Weightlessness in Satellites:

           The weight of a body is felt due to a reactionary force applied on the body by some other body (which is in contact with the first body). For example, when we stand on a plane, we feel our weight due to the reaction of the plane on our feet. If under some special circumstances the reaction of this plane becomes zero then we shall feel as our weight has also become zero. This is called "state of weightlessness". If the ropes of a descending lift are broken, then persons standing in the lift will feel this state. Weightlessness is also felt by a space-man inside an artificial satellite. Suppose an artificial satellite of mass m is revoking around the earth (mass M_e) with speed v₀ in an orbit of radius r. The necessary centripetal force is provided by the gravitational force:

The mass of a person doesn’t change but their apparent weight does change when accelerating or in a free fall.

GM_em/r² = mv²₀/2

Or

GM_e/r² = v²₀/2 … (i)

If there is a space-man of mass m’ inside the satellite, he is acted upon by two forces:

• Gravitational force GM_em/r²,
• Reaction R of the base of the satellite, in the opposite direction. Thus, there is a net force [GM_em’/r² - R] on the man.

It is directed towards the centre of the orbit and is the necessary centripetal force on the man. That is,

[GM_em’/r² - R]  = m’v²₀ / r

Or

GM_e/r² - R/m’ = v²₀ / 2

Substituting the value of v²₀ / r from eq. (1), we get

GM_e/r² - R/m’ = GM_e/r²

.˙. R = 0

Thus, the reactionary force on the man is zero. Hence he feels his weight zero. If he stands on a spring-balance, the balance will read zero. In fact, everybody inside the satellite is in a state of weightlessness.