Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A space station orbits above the ground. A astronaut is inside. The Earth's mass is and its radius .
Near a planet, ; at a distance from its centre, falls as . On the Earth's surface ; at Earth radii above the ground it is .
The law of gravitation: , with and the distance between the centres. The Earth: , .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. (a) .
Step 2. (b) ; on the ground . Up there the pull is still about as strong.
Step 3. (c) The astronaut and the station fall round the Earth together, so the floor does not push on the astronaut.
Answer: ; against ; they float because they are falling freely.
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