Question

What is the ratio of the gravitational force on an astronaut when he is in a space satellite in a circular orbit 315 km above the earth to the gravitational force on the astronaut when he is on the surface of the earth? The earth’s diameter is 12760 km.

Answer 1

Answer:

The ratio of gravitational force is 0.8920

Explanation:

The gravitational force is given by  F=$\frac{GMm}{R^{2} }$

  The gravitational force on the astronaut when he is in

           Surface of earth  F₁ =$G\frac{Mm}{R^{2} }$        eqn 1

          Circular orbit F₂ =$G\frac{Mm}{(R+h)^{2} }$           eqn 2

Where M is mass of earth,

           m is mass of astronaut

          R is radius of earth 6380 km,

         h is the distance from earth surface 315 km.

Dividing eqn 1 and 2

                   =    $\frac{R^{2} }{(R+h)^{2} }$

                   =$\frac{(6380)^{2} }{(6380+315)^{2} }$  

                     =0.8920

                  The ratio of gravitational force is 0.8920