Physics Question about gravity

Question

An astronaut floats in the space station as it moves in a circular orbit around Earth. If she stands on a bathroom scale, it reads zero. Does that mean Earth is not exerting any force on her? If not, explain why the scale reads zero. 

Answer 1

Earth is exerting gravitation force on her as usual.

There are at least two explanations, depending on your frame of reference.

1) Inertial frame of reference:

That is from the point of view of somebody not on the space station,

but observing the situation from afar.

The astronaut is falling towards the Earth (because of gravity), like

she would be if she jumped out of a plane without a parachute.

The scale reads 0, i.e., the there is no pressure on the scale, because

the scale is falling to the Earth together with the astronaut.

Unlike jumping out of a plane, the astronaut never hits the ground,

because she also has a tangential velocity.

That is, she and the whole space station were given a sideways push.

That push has given them just the right velocity, so that

for every meter they fall towards the earth, they also move sideways far enough,

so that the Earths curvature makes the ground receded one meter.

2) Frame of reference of the space station.

The scale reading notwithstanding, the astronaut is under no illusion

that she is not subject to gravity; she can perform experiments that

can show that she is experiencing a downward force.

Nevertheless, it is sometimes convenient to be able to do physics

as if gravity did not exist.

For that we introduce "fictitious forces", such as the centrifugal force.

So the astronaut understands that she is subject to gravity, but

introduced this centrifugal force opposite gravity, so that she can do

experiments the same way she would if she were really far from any

gravitational attraction.