program I used to compute this:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-solve-astro-13227.c

The list of transits I computed while solving this:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/mercury-transits.txt.bz2
https://github.com/barrycarter/bcapps/blob/master/ASTRO/venus-transits.txt.bz2

Although I believe this answer is correct, Stellarium does not agree with
me, and HORIZONS doesn't compute positions past 9999 CE, so don't put too
much faith in this answer, since there's no good way to confirm it. I
believe that I'm correct and Stellarium is wrong this far in the future, but
it could be the other way around.

Even if my calculations are correct, the uncertainty in calculating the
relevant positions (Sun, Merucry, Venus, Earth) this far in the future is
high. On their own transit pages, NASA only computes Venus transits from
2000 BCE to 4000 CE, and Mercury transits from 1601 CE to 2300 CE, even
though they could've made the same calculations I made from 13201 BCE to
17091 CE:

This suggests NASA isn't confident enough of Mercury/Venus (and Earth/Sun)
positions to predict that far in the past or future, so my results may be fairly inaccurate.

observational astronomy - Why is there a gap in this image of supernova discoveries?

The coordinate system in this image is RA and Dec. It is a coordinate system which uses the Earth's equator (projected onto the sky) as its midline.

The inverted U is the Milky Way. The Milky Way is full of dust and gas, and blocks our view of galaxies (and supernovae) behind it. There is enough dust in the plane of the galaxy to block our view in that direction. For example the galaxy IC 342 is one of the nearest galaxies, and would be brilliant if it were not close to the galactic plane. There may be other galaxies that are completely hidden.

Our galaxy's bulk not only hides supernovæ that are in other galaxies, it also hides most of the supernovæ that occur in the Milky Way

Missing Terms in Weinberg's treatment of perturbations on Newtonian Cosmology

I was reading Appendix F of Steven Weingberg's book "Cosmology". In this Appendix he works out the perturbations to a cosmological fluid described by non-relativistic hydrodynamics and Newtonian gravity.

It turns out that the first order perturbations satisfy,

$$
frac{partial delta rho }{partial t } + 3 H delta rho + H vec{X} cdot nabla delta rho + bar{rho} nabla cdot vec{v} = 0, qquad tag{1}
$$

$$
frac{partial delta vec{v}}{partial t } + H vec{X} cdot nabla delta vec{v} + H delta vec{v} = - nabla delta phi, qquad tag{2}
$$

$$
nabla^2 delta phi = 4pi G delta rho. qquad tag{3}
$$

Weinberg applies the following Fourier transform to these equations,

$$ f(vec{X},t) = int exp left( frac{i vec{q} cdot vec{X}}{a} right) f_{vec{q}}(t) mathrm{d}^3vec{q} $$,

where $f(vec{X},t)$ is a place holder for $delta vec{v}, delta rho, $ and $delta phi$.

The resulting equations he gets are,

$$
frac{mathrm d delta rho_{vec{q}}}{mathrm d t } + 3 H delta rho_{vec{q}} + frac{ibar{rho}}{a} vec{q} cdot delta vec{v}_{vec{q}} = 0 qquad tag{1'}$$

$$
frac{mathrm d delta vec{v}_{vec{q}}}{mathrm d t } + H delta vec{v}_{vec{q}} = -frac{i}{a} vec{q} delta phi_{vec{q}} qquad tag{2'}$$

$$
vec{q}^2 delta phi_{vec{q}} = -4pi G a^2 delta rho_{vec{q}} qquad tag{3'}$$.

For the most part these new equations can be obtained by making the substitution $nabla rightarrow i vec{q}/a$.

---

My question : There doesn't seem to be any terms in the transformed equations which correspond to the terms $ H vec{X} cdot nabla delta rho$ and $H vec{X} cdot nabla delta vec{v}$. Weinberg makes no comment about their absence. Is anyone aware of a legitimate mathematical reason for these terms to disappear in the transformed equations?

Can life survive on the equator of cooled and fast rotating white dwarf or neutron star?

I am going to attempt a weak answer, mods feel free to delete it, but I'm fairly certain I'm right.

Shortly - no. It's not possible. Even if you balance gravity and centrifugal force perfectly at ground level at the equator, they will very, very quickly become imbalanced as soon as you move north, south, or up from there. So quickly in fact that the gradients may be too big even for a human being not moving at all. Maybe if you're laying down, with your body oriented along the equator, but even then I think the gradients would be too big.

Maybe bacteria would survive, briefly.

I'm sure the math could be done quite easily to estimate the gradients. This is based entirely on intuition.

black hole - Interstellar movie: What is the "portal" to the other galaxy?

Yes, it is a wormhole indeed. This has been indicated quite clearly in the movie as well, when Dr. Romily explains with a pen and paper to Dr. Cooper. The explanation goes like this :

Imagine a sheet of paper to be 2-D space, then a line joining two points on the sheet of paper is the shortest distance possible to reach that point, but if due to some disturbance, the space is bent ( achieved by folding the sheet of paper), you can pierce a hole in the sheet after aligning the two points together. That is a 2-D wormhole (which is a circle indeed). So what happens when you consider a 3-D wormhole? It becomes a sphere.

Now, you can see the other end of a 2-D wormhole (which is effectively the other hole in the sheet visible from the first hole, and one can see beyond the hole in the other direction as well). Same happens with the 3-D spherical wormhole where you can see to the other side of the wormhole as well.

Now, the means to bend spacetime : Space time can be bent by having a very big mass placed inside the space time (read Einstien's General Relativity ). So, it is safe to assume that the wormhole is a space time disturbance created due to a massive object, but it is not a blackhole.

gravitational waves - What will eLISA be trying to observe?

The first observation is whether gravitation radiation exists as predicted by General Relativity. Evidence from observations of binary neutron stars says it does, but it remains a major unknown.

Gravitational astronomy will be more like listening than looking. Right now I can hear my kids playing upstairs. I can learn a lot about what they are doing just by noting that sound waves are passing, from a particular direction.

We would expect extreme gravitational events to produce particular wave forms, for example black hole mergers should make a "tone" that rises in pitch as the two event horizons merge at faster rates. Again we have lots of theory on this but if we can "hear" these events we can check if GR does correctly model gravity in these situation, or if there is something missing.

Most interesting would be if we do hear Black hole mergers, but they don't sound like what we have expected. That would mean that there is more to gravity than we understand, and would lead to new science.

solar system - If sun steals comets from other stars, then what is the primary source of comets?

It is likely that during the formation of most stars, comets are formed from the same gas and dust that the star and any planets it hosts were formed from. Extrapolating what we know and strongly believe about our own star, the Sun, it is likely that many or most stars have a cloud of comets around them analogous to our Oort-cloud (which hasn't been "proven," but is strongly suggested by observation of comets).

As stars orbit the galactic center, they pass by one another - sometimes extremely closely, sometimes not very close. During these encounters, the gravitational interactions will shake things up in the Oort-like clouds. In some cases, comets that are otherwise minding their own business, orbiting far from the star, will be kicked inward. Others will likely be ejected. Some of those ejected will eventually find themselves orbiting another star, and possibly falling inward for a close encounter with the star and any planets.

In the long run, it's likely that interstellar space is riddled with rogue comets. Many comets in our solar system may have come from there, and many of the comets formed around our sun have likely been flung off, in some cases to find new stars to orbit.

exoplanet - Is there any way a planet could form independent of a star?

Well you need to see the related question brown dwarfs and planets , because the answer to your question depends on how you define a planet.

If you demand that a "planet" has a rocky core then it seems very unlikely that a planet could form in isolation away from a parent star. The parent star is needed in order to differentiate the rocky material from the gas and allow it to condense.

On the other hand, if you wish to define a planet as simply an object below a certain mass (say the deuterium burning threshold at 13 Jupiter masses) then it seems very likely that such an object could form in isolation. They would be entirely gaseous, but there would be little to distinguish them from brown dwarfs at only slightly higher masses.

At present there are plenty of candidate "free-floating planetary mass" objects.
For example see Joergens et al. (2014); Liu et al. (2013); Zapatero-Osorio et al. (2000). Unless we have our understanding of the physics completely wrong, then it is likely that at least some of these are lower than 13 Jupiter masses. However, their origin remains unclear. It is possible they could all have formed around stars and then subsequently been ejected, but the presence of significant numbers of these objects in young star forming regions and the lack of $sim$10 Jupiter-mass objects orbiting stars, suggests that there is an alternative formation scenario that can produce such objects in isolation.

What could these formation scenarios be? These low-mass objects could just be an extension to lower masses of the fragementation process that forms stars; they could be ejected embryos that started their lives in multiple systems; they could be "failed" stellar cores that could not accrete more gas because of photoevaporation by nearby massive stars; or they could form by gravitational instability around stars with unusually massive disks and be ejected by a close encounter with another star. These possibilities are reviewed by Whitworth et al. (2006) and Chabrier et al. (2014), and are all still thought plausible to some extent.

asteroids - How can they tell no asteriods will hit earth in the next hundreds years?

A couple of points based on some basic orbital mechanics

They don't need to get a "good" view, like the clear, crisp photos of Pluto to see one coming. They only need to get a picture over time to calculate trajectory. The unclear snapshots work just fine to calculate if it'll hit us or miss us.

Also, an object as far as Mars at it's closest pass to earth, a bit over 1/2 AU, would still take a few months to reach earth if it's in solar orbit. Mostly we don't need to track anything as far out as Pluto, they can look much closer to the Earth and still have sufficient warming time. The hard part, is tracking things that approach from the Sun side, cause those are harder to see. That's why the Chelyabinsk meteor wasn't spotted. it was also on the small side, smaller than NASA is currently looking for.

The good news is that, we don't get struck by things that size very often. The Solar system is pretty enormous and pretty empty and pretty big strikes like that one are rare, like, maybe once a century.

Also, virtually all of the injuries from the Chelyabinsk meteor were from people who didn't know what to do. If you see a big fireball in the sky, it's human nature to watch it, but use some common sense. A space rock of that size will make a shock-wave that travels at roughly the speed of sound and the shock-wave can break windows, even knock over trees and buildings if it's big enough. You don't want to be standing in-front of a window when the shock wave its. Lay down next to a couch or under a table in case your building gets shaken and cover your ears. If everyone had done that, there would have been very few injuries. You only need to wait maybe 2 minutes or so to be on the safe side.

If you're in a car, stop, cause the shock-wave could knock down trees or debris in-front of you and stay in the car, cause that's safer than being outside. All told, the damage to buildings was tiny compared to natural disasters like Earthquakes, floods or volcanoes which happen to us several times a year. It's good that NASA is watching for this kind of thing, but it's also a pretty rare event.

orbit - Do orbital resonances always form naturally?

If the question is "if I throw two planets to orbit a star at random direction, would they form an orbital resonance?" -- then in general, no. A resonance is an integral ratio (1/1, 2/1, 3/5, etc.) between the periods of motion of objects -- i.e., the ratio of their periods forms a rational number. Formally speaking the odds of getting a integral ratio (let alone a strong, low-order ratio, since those are the dynamically interesting ones) if you set the system up "randomly" should be infinitesimal, because irrational numbers are (infinitely) more abundant that rationals.

However, if the orbits of one or both of the planets can change over time, then the ratio between their periods changes, and they can end up in a resonance. (Which is maybe answering the title question.) How often this happens depends on whether the planets happen to start near a strong resonance, and on how rapidly the orbits change. (If the orbit of a planet changes slowly, then it won't encounter new resonances very often; on the other hand, rapid orbital change can overwhelm the effect of weak resonances, so that the planet passes through the resonance without being caught.)

For example, it's thought that Neptune and Pluto were originally not in resonance; but the gradual outward migrations of Neptune (due to various gravitational encounters between planetesimals and the giant planets) changed its orbital period and meant that eventually it reached 2/3 resonance with Pluto, and Pluto was "captured" by the resonance, after which it stayed in resonance with Neptune.

The vast majority of objects in the Solar System are not in resonance with anything else, which is perhaps another way of answering your question. (I.e., in practice it doesn't happen very often.)

How many arms does the Milky Way galaxy have?

This is actually a really, really tough question.

Look at this diagram:

^{Purple: Norma Arm and Outer Arm.
Green: Scutum-Centaurus Arm
Pink: Carina-Sagittarius Arm
Cyan: 3 kpc Arm and Perseus Arm}

So we can slightly modify this picture by saying that there are four arms, and calling them by the following names:

Norma-Outer Arm

This arm has one end at the center of the Milky Way; this end is called the Norma Arm. It's actually quite small. However, as you continue outward along the lanes of gas, dust and stars, the Norma Arm becomes the - wait for it - Outer Arm.

Scutum-Centaurus/Crux-Scutum Arm

This arm also emanates from the center (well, duh!) and is distinguished by large numbers of clusters of red supergiants near the center (where it is referred to as the Scutum Arm) of the Milky Way. The Scutum-Sagittarius Arm is one of the Milky Way's two major arms.

Carina-Sagittarius Arm

The defining feature of this arm is that is has many H II regions, where ionized gas is plentiful. It is though that stars can form there. However, H II regions are also present in many other parts of the galaxy. Observations from the Spitzer Space Telescope seem to support these theories and prior observations.

The Spitzer results are, I think, very important for understanding our galaxy and the things in it. It confirmed the existence of all four arms, but also confirmed that the Norma-Outer Arm and Sagittarius Arm are relatively minor compared to the other two.

Near/Far 3 kpc Arm and Perseus Arm

The Near and Far 3 kpc Arms (which really are just one arm) are very close to the galactic center - about 3,000 parsecs (hence the name). The Far Arm was only discovered recently, while the Near Arm was first observed about 50 years ago. These two mini-arms are expanding outward at an enormous rate. The combined 3 kpc Arm then becomes the Perseus Arm, which extends out to about 3.5 times the distance from the center of the 3 kpc Arm. It is the other major spiral arm of the Milky Way.

---

Okay, so that's simple enough. The Milky Way has four spiral arms, right? Well . . . sort of. The discovery of the "New Outer Arm"¹ shook things up, because that would mean that the Norma-Outer Arm reaches nearly all the way around the Milky Way. That's strange and borderline inexplicable. Well, not really. But it's very interesting.

This image gives you a good idea of what it might look like:

By the way, someone at one point wondered, "Which are we in?" That, too, doesn't have a simple answer. Current observations state that we're in the Orion-Cygnus Arm, a/the midget of the galaxy (depending on whether or not there are other "mini-arms"). It's tiny - 1.1 kpc wide and 10 kpc long - and is between the Carina-Sagittarius Arm and the Perseus Arm.

Here's what it might look like:

Putting it all together, Robert Hurt made a very famous impression of what the Milky Way might look like:

NASA gives a good explanation of it here.

If you want a good overview on everything, check out this blog post, which is reasonably well-sourced. Another post explains the four-arms-vs.-two-arms issue:

Like the proverbial blind men describing an elephant, the two groups of scientists are examining very different parts of the Milky Way. The Spitzer study detected hot objects visible in infrared. The CfA study used radio telescopes which can also detect colder objects such as supernova remnants, very young star formation regions and huge clouds of hydrogen gas. So it seems as though the older established star formation regions are mostly concentrated in two spiral arms, but that the very new star formation regions and the hydrogen clouds from which they form are also developing in two additional arms.

If you were hovering above the Milky Way in a spacecraft using binoculars or a regular optical telescope, you would see two main arms. But if you also had a radio telescope with you, it would detect two more.

The other group of scientists referred to here used the Very Long Baseline Array to image the Milky Way with radio waves; their observations support the four-main arms model.

So at the moment, I think the answer is four, though two arms are more distinct that the other two.

---

¹_{Dammit, paywall! Thank goodness for arXiv.}

black hole - Proof that Parallel Universes exist

Your radio information source is wrong.
The Large Hadron Collider has not discovered mini black holes.
When it comes back on line this spring, the LHC will begin looking for mini black holes: Large Hadron Collider Could Prove the Existence of Star Trek's Parallel Universe

Journalists do like their headlines, but the gist is this:

When the Large Hadron Collider is brought back online in the spring, researchers will be looking for the existence of mini black holes. These mini black holes would lend support to string theory, which posits that different dimensions and parallel universes are possible.

No miniholes yet, maybe never.

star - How to calculate B-V colour index value percentage difference

$B-V$ corresponds to the base 10 logarithm of a flux ratio.

$$B-V = -2.5 log left(frac{f_B}{f_V}right)$$

So trying to guess what you are trying to calculate, it is the percentage change in the blue to visible flux ratio?

In which case the percentage change is
$$ p = frac{ 10^{-(B-V)_2/2.5} - 10^{-(B-V)_1/2.5}}{10^{-(B-V)_1/2.5}}times 100$$

A percentage change can of course be negative.

solar system - Why do (most of) the planets rotate counterclockwise, i.e. the same way the Sun does?

Referring to the mechanisms explaining the solar system formation and to the initial rotation of the gaseous cloud that collapsed, I understand easily why the planets orbit the Sun the same way this one rotate (say counterclockwise) but I can't figure out why this apply to planets rotation too. Thinking about that from Kepler's laws and angular momentum conservation point of view, I might conclude that the planets should rotate clockwise because the velocity of the particles that aggregated during the planets formation was higher closer to the Sun...

Apart from a short explanation, I would like to have a good reference from the literature if possible.

Edit, to make my reasoning more explicit: following Kepler's laws, the particles that aggregate on the "day side" of the proto-planets in the east-west direction relative to the ground are faster than the ones hitting on the "night side" in the west-east direction. If we add all of these contributions, the planets should rotate in the opposite direction relative to the initial cloud (i.e. relative to the actual Sun rotation). I guess something is wrong or missing there (to counterbalance the phenomenon I just described) but I can't see what it is...

New edit: References I found some published articles dealing with this kind of question but I don't have the time right now to read them carefully. If someone is motivated to do so, do not hesitate ;-) If I find the answer to my question amongst these papers, I will post it there later. Of course, you may need to use the network of an institution with a subscription to these editors to access them:

R.T. Giuli (1968a) in Icarus: http://www.sciencedirect.com/science/article/pii/0019103568900821

R.T. Giuli (1968b) in Icarus: http://www.sciencedirect.com/science/article/pii/0019103568900122

A.W. Harris (1977) in Icarus: http://www.sciencedirect.com/science/article/pii/0019103577900793

J.J. Lissauer, D.M. Kary (1991) in Icarus: http://www.sciencedirect.com/science/article/pii/001910359190145J

big bang theory - Is the time lapse considered when estimating the age of the universe?

As relativistic effects will cause clocks to run slower, a frame of reference must be chosen when considering the time of the "big bang". There is a natural and convenient choice of reference frame, based on the cosmic microwave background. The cosmic background appears to be extremely red-shifted light, indicating it is receding from us very fast, due to the expansion of the universe. If we choose a frame in which the CMB is receding equally fast in all directions, we have a convenient frame of reference. It is called the Comoving frame.

Now that we have a frame of reference, we can talk about time and distance in a way that all observers that share this frame can agree. In the comoving frame, the "big bang" occurred about 13.8 billion years ago.

To directly answer the question: The time measured is the time in the comoving frame and relativistic time dialations (time-lapse) are considered.