Physics/Orbits and Gravitation pull in space
If part of a satellite were to break off would it fall to earth or stay in orbit?
For example if a solar panel or an antenna of the ISS were to break off what would happen to it?
What would are the necessary conditions for said object to re enter earth and if so would it burn up during re entry?
In general, the answer is that the part that broke off would stay in its original orbit. An exception might be if it broke off because it was hit by something. Then it might just move to a slightly different orbit, or it might have been hit hard enough that it re-enters Earth's atmosphere.
You may have seen video of astronauts working outside the Space Shuttle or the ISS. It is true that they are either tethered to the main vehicle or wearing jet packs. But they quite comfortably can maintain position alongside the vehicle. Go to the following web site:
(The link takes you to the section of the web page we want to consider.) T^2/r^3 are the parameters of an orbit. (They are assuming M is the mass of the sun, but the formula works as well if r and M are radius of an Earth orbit and M is the mass of the Earth. That is what we are assuming here.) T tells you the time to complete an orbit and r tells you the distance to the center of the Earth. Notice that there is no term for the mass of the orbiting body. It does not matter. A feather and a car could follow each other around the Earth and maintain their original separation.
For the object to re-enter Earth's atmosphere, its orbital velocity must be decreased. Look at these web sites:
A solar panel or antenna would burn up. Special measures and heat shielding are required to avoiding burning up.
I hope this helps,