Imagine two astronauts. The first is in a satellite in geostationary orbit aroun
ID: 1381089 • Letter: I
Question
Imagine two astronauts.
The first is in a satellite in geostationary orbit around the earth.
The second is on top of a 35,786 km tall tower that has been built from the equator to space. This means that that the top of the tower is at the same height as the geostationary satellite.
Naive logic would seem to indicate that the astronaut in the satellite would experience free-fall (as do all satellites in orbit), whereas the astronaut on top of the tower would feel the effects of gravity (albeit at a reduced level due to being 35,786 km above the surface of the earth.
However, I can't believe that this would be the case. What's the flaw in my logic? Is the acceleration due to the earth's gravity zero at 35,786 km above the earth?
Explanation / Answer
They would both be free-falling. YOur mountain dweller could stand on top of the mountain, and would feel no upward force from the ground. The magic of geostationary orbit is that the gravitational force GmMr2 on an object is exactly equal to the centripetal force mv2r required to keep something moving at the speed v equivalent to one lap around the Earth per day. Since gravity provides no less or more force than exactly the centripetal force required to keep your person above the same spot on the ground, your person would not need the ground to hold herself up. She would feel weightless while standing on the mountaintop.