Expansion of Universe And Its Influence on Earth Orbit

[CarstenDierks]

Assuming the expansion of the universe as a given fact, how does it influence orbits i.e. of the Earth around the sun or other planets in the solar system? Is it also usually included into the calculation of trajectories of space crafts (i.e. Pioneer, especially with regard to the Pioneer anomaly)?
Due to the universal expansion, the radius of the Earth around the sun must be affected by it as well. The influence of the expansion on the Earth orbit is very small but should still amount to approximately 0.5 meters every year. Is it the gravitational force of the sun which keeps the Earth "on track" so the radius does not change at all?

 

[bapowell]

Is it the gravitational force of the sun which keeps the Earth "on track" so the radius does not change at all?

Yup.

 

[CarstenDierks]

OK. But does it mean that a "constant drag" of the expansion exists which tries to "push" Earth and sun apart?

And if the gravitational force of the sun (or better: the gravitational force of sun and Earth together) is large enough to act against this force, does it imply that the gravitational force of the sun is actually slightly larger than calculated because it has two components: the centripetal force to keep the Earth in orbit and the additional gravitational force to act against the "drag" of expansion?

 

[Calimero]

OK. But does it mean that a "constant drag" of the expansion exists which tries to "push" Earth and sun apart?

And if the gravitational force of the sun (or better: the gravitational force of sun and Earth together) is large enough to act against this force, does it imply that the gravitational force of the sun is actually slightly larger than calculated because it has two components: the centripetal force to keep the Earth in orbit and the additional gravitational force to act against the "drag" of expansion?

You should make a difference between expansion and accelerated expansion. In the first case things are just on their way, and since no force is acting on them, no force is needed to hold them together. In fact, gravity is here expected to slow down, or reverse expansion.

If you are talking about accelerated expansion or dark energy, things are little bit different. My guess is that Earth's orbit would not be exactly the same with or without DE, or that equilibrium point is a little bit stretched away from Sun. That does not mean that Solar system is expanding, it just means that if DE suddenly disappears orbits would shrink for very tiny amount.

 

[marcus]

OK. But does it mean that a "constant drag" of the expansion exists which tries to "push" Earth and sun apart?

And if the gravitational force of the sun (or better: the gravitational force of sun and Earth together) is large enough to act against this force,..

Carsten, Powell is already engaged in this thread and he knows the stuff thoroughly so I would normally not jump in. He'll probably get back sometime today.

What your question is basically about is how to intuitively picture the expansion process, how to "feel" it with your acquired physics hunches, what familiar physical analogies to use. In a sense the mathematical reality is the same for everybody but different people may prefer different words and images.

Since you wrote me a PM asking about this, maybe I'll jump in, but hopefully Powell will still give his description of how to look at it. It's good to get several different takes and see which one is clearest for you.

My view is that galaxies experience only small accelerations due to forces around them and (compared with light) have only trivial or negligible speeds in their surroundings. You talk in terms of forces, but in my view of expansion force plays no role. It is negligible. Very large scale distances expand because geometry is dynamic, vintage 1915 Gen Rel is a story about dynamic geometry, how distances change. We have no right to expect that distances will not. But at present the overall expansion rate is only 1/140 of one percent per million years. And only concerns widely separated points or observers which are not gravitationally bound (it doesn't involve clusters of stars or clusters of galaxies because they are bound by gravity in stable configurations.)

What is basic in the way I approach this, intuitively, is the ancient light of the cosmic microwave background. You know you are stationary relative to Background if you have no doppler hotspot. If you are moving you will see a hotspot ahead and a coldspot astern.
As far as we can tell, galaxies are all approximately at rest relative Background. The deviations that have been detected are quite small. (on order 1/1000 of c).

What the Hubble law talks about is the rate of increase of distances between observers which are at rest relative CMB. It describes a simple feature of the dynamic geometry we happen to be in. It says v = Hd where d is a distance and v is the rate that distances is increasing. Distances are measured between stationary observers, ideally. In practice, between widely separated galaxies considered to be approximately stationary.

Maybe other people will give you some different intuitive takes.
In Gen Rel, what is called the "gravitational field" is actually a distance function which describes a geometry. And which is dynamic, it changes on its own and in response to matter, according to the 1915 GR equation. So our best (essentially our only) way to understand gravity at present requires us to chuck out Euclid and a bunch of static-geometry-type expectations. That's the part that takes getting used to.

 

[CarstenDierks]

Thank you for the answers!

The influence of the expansion is very tiny in terms of our everyday world. However, regarding the Pioneer anomaly, there is a very tiny discrepancy which leads to the deviation in its flight path.

So if the gravitational force of the Earth is slightly larger than calculated, could it be the reason why the Pioneer probes are closer to the sun than foreseen?