What is the ratio of Earth’s gravitational force on a

kwisangqaquqw3

kwisangqaquqw3

Answered question

2022-05-09

What is the ratio of Earth’s gravitational force on a satellite when it is on the ground to the gravitational force exerted when the satellite is orbiting at an altitude of 890 km?

Answer & Explanation

overnachtt9xyx

overnachtt9xyx

Beginner2022-05-10Added 14 answers

Step 1
Given data
*The given altitude is h = 890   k m = 0.890 × × 10 6   m
*The distance between the earth and satellite is d = 6.38 × 10 6   m
Step 2
The expression for the gravitational force exerted by the earth on the satellite is given as
F = G M m d 2   ( 1 )
*Here G is the gravitational constant, M is the mass of the earth and m is the mass of the satellite
The expression for the gravitational force exerted by the earth on the satellite at an altitude is given as,
F 1 = G M m ( d + h ) 2   ( 2 )
Divide equation (1) by (2) we get
F F 1 = ( G M m d 2 ) ( G M m ( d + h ) 2 ) = ( d + h ) 2 d 2 = ( 6.38 × 10 6   m + 0.890 × 10 6   m ) 2 ( 6.38 × 10 6   m ) 2 = 1.29
Thus the ratio of the gravitational force exerted by the earth on the satellite to the gravitational force exerted by the earth on the satellite at an altitude is F F 1 = 1.29

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Force, Motion and Energy

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?