# If an object is orbiting another body, don't both the orbiting object and an observer "know" that the orbiting object is moving?

In many relativity illustrations, it is mentioned that someone in a spaceship believes he is standing still and the observers are moving and vice versa. The example of a light-beam clock slowing down for an observer but not for the passenger of the ship is often how relativity is explained.

But if the ship is in orbit about another body, the I think the passengers can measure this speed. Does the mirror clock argument still work?

Well Yes, but actually no. You know that Earth is orbiting the Sun, because you can observe relative motion of Sun to the other (fixed) stars on the sky. But let Say now, that we don't have any other Stars or reference objects. And let's introduce 2D polar coordinates. Let say, that we are on the Sun, and we believe We are stationary. We can then expres position of Earth as:

$$\textbf{r}=r_0(\cos \phi, \sin \phi)=r_0(\cos \omega t, \sin \omega t).$$

But we can se, that if we set the coordinate system to the system of Earth we se $$\textbf{r}_{Sun-reference}=-\textbf{r}_{Earth-reference}$$, ergo: $$\textbf{r}=r_0(\cos \phi, -\sin \phi)=r_0(\cos \omega t, -\sin \omega t)$$.

We can observe, that we don't have any special effect in the motion, which will show us, which object is actually orbiting around other. But it can be seen, that the rotation changes sign (clockwise to counterclockwise and vice versa.

Bear in mind, that this is only explanation, why you can't know if you are moving or not, if you observe orbiting. I would be happy to see any comments if this is really valid explanation if this case, or should I've been using Lorentz transformations.

• can't you detect acceleration? if one object revolves around another, one experiences acceleration and the other does not, irrespective of other objects, I think. Jan 31, 2021 at 9:45
• As long as we have gravitation, which connects 2 bodies, they both feel it... but It should work also without... Probably I should rewrite with Lorentz transform...
– Vid
Jan 31, 2021 at 9:53
• But... orbiting is not inertial frame of reference... I believe, that you cant determine if you are standing still or travelling only if you travel without acceleration, which is not true for orbiting.
– Vid
Jan 31, 2021 at 9:56