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The force of gravitation between two objects is given by the formula` F = G*(m1*m2)/r^2` where G is a constant, m1 and m2 denote the mass of the objects and r is the distance between them.
The distance between an astronaut and the center of mass of the Earth is larger than the distance between a person standing on the surface of the Earth and the center of the Earth. But the reason behind why astronauts experience weightlessness is not an absence of the gravitational force of attraction between the Earth and the space craft. If that were the case, the space craft would not revolve around the Earth. As a matter of fact, the force with which an astronaut is attracted by the Earth is reduced only by 10% by the increase in the distance.
An astronaut experiences weightlessness due the fact that as the space craft revolves around the Earth, the astronaut is continuously falling towards the Earth. This is similar to what a person standing in an elevator that is falling freely would experience. The person would be weightless as the elevator falls.
It is a common misconception that it is the absence of the gravitational force of attraction that results in weightlessness.
According to Newton's law of universal gravitation when there are two bodies with mass `m_(2)`
an attractive force is acting between them. That force can be expressed as,
`F = G(m_(1)m_(2))/r^2`
where r - the distance between the bodies
G - gravitational constant
so the gravitational force that is acting between our body and the earth is felt as weight. When we go into outer space the distance between our body and the earth is increased and the gravitational force is reduced. That the attractive force that is acting on our body is weakened. Therefore we feel like we weight less. Actually what has happened is that the force which drag us towards the earth has been weakened.
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