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Let's have two objects touching each other, i.e. me standing on the earth. We propel the smaller object directly away from the larger, i.e. I jump. The objects move apart, slow down and then return along the same path. According to Einstein, what's happening here is that the mass of the objects are bending space causing the straight line of my momentum to appear to bend in a 180 degree angle. However, because Einstein also says that this bending of space is happening in the forth dimension we can safely assume that we are not dealing with Euclidian geometry.

So according to the math what is that angle if not 180 degrees? Also that bend causes an acceleration of 9.8 m/s/s, correct? Would different angles change that acceleration? More precisely what is the relationship between the angle and the acceleration?

Bonus(?) question: What does that bend look like at a black hole?

Richard S
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  • Your question needs more focus, but for a projection of the proper radius into an extra space dimension see Flamm's paraboloid, and for the angle of lightcones (45° in flat spacetime and generally, but not necessarily bent in curved spacetime) see the coordinate dependend spacetime diagrams – Yukterez Nov 10 '23 at 14:48

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Here's a spacetime diagram that illustrates your jump:

enter image description here

No 180° U-turn anywhere in sight. In fact, the angles in the diagram don't really mean a lot because they depend on the relative scale of the time and space axes. The time axis in my diagram is hugely compressed as compared with the usual convention in which, the world line of a photon makes a 45° angle with the space and time axes.

If I drew the diagram true to that scale, then my sheet of paper would need to be tens of kilomters long to acomodate the time axis. and the angles between your world line and the Earth's world line would be imperceptible.

Solomon Slow
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