general relativity - Is there 'friction' in spacetime?

So, if all the bodies are embedded in space-time and moves through it, is there some kind of 'friction' with space time of the planets? For example, the Earth suffers friction when moving near the sun due the curvature and General Relativity and loses energy?

If a planet loses energy due to friction can this energy loss be measured?

Answer

I think the question suggests you are thinking of space-time as if it were e.g. a substance, like a fluid, that we move through. That's not how we view space-time, at least in pure general relativity.

But the question you ask is a deceptively simple one and it raises some complex questions. And I don't think we actually can answer them exactly because I'm not sure we have a definitive answer to the most basic question hidden in your answer: What is space-time?

is there some kind of 'friction' with space time of the planets?

There is a "kind" of friction, but perhaps "interaction" would be a better choice of word, as I'd prefer to avoid the notion of classical friction forces.

We say that when an object moves through space time it distorts space time - stretches it, compresses it. Mass creates distortions we describe as gravity.

It's a little deeper than that.

We also know, thanks to the wonderful LIGO experiments, that these gravitational effects do distort space in a wave-like way. And an object can lose energy (has to, in fact) when it creates such waves.

Which leads us to this:

if a planet loses energy due to friction can this energy loss be measured?

No (I suppose I should say, not at our technological level). It's tiny.

The gravitational waves we have measured (which represent the closest thing to your friction loss) are due to the collisions of huge black holes, and the disturbance they make is so small that LIGO scientists are pushing the boundaries of measurement to detect them at all. A planet is a tiny thing compared to those black holes and it barely makes a dent, as it were, in space time by comparison.

But it's worth saying that our current understanding of space-time is a little basic. We don't have a clear idea of how the quantum world fits into the grand scale of relativistic space-time. At present we have two models, one of a small scale space-time filled with a sea of virtual particles and the other of a pure, clean empty space time with the odd idealized gravitational mass in it. We don't have a single theory connecting them, so we don't really have a proper theory of space-time (or perhaps something deeper than that is needed - no one knows).