4 ms·

This is correct. The simplification being made is that the original orbit was circular, so if you increase the debris' velocity, the current point is now the lo

This is correct. The simplification being made is that the original orbit was circular, so if you increase the debris' velocity, the current point is now the low point of the new orbit.

tgb 6y ago
Even for circular orbits, is that the case? The new low point would be lower if impulse is not parallel to the velocity.
- sand500 6y ago
  Correct, so basically the lowest point(periapsis) of the new orbit cannot be any higher than the point where the collision happened.
  - TeMPOraL 6y ago
    Another way to think about it is, an orbit around a single body is entirely defined[0] by your current position and your instantaneous velocity. Six numbers. Where you are, which direction you're going, and how fast. Such orbits are closed, which means wherever you are right now, you'll return to that exact point later. So if you're at point P in your orbit and suddenly kinetic energy was added, your velocity changes in some arbitrary way. While you aren't sure where you'll go and when you'll get there, as long as the new (position, velocity) pair still defines a closed orbit around the body, you can be damn sure you'll return to the exact point where you are now. From this follows that the lowest point of your new orbit cannot be higher than where you are now, and the highest point of your orbit cannot be lower. -- [0] - Ignoring gravitational effects of other bodies, residual drag, magnetic fields, solar pressure, etc. None of these matter on the scale of days to months.
- xyzzyz 6y ago
  Yes, if you start from roughly circular orbit, and the impulse is in the opposite direction to the direction of travel, it will slow you down and then the location of impulse is now the new highest point on orbit, and the lowest point after the impulse is even lower than before it.

4 ms·

This is correct. The simplification being made is that the original orbit was circular, so if you increase the debris' velocity, the current point is now the lo

by omegaham 6y ago

This is correct. The simplification being made is that the original orbit was circular, so if you increase the debris' velocity, the current point is now the low point of the new orbit.

tgb 6y ago
Even for circular orbits, is that the case? The new low point would be lower if impulse is not parallel to the velocity.
- sand500 6y ago
  Correct, so basically the lowest point(periapsis) of the new orbit cannot be any higher than the point where the collision happened.
  - TeMPOraL 6y ago
    Another way to think about it is, an orbit around a single body is entirely defined[0] by your current position and your instantaneous velocity. Six numbers. Where you are, which direction you're going, and how fast. Such orbits are closed, which means wherever you are right now, you'll return to that exact point later. So if you're at point P in your orbit and suddenly kinetic energy was added, your velocity changes in some arbitrary way. While you aren't sure where you'll go and when you'll get there, as long as the new (position, velocity) pair still defines a closed orbit around the body, you can be damn sure you'll return to the exact point where you are now. From this follows that the lowest point of your new orbit cannot be higher than where you are now, and the highest point of your orbit cannot be lower. -- [0] - Ignoring gravitational effects of other bodies, residual drag, magnetic fields, solar pressure, etc. None of these matter on the scale of days to months.
- xyzzyz 6y ago
  Yes, if you start from roughly circular orbit, and the impulse is in the opposite direction to the direction of travel, it will slow you down and then the location of impulse is now the new highest point on orbit, and the lowest point after the impulse is even lower than before it.