Question

How does gravity on a satellite (like the International Space Station) compare to gravity on Earth's surface? Why is that the case? Why do astronauts float around when they're in space?

Answer 1

The gravitational force on a object decrease with its distance from earth. On a satellite which is orbiting earth very high above the earth surface, the gravitational force of earth is smaller. But this is not very low. The main reason for the astronauts to float around when they are in satellites such as International Space Center is because they are orbiting the earth due to which another force, the centripetal force, is acting on them. This centripetal force has the same magnitude as that of gravitational force but in opposite direction. So they cancel each other and net force on astronauts in ISS is zero. This is why they float around.

Though if you are very far away from the earth's surface then the earth's gravitational pull will be negligible and you will float freely even if you are not orbiting earth.