What does not accelerate?

Question

According to special (& galilean) relativity, there is no difference between constant movement or not moving at all but it is possible to detect acceleration and rotation is acceleration.
The earth rotates around the sun and the sun rotates around Sagetarius A* (the black hole in the center of the milky way).
So, there should be small accelerations directed to the center of rotation all the time.
Are those accelerations detectable? I think that it should be easily possible to detect the earths rotation around the sun but what about the rotation of the milky way?
Also, does the milky way accelerate in any direction or is it moving constantly?

mike stone · Accepted Answer

For objects moving under gravity, the centre of mass is in free fall so one cannot directly use an accelerometer to detect any acceleration of the centre of mass. If, however, the gravitational field is not unform (as is the case of the earth orbiting the sun) and the body is stuck together so as to move as a whole (as is the earth), then some parts of the body are not in free fall and the mismatch between their dragged-along motion and local free fall is detectable. We call the resulting effects tidal forces as they are the origin of the ocean tides.

Correct answer by mike stone on October 2, 2021

R.W. Bird · Answer

I have read that the Milky Way and Andromeda are falling toward each other and that the two of them are falling together toward a region of the sky which contains a large cluster of galaxies. It occurs to me that if you assume that the galaxies are uniformly distributed throughout the universe, then the net force on any one of them would be zero. That means that gravity would not oppose the expansion of the universe.

Answered by R.W. Bird on October 2, 2021

What does not accelerate?

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