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GSV Sleeper Service
2009-Apr-22, 09:31 AM
Hello.

Are the distances between the planets in our solar system increased due to the expansion of the universe? I would assume so. If this is correct by how much and how would one calculate it?

Thank you.

(I tried to search this site which usually finds me the answer(s) I need but it is down at the moment, if that has been answered before I apologise)

novaderrik
2009-Apr-22, 09:50 AM
the expansion of the universe really only applies when you get up to the inter galactic scale- below that, local forces tend to hold things together.
at least that's the way i understand it.

grant hutchison
2009-Apr-22, 01:00 PM
Yes, objects smaller than galaxy clusters are too strongly bound to participate in the general expansion of the Universe.
Lineweaver and Davis discuss this towards the end of their Scientific American article (http://www.sciam.com/article.cfm?id=misconceptions-about-the-2005-03) about the Big Bang. (See the section Is Brooklyn Expanding? on page five.)

Grant Hutchison

GSV Sleeper Service
2009-Apr-22, 02:12 PM
Yes, objects smaller than galaxy clusters are too strongly bound to participate in the general expansion of the Universe.
Lineweaver and Davis discuss this towards the end of their Scientific American article (http://www.sciam.com/article.cfm?id=misconceptions-about-the-2005-03) about the Big Bang. (See the section Is Brooklyn Expanding? on page five.)

Grant Hutchison

Thank you that article is perfect.

Ken G
2009-Apr-22, 04:43 PM
Note also that one way to think about this is that whatever is "causing" the universe on huge scales to expand (which in some very general sense would appear to be "gravity", even without dark energy) does have a tiny influence on our solar system, but the main gravity that affects our solar system comes from the Sun, and that is what controls the orbits of the planets (so the orbits would be predicted to expand but only an extremely tiny and unmeasurable amount in relation to how the Sun reins them in).

grant hutchison
2009-Apr-22, 04:55 PM
so the orbits would be predicted to expand but only an extremely tiny and unmeasurable amount in relation to how the Sun reins them in.And (according to Lineweaver and Davis) this would be a fixed offset in orbital radius induced by the acceleration of the Universe's expansion. There would be no offset if the Universe were expanding at a constant rate, and there would be continuous growth only if the acceleration of the Universe's expansion were itself increasing with time (a "Big Rip").

Grant Hutchison

agingjb
2009-Apr-22, 07:14 PM
The expansion of space is given as about 70km/s per megaparsec (no clue if or how this varies). Someone can work that out for the annual expansion of the Earth's orbit. It's small. My first try came out at a tenth of a millimetre, but I've almost certainly lost or gained an order of magnitude somewhere. 400 kilometres since the Earth was formed?

publius
2009-Apr-22, 07:24 PM
You know, there can be a lot of confusion over this, and I've been cornfused on it myself.

In a straight FLRW universe with no cosmological constant, the "cosmological tide" would always be *compressive*, as the gravity is slowing down the expansion (which is an initial condition on the scale factor, we've "thrown" all the mass apart -- see the thread about the simple Newtonian model).

It is only when we throw Lambda (dark energy) in, and during the stage when Lambda "takes over" after the regular matter density falls below a critical value do we get the "rip tide".

The behavior of a local system in the presence of such a Lambda rip tide can be analyzed by the Schwarzschild-deSitter metric, which is a solution for a point mess immersed in a lambda background.

g_00, looks something like this:

1 - R/r - kr^2,

where k depends on Lamdba (and would be very small) and R is the usual Schwarzschild radius. The Newton potential (weak field where g_00 is close to 1) goes as just -R/r - kr^2. The second term gives you a linear, radially repulsive g(r) which acts against the normal inverse square term.


For the currently accepted value of Lambda, k would be so small as to make this undectable on the solar system scale.

Without Lamdba and with a compressive tide, you can just about change the sign of k and get a slight linear compressive cosmological tide component, but that would vary with time, decreasing with the cosmological density as the universe expanded, and increase if it started collapsing back on itself. And that of course assumes a perfectly uniform mass distribution -- lumpiness would change everything when the average density was small, as it is now.

-Richard