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

The ratio of gravitational force is 0.8920

Step-by-step explanation:

The gravitational force is given by F=
`(GMm)/(R^(2) )`

The gravitational force on the astronaut when he is in

Surface of earth F₁ =
`G(Mm)/(R^(2) )` eqn 1

Circular orbit F₂ =
`G(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

=
`(R^(2) )/((R+h)^(2) )`

=
`((6380)^(2) )/((6380+315)^(2) )`

=0.8920

The ratio of gravitational force is 0.8920