I've read that orbiting objects like the space station stay in orbit because they are falling at the same rate the Earth is curving away underneath them.
What I don’t understand is their downward velocity should be increasing because it is caused by gravity / acceleration due to gravity. Shouldn’t it be “falling” with a greater velocity the longer it travels? Does it reach a terminal velocity like that of a skydiver? If so Why?
Asked by: Geoff from New Jersey
No, Geoff, the answer to your conundrum is not related to the concept of "terminal velocity" (in which the air resistance balances the gravitational acceleration). You are conflating two things: "falling" and "getting closer to the center of the Earth".
The International Space StationImage Credit:
In everyday experience, when you fall, you move downward, i.e. closer to the Earth's center. But the satellite, although "falling" (this is perhaps an unfortunate choice of words) is staying at the same distance away from the Earth as it moves (we're assuming here a perfectly circular orbit for simplicity).
The reason that velocity usually increases when one falls is because of conservation of energy: gravitational potential energy, measured by distance from Earth's center, is decreasing, so kinetic energy, measured by the falling body's velocity, must increase in just such a way as to keep the total energy (kinetic plus potential) a constant.
This same argument tells you that if the body does not get closer to the Earth, its potential energy stays the same, so the kinetic energy must also stay the same.
Alan Chodos, PhD
Associate Executive Officer
American Physical Society