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Someone with a background in mathematics and limited knowledge of physics asks the following question:

Starting from rest, a spaceship is momentarily pushed with a specific amount of kinetic energy in a chosen direction. What is the resulting locus of velocities, considering all possible directions, after one unit of time (one second)? That is the spaceship itself has some velocity and I want to know how the perturbation due to the black hole affects the velocities, considering all possible directions. I also assume that the conditions in all points around the spaceship are identical and the curvature is zero.

Following this initial impulse, the spaceship navigates with a certain velocity. However, once affected by the gravitational pull of a black hole, the resulting velocity may differ in both direction and magnitude.

Consideration is given to the following cases:

  • The spaceship is located far from the black hole.

  • The spaceship is situated close to the event horizon.

  • The spaceship crosses the event horizon.

By the way, I choose the local coordinate system. The Euclidean!

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  • $\begingroup$ I tried to use Newton's energy conservation and force laws. Those approximations are good only far from the event horizon. To understand what happens close to a black hole, you have to learn General Relativity. $\endgroup$
    – Ghoster
    Commented Apr 4 at 20:02
  • $\begingroup$ I am from mathematics and a bit too old to learn general relativity :) I just hope some one can give me some clue how to deal with the problem $\endgroup$
    – Majid
    Commented Apr 4 at 20:06
  • $\begingroup$ Then you will have to rely on getting an answer rather than doing the calculation yourself. $\endgroup$
    – Ghoster
    Commented Apr 4 at 20:08
  • $\begingroup$ a circle, case 1 Why are you talking about circles rather than spheres? Space is three-dimensional, not two-dimensional. $\endgroup$
    – Ghoster
    Commented Apr 4 at 20:09
  • $\begingroup$ In Newtonian physics, maximum power doesn’t cause a particular velocity. It causes a particular acceleration. If the engines keep providing thrust, the rocket keeps going faster and faster. $\endgroup$
    – Ghoster
    Commented Apr 4 at 20:13

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