It doesn't work that way.

If you, in circular orbit at 500 km throw a rock vertically upwards, you have injected into an elliptical orbit. It will reach a peak, turn over and come down again, but you will have gone past that point already. It will then descend below your altitude, reach a minimum (if it doesn't graze the atmosphere), and come back up again. This time, it will have travelled faster and (I think) it will come back to meet you - hitting the bottom of your orbiter.

The pendulums don't work like that because your circular orbit is already the response of everything on the spacecraft to the centripetal acceleration of gravity. If you give the pendulum a tiny nudge, it will swing slowly up and over the top.

Look at pictures of astronauts spacewalking in the old Gemini days. The astronaut is attached to the capsule by a safety line. Does he swing like a pendulum bob? Does he heck!

In short, Jacob, you are wrong, damn wrong.

Be very careful about how you use physics in a non-inertial reference frame!