What is the reason for weightlessness in satellite:

CONCEPT:

• Weightlessness: The weight of a body is the force with which it is attracted towards the center of the earth.
• When a body is stationary with respect to the earth, its weight equals gravity. This weight of the body is known as its static or true weight.  

EXPLANATION:

Weightlessness in a Satellite:

• A satellite, which does not produce its own gravity moves around the earth in a circular orbit under the action of gravity.
• The acceleration of the satellite is \(\frac{{GM}}{{{R^2}}}\) towards the center of the earth.
• If a body of mass m placed on a surface inside a satellite moving around the earth. Then force on the body is

The gravitational pull of the earth is
\(F = G\frac{{{M_1}{M_2}}}{{{R^2}}}\)           ----- (1)

The reaction by the surface = R

By Newton’s  second law,

\(G\frac{{{M_1}{M_2}}}{{{R^2}}} - R = ma\)

\(\Rightarrow G\frac{{{M_1}{M_2}}}{{{R^2}}} - R = m\left( {\frac{{GM}}{{{R^2}}}} \right)\)

⇒ R = 0

• Thus the surface does not exert any force on the body and hence its apparent weight is zero.
• A body needs no support to stay at rest in the satellite and hence all positions are equally comfortable. Such a state is called weightlessness.