The weight of an object (or body) is felt due to the attraction force acting on it. If the attraction force is zero then the state of weightlessness is felt. For example, if a person jumps freely downwards, then there is no attraction force applied to the person. Hence, weightlessness is felt.
In artificial satellites the objects are in a state of weightlessness. This truth can be understood as follows :
Suppose the mass of the Earth is M and M’ is the mass of any satellite which is revolving with an orbital speed v0 in an orbit of radius r. The necessary centripetal force is obtained from the gravitational force.
Suppose inside the satellite at its surface an object of mass m is kept on which the reaction force is R opposite in direction to its weight W. Hence, equation of motion of the object :
This means that the weight of the body is zero. In other words it can be said that in artificial satellites objects are in a state of weightlessness.
