Is expansion slowing down galaxies?

June 16, 2009 11:09 AM

Does expansion of the universe decelerate orbits of planets and/or rotation of galaxies?

My understanding of the expansion of the universe is that, essentially, new space is appearing everywhere. I've heard it said that gravity holds solar systems and galaxies together, and they don't expand or grow in size from this inflation. However, the space between galaxies does grow, because gravity at these distances can't compete with the expansion. (Correct me if any of this is wrong.)

That leaves me wondering... If gravity is overcoming the small amount of inflation within solar systems and galaxies, then it must come at a cost. Gravity doesn't introduce new energy into a system, so my intuition says correcting the orbit of a body to its original distance must come at a cost of orbital speed.

Is this thinking correct, or am I missing something?

posted by knave to science & nature (11 comments total)

Just a quick note: you're misusing the term "inflation" here. Inflation refers to a specific epoch of expansion that happened soon after the big bang, not the ongoing expansion that's happening now.
posted by mr_roboto at 11:18 AM on June 16

I see where your intuition is coming from there, but my guess is No. Because think of it like this. Gravity is all about the curvature of spacetime, right? and expansion is all about the...expansion of spacetime, right? So then add them together and you get some combination of stretching and curving of spacetime. It's conceivable those could cancel each other out, as you say. I can sort of convince myself of that by thinking of a rock sitting on silly putty while it is expanding. As the putty expands, the slope of the indentation would get smaller, but for the fact that now the putty is thinner, so overall the slope remains the same. No need to bring angular momentum and velocity into the picture. I don't know, my two cents.
posted by metastability at 11:57 AM on June 16

Um... metastability, that analogy doesn't make any sense whatsoever. There is no "putty" in spacetime.
posted by vernondalhart at 12:10 PM on June 16 [1 favorite]

Wikipedia knows everything. Not quite true, but this article is pretty good; especially read the section on "Local perturbations".
posted by nat at 12:15 PM on June 16

Not to put words in anybody's mouth, but I think in the above analogy, putty and rocks are being used instead of the rubber sheets and bowling balls in the more familiar version.
posted by xbonesgt at 12:16 PM on June 16

Ah, let me highlight the important sentence: "However this does not cause the objects to grow steadily or to disintegrate; unless they are very weakly bound, they will simply settle into an equilibrium state which is slightly (undetectably) larger than it would otherwise have been."
posted by nat at 12:16 PM on June 16

Except that while nicely visual, that image is ultimately flawed; it presents massive objects as somehow sitting on top of spacetime, which is itself sitting in a larger space; none of this is actually true. That analogy is no better than his, and equally fails to answer the question.
posted by vernondalhart at 12:19 PM on June 16

> That analogy is no better than his, and equally fails to answer the question.
oh, I agree. :) I was just pointing out that the concept was a known (if incorrect) one, even though the vocabulary wasn't.
posted by xbonesgt at 12:24 PM on June 16

Short answer: Its not easy to take geometries which apply to the Universe as a whole and infer correctly how they would work at a local level. Expansion is a gross feature of the Universe based on its larger geometry. Matter, including those in solar systems, may obey a different local geometry. In the case of our solar system for example, orbital deviations are more affected by the Milky Way than by the cosmic expansion.

All that said, cosmic geometry could be considered as a perturbation on orbits. This paper calculates the effects of different geometries on local orbits and concludes that the effect, if any, is too small to measure. Over the entire lifespan of the solar system for example, the fractional change of the Earth's orbit might be 10^(-23).

Gravity doesn't introduce new energy into a system, so my intuition says correcting the orbit of a body to its original distance must come at a cost of orbital speed.

Thats a good observation. The energy can also be absorbed into the galaxy as a whole to which the solar system is bound. This would create an additional term in the galactic virial theorem.
posted by vacapinta at 1:30 PM on June 16

I'm going to introduce a small complication by way of dark energy. Yes, the universe is expanding, as an intrinsic part of the Big Bang. But from around 5 billion years ago, dark energy began to accelerate this expansion.

As I understand it, the expansion of space-time is homogeneous everywhere in the universe due. Both this basic expansion and dark energy does not, at this stage, affect matter that is already gravitationally "clumped" together (i.e. the Earth itself is not getting larger due to expansion or dark energy, but the distance between the Earth and the Moon is increasing, at the rate of a few millimeters per year (the contribution of dark energy to this increase is likely extremely small)).

The power of dark energy is roughly 30 proton masses per cubic meter - i.e. very small at local distances. The rate of expansion of the universe is roughly 100km/s per megaparsec (1 Parsec = 3.26 light years or 3.08568025 × 10¹³ kilometers), and a megaparsec is 1 million parsecs, so again, its contribution is very small over astronomically small distances, including the width of most galaxies. (Our Milky Way galaxy is roughly 100,000 light years in diameter, or 30 parsecs)). Gravity is still more powerful than both of these over incredible distances: we are on a (very slow) collision course with the Andromeda Galaxy due to gravity, for example.

Dark energy is repulsive, and piggybacks on the expansion of the universe - as more space is created, there is more of a medium for dark energy to work in, and thus it gains in power. Conversely, as more space is created, gravity grows weaker, following the inverse square law.

Possibly very very far in the future (a trillion years or so), as the power of Dark Energy grows with the expansion of space, the cosmos might experience what is called "The Big Rip", with dark energy tearing apart space-time at local, human-understandable distances. And you're quite correct that larger orbits are slower. But the contribution of both expansion and dark energy to orbits are very very small at this stage.

You might enjoy listening to this podcast from the excellent Astronomy Cast for more information.
posted by Bora Horza Gobuchul at 1:57 PM on June 16

I started thinking about this, but I'm going to go with "what vacapinta said," it's actually trickier to think about than it first seems.

An aside: on the "putty issue." The way it's usually presented is incorrect/highly misleading (yet annoyingly it still pops up everywhere). A better but equally simple mental picture is to first to remember that general relativity is about the curvature of spacetime not just space.

Draw a set of axis with the speed of light multiplied by time on the vertical and spatial position along the horizontal axis. Consider being at rest with respect to the solar system. If you plot the worldline of the sun it goes straight up the vertical. The worldline for the earth curls round this in a spiral (but it's almost a straight line since the speed of light is large).

This is a lot simpler on paper than words...
posted by Erberus at 3:27 PM on June 16