space stations geo sync at 1000 km
Consider an “island” at an orbital altitude of 1000 km travelling at 3.08 km/s. The island is stationary over a point on the Earth. Obviously the island will not orbit there, but immediately deorbit into the Earth.
What force would it take to “hold” the island in orbit stationary over a point on Earth?
My thinking is as follows. I expect I’ve got something wrong, so any comments welcome!
At geo sync orbit (36k km)
Orbital speed 3.08 km/s
Gravity 0.2217 m/s^2
At 1000 km altitude
Orbital speed 7.35 km/s
Gravity 7.5 m/s^2
The orbital speed difference is 7.35 km/s(1000) - 3.08 km/sec(geosync) = 4.27 km/s
The gravitationsal difference is 7.5 m/s^2(1000) - 0.2217m/s^2(geosync) = 7.3 m/s^2
The geo sync speed balances 0.2217 m/s^2. So, I need to be applying and upward force that provides an acceleration of 7.3 m/s^2, or about 70% of 1G.