# Ball thrown up always moves at constant speed

When a ball is thrown up straight overhead. It just follows the curved space with the speed it is being released and seems as if the ball gradually slows down to zero at the top most and return to earth.

If I'm right, according to Newtonian physics, the ball speed is zero at the top. And according to Einstein physics, the ball speed doesn't slows at all, it travel with the same speed it is being released.

So if an object is placed at the top most height the ball achieve. What impact the object would have with the ball at the top most, with zero speed or the speed it is being released.

## Answers and Replies

WannabeNewton
Science Advisor
And according to Einstein physics, the ball speed doesn't slows at all, it travel with the same speed it is being released.

No that isn't true. GR says the ball follows a geodesic of the space-time so that its 4-velocity is constant along its worldline; more precisely the 4-velocity of the ball is parallel transported along the geodesic worldline. But you're talking about the 3-velocity of the ball which is quite different from the 4-velocity. The 3-velocity can only be made sense of relative to some coordinate system or reference frame. If the reference frame is fixed to the Earth, such as in your example, then the 3-velocity of the ball will in fact behave in exactly the same way in both Newtonian gravity and GR, modulo higher order special relativistic effects.

PeterDonis
Mentor
2020 Award
if an object is placed at the top most height the ball achieve. What impact the object would have with the ball at the top most, with zero speed or the speed it is being released.

Zero speed. As WannabeNewton pointed out, "speed" in the sense you are using the term (3-velocity) can only be defined relative to some coordinate system or reference frame. Since the object placed at the topmost height the ball achieves is at rest relative to the Earth, the obvious reference frame to use is one fixed relative to the Earth, and as WBN said, in this frame the ball's speed is zero when it passes the object.

However, we can also reach the same conclusion regarding the relative speed of the object and the ball when they meet by using a frame in which the ball is at rest. As long as the maximum height the ball reaches is not very large, so that the effects of tidal gravity can be neglected, we can construct a local inertial frame covering the entire experiment, in which the ball is always at rest. In this frame, both the ground and the object at the topmost height the ball achieves are accelerated and follow hyperbolic worldlines; and the hyperbolic worldline of the object is just tangent to the ball's worldline (i.e., to the time axis of the local inertial frame), indicating zero speed in this reference frame, at the instant when the ball reaches the object's height. So in this frame as well, we can derive the correct conclusion that the ball and the object have zero relative speed when they meet.

George Jones
Staff Emeritus
Science Advisor
Gold Member
I think the fact that the ball has zero 4-acceleration is confusing [/PLAIN] [Broken]

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