I Gravity invariant with motion?

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In simple examples of throwing a ball upward and observing it's arc, the calculations include a constant vector acting downward on the ball throughout it's flight. Without getting into the complications of that vector changing magnitude with altitude, it does not change with respect to the speed of the ball... it is a constant acceleration in the direction of the field.

So when the ball is at peak altitude v = 0 that vector is g = -x
And, when the ball is moving in flight that vector is still g = -x

Now that does not seem so strange because as a geodesic perspective the local curvature is what it is despite the apparent change in the ball's speed. Is the ball's 4speed locally constant?

But since the ball is in free fall can I take it as an inertial reference frame and imagine the Earth receding, pausing, and approaching, because where would the energy come from for it to accelerate like that? But in either case, it then looks like the gravitational force is a constant regardless of the relative motion of the source (Earth) or observer (ball).

Don't moving charges also have constant acceleration in the direction of the field? Without considering the change in distance, is the force (local instantaneous) between moving charges also constant regardless of the relative motion of the charges?

I'll pause here to learn if I'm already off the rails before advancing more questions...
Thanks :)
 

A.T.

Science Advisor
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....I take it as an inertial reference frame and imagine the Earth receding....
It's only locally an inertial frame, not when you extend it to include the entire Earth.
 
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Is the ball's 4speed locally constant?
Yes. The norm of the four velocity is always c. It is essentially normalized to make that true.

imagine the Earth receding, pausing, and approaching, because where would the energy come from for it to accelerate like that?
There is an unbalanced real force pushing upwards which caused the acceleration. If you follow the energy flow you pretty quickly get to a point where you cannot use the flat spacetime local approximation any more.

But in either case, it then looks like the gravitational force is a constant regardless of the relative motion of the source (Earth) or observer (ball).
The gravitational force is 0 in the local inertial frame, by definition. It is nonzero in the ground frame, which is non inertial.
 

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