Is the Milky Way winding up like spaghetti on a fork, or spinning out like frosting in a blender?
Neither. The Milky Way has already completed something like 20 full revolutions, IIRC, so if it were winding up or spooling off, it would be a huge coincidence for it to be in its present, fairly "relaxed" configuration just at the time at which we happen to observe it. Furthermore, most spiral galaxies have similarly "loose" spiral arms.
As far as I know, the favoured model explains this by interpreting the arms as transitory phenomena rather than material structures. What we see are simply regions which are currently brighter than the rest of the galactic disk, and those regions travel differently than the stars themselves. So, at most distances from the centre of rotation, the arms will either travel faster than the stars, and therefore periodically catch up with and pass by longer-lived stars, or vice versa travel slower than the stars, and therefore it's the stars which catch up with and pass by the arms. There may theoretically be a distance at which the two speeds coincide, but I don't think this is the case.
To visualize, think of the stars like Muslim pilgrims walking around the Qaaba, and think of the arms as The Wave performed by the audience in a sports arena. Mentally combine the two, and you have two rotational motions going on concurrently, one which is due to the actual motion of the pilgrims/particles/stars, and one which is a kind of signal passed along by the particles and made up of different particles at different times.
Anyway, the arms are assumed to be rotating with a constant angular speed, with no winding in either direction. This would be impossible if they were material structures, unless one imagines them being actually physically connected, which is clearly preposterous. But it's entirely possible for a transitory signal to behave that way.
All that being said, it's been a while since I've studied this, and there's a chance that more recent results have invalidated this model in the meantime. If so, I trust one of the more learned members will correct me ere long. :)
There are two leading theories to explain spiral arms of galaxies [and the winding dilemma] - the spiral density wave and self sustaining star formation theory. It appears both theories are probably true. See http://www.kcvs.ca/martin/astro/au/unit5/123/chp12_3.html for discussion.
Not in any significant way.
Again, not in any significant way. Earth is radiating some 300W of gravitational waves, which leads to an orbital decay, but this is something like a proton diameter per year if I remember correctly.
For stars in the galaxy, it is even less. The gravitational influence of nearby stars is much more important, and can modify the orbits. But there is no general trend towards (or away from) the central black hole.
If their orbit is too low (<400km), they have significant drag from the atmosphere and will crash after a while.
If their orbit is high enough, it is stable.
This is not relevant for planetary orbits or orbits of stars in galaxies.
Nice fact to know. I'd like to put that in the Astronomy reference library. Anybody (maybe Mfb?) have a link to some source for it.
EDIT: I found one: Wikipedia
"If we use the previous values for the Sun and the Earth, we find that the Earth's orbit shrinks by 1.1×10−20 meter per second. This is 3.5×10−13 m per year which is about 1/300 the diameter of a hydrogen atom. The effect of gravitational radiation on the size of the Earth's orbit is negligible over the age of the universe. This is not true for closer orbits."
The Wikipedia article gives the formulas one would need to calculate the rate of energy loss and the decrease in orbit radius.
EDIT: I used the formula for power output from binary system, from that article, and typed this into google calculator:
"32/5*G^4/c^5*(mass of earth*mass of sun)^2(mass of earth+mass of sun)/(1 AU) ^5="
and it said "196 watts"
I am imagining how I would use a ball on a string to send out radio waves. I would put a static charge on the ball, perhaps by rubbing it with cat's fur or silk, and then I would would whirl the electrically charged ball around say 1 revolution per second, sending out 1 Herz radio waves.
So the orbiting Earth is sending out gravity waves. One knows about Hulse&Taylor Nobel prize for observing a binary pulsar doing this, but I never heard the watt figure for Earth, till now.
Not sure if this is too far off topic. The earth's motion is prograde around the sun, meaning the sunset side of the planet is always on the trailing edge of the earth's orbit around the sun. Since the sunset side is warmer on average, wouldn't this side emit more black-body radiation, causing a net thrust working to increase the earth's velocity about the sun? It'd be a small effect even on cosmological timescales, but it could easily counteract a 200W loss from gravitational waves.
As long as the sun continues to shine, that is.
Oh, 200W instead of 300W. It is an interesting coincidence that those large and small numbers come together and the result is comparable to the power of a human.
@Shovel: Maybe. But there is also the Poynting–Robertson effect in the opposite direction. I get a force of ~58kN, multiplied by the speed of earth this corresponds to ~1.7GW.
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