# Momentum of far distant star

1. Feb 16, 2009

### old ned

So far i understand that a star many light years away from us can be moving at the speed of light, but this breaks no rules as it is traveling with space.
But how about the star's momentum relative to us on Earth, i can only guess as it is moving away from us at the speed of light it's momentum would be the same as a star actually traveling through space.
But then that sounds strange, as the universe would be gaining energy as it gets older

Thank you, old ned.

2. Feb 16, 2009

### marcus

It's good to talk out the conceptually confusing stuff. A lot of people's problems just come from how you think about something, how you picture it.

You might get some benefit from the first few posts in the balloon sticky thread. And from watching the Ned Wright balloon model animations. That model can teach you the idea of being at rest with respect to the CMB. Or equivalently, at rest wrt the expansion process itself. This is an ever-present idea in cosmology that has been used since the 1930s even before the CMB was known.
Then it was called "at rest wrt the Hubble flow". Also "comoving with the Hubble flow" but that is a bad terminology because it suggests motion. It is really an idea of rest.

In the balloon model, things at rest are what stays at the same latitude longitude on the balloon.

Galaxies have neglible motion, none of them are moving very much (only a few hundred km/s which is small compared to typical distance expansion rates.)
The Hubble law is about things which are at rest. It says the distance between them increases about 1/140 of a percent every million years.

The whole point of General Relativity is that geometry is dynamic. We have no right to expect distances to stay the same. Distances between stationary objects can change, and do change on a regular basis.

Euclid geometry is not real. Nature does not have Euclid geometry. It just happens to be a good approximation where we live because where we live the density of matter (which influences geometry) is very low, so Nature's geometry is very nearly flat (aka Euclidean). At our scale the percentage deviations are very small so we can neglect them. And the percentage expansion rate is very small as well. But on a much larger scale you simply can't expect distances to stay the same. The change GR tells us about is no longer negligible.

Distances increasing or decreasing like that is not ordinary motion, however! If you pick out any galaxy which has redshift 1.4, then the presentday distance to that galaxy is currently increasing at the rate c. But it is not good to imagine that the galaxy is moving.
It may have some small private random motion of a few hundred km/s, just as we do. But that is negligible.

So you don't have to worry about its momentum. Consider that as negligible too.

Old ned, has this helped at all? Are you still confused? If so keep asking. I or somebody will probably respond.

Last edited: Feb 16, 2009
3. Feb 16, 2009

### v2kkim

One interesting case may be about a very fast orbiting star around a heavy black hole.
So the star has 2 components in motion, one moving away due to space expansion and another local circular motion. When we calculate the red shift, these 2 components need to be treated differently. Obviously the one can go larger than 'c' but not another one. The right cal method may be to calculate the local motion effect first using relativistic doffler effect and then apply space expansion effect.
Obviously space expansion is a holy great principle, which makes the object distance increase instantly across the board (universe) regardless of the mess or charge whatever of the objects. For me, time and distance seem to be similar, because they increase monotonously only in one direction -- increase.

4. Feb 16, 2009

### Chronos

That is peculiar motion and will not exceed more than a small fraction of light speed.