Gravitation Reasonings

An astronaut in a space capsule orbiting the earth experiences weightlessness. Why?

OR: A person sitting in an artificial satellite revolving around the earth feels weightless. Why?

The space capsule revolving around the earth in a circular orbit is in a balanced condition. The centripetal force of the capsule is equal to the gravitational force between the earth and the capsule. So, the only force of gravity experienced by the astronaut is that which is due to the gravitational force exerted by the space capsule. But the capsule is small, so this force is negligibly small and the astronaut does not experience any gravity. Hence, the astronaut in a space capsule orbiting around the earth experiences weightlessness.