Is there gravity in space?

This question comes from a final year school student, trying to answer a question about astronauts in spacestations.

Well, having seen numerous videos of astronauts, the answer would seem to be no. They float around quite happily, scientists refer to them as being in a zero gravity environment, their leg muscles don’t get enough exercise, and so on.

But hang on. If there were no gravity up there, the space station would just float away from the earth. It is clearly the force of gravity that holds the space station in orbit around the earth. (It provides the centripetal force that moves the station in a circle around the earth.) So how come the astronauts don’t feel it?

To answer this we should first think about why we feel heavy when we are standing on the earth. Like much of physics, it’s all Newton. First of all, Gravity exerts a downward force on me. This force is then transmitted to the ground. The ground exerts an equal and opposite force back on me (Newton 3). Consequenty I experience both the force of gravity, and the reaction of the ground, which, being equal and opposite, combine to give zero net force. By Newton’s second law, I therefore do no accelerate, and stay standing. But the reason I feel heavy is that I feel the ground’s reaction on me. (See the feline example.)

Now, in earth orbit, things are slightly different. Our astronaut has the force of gravity acting on him, as before – which means an acceleration (centripetal) towards the earth.  But, crucially, he fails to transfer any of this to the ground. That is because the ‘ground’ (that is, the space station) also has the force of gravity acting on it, and it is accelerating towards the earth, at the same rate as the astronaut.  Just like being in a falling lift. The ground no longer exerts a force back on the astronaut, and he feels weightless. If he were to stand on a set of scales, it would read zero.

The relationship between gravity and acceleration is pretty well what General Relativity is all about.

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