Body A is sitting on a chair at sea level.
Body B is sitting on a chair on a tall mountain.
Body A mass = Body B mass
Not sure how to ask this question – but I want to know, given all of the movements they both would experience: the earth rotating about its axis, the earth revolving around the sun, the solar system revolving around the center of the galaxy, etc., which Body would be accelerating more? A more than B, B more than A, or equal? I don't think the usual formulas regarding acceleration can answer this, but again I'm not sure.
Thanks for your time!
Best Answer
Given the fact you're talking about rotation, you'd be asking about centripetal acceleration.
The person on the mountain is further away, so for that person their distance from earth's center is greater. But the person on the mountain would also have a greater tangential speed since they move a greater distance in the same amount of time.
But note that centripetal acceleration is given by $$a=\frac {v^2}{r}$$ which means that although the acceleration drops off as $\frac 1r$, it also increases as the square of the velocity. This means that the centripetal acceleration for the person on the mountain is greater. Now as for your question regarding the sun, solar system, galaxy etc., given that both observers are in the same frame of reference about these bodies (earth's surface), the amount they accelerate about these bodies is the same.
Ignoring rotation, since they are both in a stationary frame of reference (earth’s surface), neither of them are accelerating from the point of view of someone on earth’s surface, nor are they moving with respect to each other.