At what speed is our solar system expanding, and if it is, why don't the positions of the sun and planets change, or grow farther apart? Why is the Big Dipper still where it is?
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Expansion only happens at higher scales, gravitationally bounded structures like planetary systems or even galaxies are unaffected. – Photon Jan 18 '16 at 18:36
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2Possible duplicate of https://physics.stackexchange.com/q/70047/. See also https://physics.stackexchange.com/q/71649/ and https://physics.stackexchange.com/q/228385/. – HDE 226868 Jan 18 '16 at 18:54
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Related: http://physics.stackexchange.com/q/2110/2451 and links therein. – Qmechanic Jan 18 '16 at 19:06
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an interesting point of view in this page cited by HDE Evidence that the Solar System is expanding like the Universe? – Jan 18 '16 at 19:14
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so what your saying is that gravity is the glue so to speak, and is totally dependent on Mass,and that gravity never releases it's hold on objects through centrifugal and centripetal forces? In other words Mass is Gravity, and is unaffected by expansion. I do know that gravity is considered the 4th strongest force in the universe, but I feel it's more important than that now Thanks Mark S – Mark Sottile Jan 18 '16 at 19:24
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Well, the nuclear forces are short ranged and the electromagnetic force is disabled due to all big bodies being electrically neutral, so gravity is the only force still in the game on large scales. – Photon Jan 18 '16 at 19:50
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Our solar system isn't expanding, because it's bound by gravity. Even though space is expanding, the positions of objects in the solar system stay the same because gravity pulls them back.
This is true for all gravitationally bound objects, even galaxies and galaxy clusters.

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What do you mean by "bound by gravity"? Do you mean that, for example, a comet on a parabolic trajectory around our Sun will be affected by space expanding (since it is not bound to a closed orbit), but a comet on an elliptical trajectory will not? Or do you mean that if the gravitational force is of sufficient strength then you won't notice the effects due to space expanding? – mbeckish Jan 18 '16 at 19:31
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I thing gravity is under appreciated. Without it we wouldn't have an atmosphere, or suns or planets. Thank God for Gravity. – Mark Sottile Jan 18 '16 at 19:35
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In general the expansion of space competes with the attraction of gravity. At local over-densities (which are now galaxies, galaxy clusters, etc), the force from gravity can be strong enough to pull everything together faster than space can expand them apart. The recessional velocity due to the expansion of space scales linearly with distance, hence gravity dominates on small scales and expansion dominates at large scales (in between galaxies). – Judge Jan 18 '16 at 20:03
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@Mark Sottile, yes indirectly. No gravity, no structure formation (cool visualizations of simulated structure formation), no galaxies, no solar systems, no us. – Judge Jan 18 '16 at 20:08
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Space without mass expands. The average expansion rate for large scales parsec and above measured is 73km/s. This expansion is calculated for average densities of space volume however this must vary significantly through voids and large mass concentrations. It would be interesting to mesure its variation through different mass densities within space to see if the relation between mass and space expansion is linear. – Barnaby Jun 06 '16 at 15:24
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And if you still need an answer for your speed of expansion (of the universe, because the solar system isn't expanding just by itself), it is measured to be about 74.3 km/s per megaparsec (a megaparsec being about 3 million light-years)

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