In an accidental explosion, a satellite breaks in half while in circular orbit about earth. one half is brought momentarily to rest. what is the fate of the half brought to rest? what happens to the other half?
When a satellite breaks in half while in a circular orbit about the Earth, the fate of the half brought to rest and the other half depends on the initial conditions and the nature of the explosion. Let me explain the possible scenarios:
1. If the explosion occurs without any additional forces acting on the fragments:
- The half brought to rest will no longer be in orbit and will start to fall towards the Earth due to gravity.
- The other half will continue to orbit the Earth as before, unaffected by the explosion since no external force has acted upon it.
2. If the explosion imparts velocity to both fragments:
- The half brought to rest will continue to fall towards the Earth due to gravity.
- The other half will acquire a different orbit depending on the velocity imparted by the explosion. It may move to a different circular orbit, transition to an elliptical orbit, or even escape the Earth's gravitational pull and go into an unbounded trajectory.
3. If the explosion happens in a way that imparts opposing velocities to the fragments:
- The half brought to rest will fall towards the Earth due to gravity but might also have some residual velocity in the opposite direction. This might cause it to either:
a) Crash into the Earth.
b) Enter an elliptical orbit with its lowest point close to the Earth's surface, eventually crashing.
c) Escape the Earth's gravitational pull if the remaining velocity is high enough.
- The other half will also have a combination of its original velocity and the velocity imparted by the explosion. It will continue to orbit the Earth, but with a slightly different trajectory.
It's important to note that these scenarios assume no additional influences or perturbations (like atmospheric drag) affect the fragments. In reality, such factors could further alter the fate of the fragments.