celestial mechanics - How do rogue planets orbit around stars in other planetary systems?

Capture of any object is never common. A rogue planet that passes a star will be accelerated by the star's gravity, and provided that it doesn't hit anything will pass the star in a hyperbolic path.

For capture to occur, the rogue planet has to lose momentum, and there are a few ways in which this can happen. The most general way is for the rogue planet to interact with one of the stars existing planets. If the rogue planet passes close one of the star's orbiting planets, it can interact gravitationally, and transfer momentum to the planet, and slow down in the process. This is rather like the reverse of a gravitational slingshot.

It is also possible that a double planet can be captured, if one of the bodies transfers momentum to the other. One of the double planet will escape, the other is captured by the star's gravity.

Capture of rogue planets is very rare. There is no evidence that it has occurred in our solar system (never in 4.7 billion years is a big Never) though some have speculated that Sedna might be a captured object. But we know that captures like this are possible, as Jupiter and Saturn have a collection of moons, some of which seem to have been captured from the asteroid belt.

biochemistry - What are the units of Q10 (temperature sensitivity)?

Figure. A schematic diagram showing the effect of the temperature on the stability of an enzyme catalysed reaction. The curves show the percentage activity remaining as the incubation period increases. From the top they represent equal increases in the incubation temperature (50 °C, 55 °C, 60 °C, 65 °C and 70 °C).

The $Q_{10}$ is a unitless number, that summarizes the effect of raising temperature 10°C on the rate of a chemical reaction. A $Q_{10}$ of 2.0 suggests that raising the temperature of a system by 10 °C will effectively double the rate of the reaction. This value would be expected for most chemical reactions occurring within normal physiological temperatures.

Mathematically, $Q_{10}$ can be represented by the following expression:

$$Q_{10}=left(frac{k_2}{k_1}right)^{frac{10}{t_2-t_1}}$$

$t_2$ = higher temperature
$k_2$ = rate at $t_2$
$t_1$ = lower temperature
$k_1$ = rate at $t_1$

Usually the temperature difference is about 10 °C, then you can simplify the equation

$$Q_{10}=left(frac{k_1}{k_2}right)^{frac{10}{10}}=frac{k_1}{k_2}$$

Edit: You can easily calculate $k$ form Arrhenius equation

$$k=Ae^{frac{-Delta G^*}{RT}}$$

where $k$ is the kinetic rate constant for the reaction, $A$ is the Arrhenius constant, also known as the frequency factor, $-Delta G^*$ is the standard free energy of activation ($kJ/mol$) which depends on entropic and enthalpic factors, $R$ is the gas law constant and $T$ is the absolute temperature.

interstellar travel - The fastest Probe we could build now

Even when launched by one of the most powerful rockets on Earth, boosted by a gravitational slingshot around Jupiter, and further accelerated by a radioisotope thruster, that probe would take about 28,000 years to reach α Centauri. Quoting British author Douglas Adams, McNutt quips: “Space is big. Really big.”

impact - How ready are we to deal with a asteroid/comet/giant-meteor on a collision course with Earth?

The short answer is "not very, but we're getting better".

In the case of particularly large Earth orbit intersecting bodies, kilometers across and bigger, they're fairly well known and tracked. We'd probably get months to years of warning. Technologically, we've probably got the capability of diverting such an object if we have enough warning, but it'd likely be the most complex human endeavor ever. Blowing it up is unlikely to help, we'd need a nice long shove from as far away as possible to divert it.

The bigger problem is smaller bodies in the tens to hundreds of metres. Some of these are known about and tracked, but plenty more aren't. The Chelyabinsk meteor was about 20 metres across and, in terms of size/density/speed/impact angle wasn't that far off being a city killer. We never saw it coming. (Ironically, a very similar but unrelated 30m object was being tracked through a near-miss that same day.)

I'd suggest that a city-killer impact with little or no warning is still quite possible. Something capable of taking out, say, a small country we'd probably have some warning of, but probably not enough. A mass-extinction event we'd probably have lots of warning for, but doing anything about it would be a very big challenge.

exoplanet - Is it possible to know if a planet is located in the Habitable Zone knowing it's properties?

The habitable zone is, roughly, defined as the region around a star in which a planet could have liquid surface water. So if the surface temperature of the planet is between 0 and 100*C then the planet is in the habitable zone. The converse, however, is not true.

The reason for this definition is that the sort of chemical reactions that are needed for life work best when there are complex molecules dissolved in some kind of solvent, and the best polar solvent is H2O.

If you know the distance a planet is from its star, the temperature can be estimated from the properties of the star and the atmosphere of the planet. Not every planet in the habitable zone actually has liquid water. Venus, Earth and Mars are all in the Habitable zone of the sun, since they could all have liquid water if they had the right atmosphere. But of course only Earth actually does have liquid water in any substantial amounts.

So just being in the habitable zone, doesn't make a planet certainly suitable for life, and even if water does exist on the surface, it does not mean that humans could inhabit the planet.

light - Is the colour of a wave from a far galaxy the same for us as for a galaxy which lies between?

If I understand you right, you're asking whether or not the redshift of the photons emitted from a far-away galaxy happens the instant it leaves the galaxy.

Redshift is gradual…

If so, the answer is no. The redshifting of photons happen gradually as they travel through the expanding Universe. You can find the derivation here where you'll see that every infinitesimally small increase $da$ of the scale factor $a$ of the Universe (its "size") increases the photon's redshift by an amount $dz$, or, in terms of wavelength, by an amount $dlambda$.

If galaxy $B$ lies at redshift $z_mathrm{B}$, then an observer in galaxy $A$ at redshift $z_mathrm{A}$ lying between us and $B$ (so that $z_mathrm{A}<z_mathrm{B}$) would measure $B$'s redshift to be
$$
z_mathrm{B,seen,from,A} = frac{1+z_mathrm{B}}{1+z_mathrm{A}} - 1,
$$
which is less than $z_mathrm{B}$.

…at least in our Universe

The redshifting is not due to the source moving away from us. If the expansion hadn't been gradual, but we instead lived in a crazy universe that were static when the distant galaxy emitted the light, and static when we observe, but somehow expanded suddenly by some factor in the meantime, then we would still observe a redshift, even though the galaxy were static both when it emitted the light and when we observed it.

evolution - Why are there nail growth differences between humans and other mammals?

Cat claws are growing all the time, like horse hooves, or human nails. However, cats and horses usually use their claws/hooves, so they get shortened through mechanical action.

An indoor cat may need their claws trimmed if it doesn't use them enough (that's why cats will want to scratch everywhere), or if has supernumerary toes that don't normally touch the ground. Similarly, cattle that doesn't get to move will suffer from hoof overgrowth, which appears to be very uncomfortable to the animal.

Consequently, if you were to use your fingernails more often for digging and scratching, you wouldn't have to trim them all the time.

Would a telescope that uses Fresnel lenses be more practical than using regular lenses?

The main advantage of a Fresnel lens is its reduced mass compared to a normal lens. Its disadvantages include difficulty of manufacture and diffraction from the discontinuities in the aperture, these I suspect are killers given the practicality of the alternatives, reflecting telescopes, to a Fresnel lens refactor.

Diffraction will give reduced contrast in the image, already noticeable in a reflector with partially obstructed aperture, but may well be worse with a Fresnel lens. But the difficulty in manufacture may well be the real limit given the relative ease of manufacturing large mirrors.

While I'm at it; it seems as thought making a achromatic Fresnel multiplet might be quite fiddly.

We might also note where there is no alternative, systems analogous to Fresnel lenses are used. The example I have in mind are grazing incidence x-ray telescopes.

gravity - How can I calculate how the debris of an object ripped apart at the Roche limit will spread out?

I think there are two key aspects to the answer. 1) Solid/rocky bodies should tend to collide before they reach the Roche limit. 2) When gaseous bodies reach the Roche limit (and undergo 'Roche-Lobe Overflow'), the dynamics are basically those of test-bodies and are fairly straightforward and well understood from binary stellar dynamics. To expand on both:

1) Rocky Roche Limit. If you are thinking about a gaseous donor (the object being disrupted), then this is an irrelevant point, but It sounds like rocky is what you had in mind. To an order of magnitude, the Roche limit is the same as the Hill sphere, or the Tidal Radius (e.g. Rees 1988) --- which is simply the radius at which the density of the donor equals the average density of the primary in a sphere of that radius:

$$R_t^3/M approx r^3/m rightarrow R_t approx r left( M/m right)^{1/3}$$

Rocky material varies very little in density (e.g. Iron meteorites are only about twice as dense as chrondritic ones), which means that the densities will only match very near the radius of the primary. The tidal bulge in the secondary (donor) also makes it easier for the objects to collide before meeting this criteria.

e.g.

2) Gaseous Roche Lobe Overflow. Basically every text on stars and star systems will have a section on mass transferring binaries which will describe the dynamics of mass transfer (this PDF is by Philipp Podsiadlowski who is a wizard of the field). In the type of situation you are describing, like in (semi-)stable binary systems, it is a very gradual process where material is slowly syphoned off of the donor. This material can either form an accretion disk (high angular momentum material) and gradually accrete onto the primary, or directly impact the primary (low angular momentum material).

e.g.

artificial satellite - Calculating Postition of ISS / Hubble in space

The orbit of the ISS does vary. Drag from the very thin atmosphere slowly causes the orbit to lower, and the speed to increase. So the ISS needs to be boosted about a couple of times a month.

Its position can be predicted, at least in the short term, and websites such as Heavens Above publish current position, predictions, and orbital information.

physiology - Can the body of any organism on Earth live without impairment both in vacuum, and within Earth's atmosphere?

Adding to Noah's answer, some lichens can survive the vacuum of space too. In an experiment led by Leopoldo Sancho from the Complutense University of Madrid, two species of lichen - Rhizocarpon geographicum and Xanthoria elegans - were sealed in a capsule and launched on a Russian Soyuz rocket on 31 May 2005. The lichens were in perfect condition when observed after the return to earth.

star - How loud would the Sun be?

The Sun is immensely loud. The surface generates thousands to tens of thousands of watts of sound power for every square meter. That's something like 10x to 100x the power flux through the speakers at a rock concert, or out the front of a police siren. Except the "speaker surface" in this case is the entire surface of the Sun, some 10,000 times larger than the surface area of Earth.

Despite what "user10094" said, we do in fact know what the Sun "sounds" like -- instruments like SDO's HMI or SOHO's MDI or the ground-based GONG observatory measure the Doppler shift everywhere on the visible surface of the Sun, and we can actually see sound waves (well, infrasound waves) resonating in the Sun as a whole! Pretty cool, eh? Since the Sun is large, the sound waves resonate at very deep frequencies -- typical resonant modes have 5 minute periods, and there are about a million of them going all at once.

The resonant modes in the Sun are excited by something. That something is the tremendous broadband rushing of convective turbulence. Heat gets brought to the surface of the Sun by convection -- hot material rises through the outer layers, reaches the surface, cools off (by radiating sunlight), and sinks. The "typical" convection cell is about the size of Texas, and is called a "granule" because they look like little grains when viewed through a telescope. Each one (the size of Texas, remember) rises, disperses its light, and sinks in five minutes. That produces a heck of a racket. There are something like 10 million of those all over the surface of the Sun at any one time. Most of that sound energy just gets reflected right back down into the Sun, but some of it gets out into the solar chromosphere and corona. No one can be sure, yet, just how much of that sound energy gets out, but it's most likely between about 30 and about 300 watts per square meter of surface, on average. The uncertainty comes because the surface dynamics of the Sun are tricky. In the deep interior, we can pretend the solar magnetic field doesn't affect the physics much and use hydrodynamics, and in the exterior (corona) we can pretend the gas itself doesn't affect the physics much. At the boundary layers above the visible surface, neither approximation applies and the physics gets too tricky to be tractable (yet).

In terms of dBA, if all that leaked sound could somehow propagate to Earth, well let's see... Sunlight at Earth is attenuated about 10,000 times by distance (i.e. it's 10,000 times brighter at the surface of the Sun), so if 200 W/m2 of sound at the Sun could somehow propagate out to Earth it would yield a sound intensity of about 20 mW/m2. 0dB is about 1pW/m2 , so that's about 100dB. At Earth, some 150,000,000 kilometers from the sound source. Good thing sound doesn't travel through space, eh?

The good folks at the SOHO/MDI project created some sound files of resonant solar oscillations by speeding up the data from their instrument by 43,000 times. You can hear those here, at the Solar Center website. Someone else did the same thing with the SDO/HMI instrument, and superposed the sounds on first-light videos from SDO. Both of those sounds, which sound sort of like rubber bands twanging, are heavily filtered from the data -- a particular resonant spatial mode (shape of a resonant sound) is being extracted from the data, and so you hear mainly that particular resonant mode. The actual unfiltered sound is far more cacophonous, and to the ear would sound less like a resonant sound and more like noise.

senescence - Have any mutations or genetic loci been associated with exceptional longevity in humans?

Individuals that avoid age-related diseases into later life are known as 'exceptional survivors', and have increased longevity compared to their 'controls' (those that were born at a similar time, yet have 'aged' and died sooner). The Leiden Study determined that in these long-lived individuals there is a considerable genetic component contributing to the survival [Schoenmaker et al] (although this could equally be epigenetic - or even more likely, a combination of both).

I have read about studies that have identified genetic mutations that cause premature aging phenotypes (for instance mutations in the WRN gene cause Werner's Syndrome [Yu et al]).

I have yet to discover any studies that determine any genes/regions associated with resistance to age-related disease (i.e. those that age 'well'). My question is whether anyone knows of any such studies?

Arguably studies that have looked into predisposition to age-related diseases have found some mutations - for instance mutations within the 9p21 genetic locus (i.e. p16INK4a/CDKN2A) have been associated with heart disease and stroke independently (2 age-related diseases) [Wahlstrand et al]. Therefore individuals without any of these risk-increasing alleles could be considered predisposed to exceptional survival - but I see this as separate to my question. Are there any protective alleles/genes/loci that increase 'global' survival? Are there a few protective alleles, or many with small effects? Or are the exceptional survivors just without any disease-causing/risk-increasing alleles?

I am interested in published research (of course), but also in peoples general perceptions of the topic; there are plenty of theories of aging and longevity, but few facts - so please state what you 'believe', and explain why this is the case.

Thanks for your time.

p.s. I am aware that you can genetically modify lab models (e.g. C. elegans eat-2 mutants [Lakowski et al]) to live longer. I am interested in naturally occurring variants, specifically in humans (or that at least relate to human aging).

---

Update (11 May 2012)

I have found a study, published earlier this year, that finds a single genetic polymorphism to be associated (after correction for multiple testing) with centenarians [Sebastiani et al]. The SNP is in TOMM40/APOE (in LD), which is certainly interesting given the previous links between APOE and Alzheimer's (an age-related disease).

However, I am not convinced by the experimental design; they use age-at-death in centenarians as their cases (having genotyped them), and they use alive population controls as the controls. Whilst there is unlikely all these individual will become long-lived, a better design (to gain more power) would have been to use individuals who have died from 'premature' (e.g. between 60 and 70) age-related disease. So I am still waiting for a convincing study, but this does look promising!

galaxy cluster - Are high-speed galactic collisions survivable?

Interesting question. I did a bit of reading and gave it some thought and and I can sort of give an answer, though I invite corrections and input from anyone more knowledgeable than me.

First, those 2 galaxies are enormous. I didn't see specific sizes listed, but per this paper:

1.2-1.5 x 10^14 solar mass fossil group

That's about 100 Andromeda galaxies. Also, since what we're seeing is 4.6 billion years old, it's reasonable to assume that those 2 galaxies probably have more free dust and gas and, being larger, the gravitational collision is happening at higher speed.

That's really the question with how much background x-ray radiation you get when 2 galaxies collide. how much free gas and dust and how fast the galaxies move into each other. My guess is that being larger, and younger, those 2 galaxies are glowing much more brightly than the Milky-way and Andromeda will 4 billion years from now.

As to how intense the glow is, my hunch agrees with yours, it's probably not very bright if you're there. The faint glow and the 2 bright eyes you see in the picture are long exposures. This site (scroll to the bottom) says it's 19 hours and 30 minutes of exposure. Andromeda, for example is barely visible to the naked eye, but when photographed it's made many times brighter. I'm not smart enough to say for 100% sure, but my guess is that the faint purple glow would be barely visible, if visible at all, assuming it even reached into the visible spectrum, which X-ray's don't. Chandra might be setting the color to a visible spectrum in the picture.

How dangerous is it? Again, I'm guessing, but I think in the Milky-way-Andromeda collision, we'd probably get more UV from the sun than we would from high speed gas and dust collisions, but that's just a guess. It would be kind of fun if the entire night sky glowed a little bit though.

As far as the Milky-way-Andromeda collision, Wikipedia says that there won't be much free gas in the collision, here, so it's a safe bet there won't be any visible glow in the sky and not even that much of an acceleration of new star formation, though there should be some. The Milky-way currently forms about 7 new stars every year, and that I imagine will gradually slow down over the next 4 billion years, then speed up significantly as the collision gets underway, but from the point of view of Earth, I don't think there's any guarantee we'd get a close look at any new star formations.

Here's a fun article/interview on the collision between the Milky Way and Andromeda, though I think Roeland van der Marel might be exaggerating the new star formation a bit if we're to believe Wikipedia where it says there won't be much free gas.

As for the speed of our collision, Andromeda is currently heading towards us (or, we're heading towards it, whichever you prefer) at about 110 km/s source. and it's currently about 2.5 million light years away. Source.

Covering 2.5 million light years (about 24 million trillion km) in 4 billion years (126 million billion seconds), works out to an average speed of 190 km/s, so we can roughly estimate that the speed of impact between our two galaxies will reach a peak somewhere around 270 or so km/s. But (see video you also have to take into account the rotation speed and it appears (video above) the rotations will be going in opposite directions when the galaxies collide. We orbit the Milky way at about 250 km/s and Andromeda, being larger, probably a bit faster orbit speed. Adding the 2 velocities together, in our neck of the woods, we might see some relative velocity and some gas & dust collisions at (guessing here, cause I don't know if the rotations will slow down as the galaxies approach), but lets say 500 to 600 km/s or so. For any close bright stars from Andromeda, that could be fast enough for visible changes to a few near-by Andromeda stars in constellations over a single human lifetime.

Perhaps, we'll pass through an oort cloud of another star every few thousand years or so, perhaps even the occasional kuiper belt equivalent, every ten or 50 million years - er, maybe. We could see some very impressive meteor showers and perhaps an occasional, slightly more frequent, dinosaur killing level comet or meteor impact - but I'm just speculating. There might be lots of interesting things to see between 4 and 5 billion years from now.

When stars form they can be (per this website) 100 to 200 times brighter than they are during their main sequence, so if our solar-system finds itself nearish to a colliding gas cloud and some new star formation, that could be interesting. Likewise if we pass near the core of Andromeda we might, for a while, have a very bright night sky.

human biology - How many genes do we share with our mother?

Say x is the percentage of an allele in your mom (or cousin, or brother). Say c is the filial similarity (brother=.5, son=.5, cousins=.125, etc.) of the allele. Say y is the general probability of having that allele in that population (assuming mom is the same species with you). Say f(x,y) is the expected value of the number of allele that you have.

Then f(x,y)= c * x+ (1-c) *y

In other word. There is no contradiction in the idea that we are 98% similar with monkeys and yet only 50% similar with our own mom.

Here, the world similar is used in totally different sense.

f(x,y) is 99% for most allele. Now let gy(x)=f(x,y) then

gy'(x) is c.

In other word, for every allele your mom have, it'll improve the expected value of you having the same allele by half. For each allele your cousin has, it'll improve the expected value of you having the same allele by 1/8th. That is for the same y. For most y, similarity is 100% nevertheless.

Say Ann, Beth, and Cindy has AA, Aa, and aa alleles.

Then Ann's sons have 25% higher expected value of having A alleles than Beth, and Beth have 25% higher expected value of having A alleles than Cindy. I say nothing of actual probability distribution.

Ann's cousins have .0625% higher expected value of A occurrence than Beth's cousins and .125% expected value of A occurrence than Cindy's cousins

Disclaimer: We do not take into account that people mate with those who are genetically similar but not too similar (i.e. no inbreeding).

Another way to see this is to look at y. For rare genes y is small. Hence.

50-50 is for genes that are rare and family specific. If your mother is color blind (100% carrier), the expected value of the number of color blind carrier is improved by 50%. It doesn't mean you'll be color blind. We'll have to go to the technicality of dominant vs recessive. But that's the idea.

For genes that are NOT rare, say genes that make you have 2 feet and 2 hand, you still share all your mom's genes. That's because everybody have that. Your mom have that, and your dad have that, and so is everyone else, including chimps.

Is this what most directly answer your question?

Again the issue is rarity. For rare genes P(You have it|mom have it) is 50%.

For common genes,

P(You have it|mom have it) = P(You have it and mom have it)/P(mom have it). //By bayesian rule

That is 1/1, which is true.

It's just obvious, probability = 1, that everybody has it.

Source: selfish gene by Richard Dawkins
I am a mathematician. Now prove me wrong.