A satellite is in a circular orbit around the Earth. If its orbital radius is 4R, what is the gravitational force acting on it compared to that at the surface of the Earth?
Practice Questions
1 question
Q1
A satellite is in a circular orbit around the Earth. If its orbital radius is 4R, what is the gravitational force acting on it compared to that at the surface of the Earth?
1/4
1/16
1/8
1/2
The gravitational force decreases with the square of the distance. At 4R, the force is 1/(4^2) = 1/16 of the force at the surface.
Questions & Step-by-step Solutions
1 item
Q
Q: A satellite is in a circular orbit around the Earth. If its orbital radius is 4R, what is the gravitational force acting on it compared to that at the surface of the Earth?
Solution: The gravitational force decreases with the square of the distance. At 4R, the force is 1/(4^2) = 1/16 of the force at the surface.
Steps: 7
Step 1: Understand that the gravitational force depends on the distance from the center of the Earth.
Step 2: Know that 'R' is the radius of the Earth, so '4R' means the satellite is 4 times the radius of the Earth away from the center.
Step 3: Remember the formula for gravitational force: it decreases with the square of the distance from the center of the Earth.
Step 4: Calculate the factor by which the distance increases: since the satellite is at '4R', the distance is 4 times greater than at the surface.
Step 5: Use the formula for gravitational force decrease: if the distance increases by a factor of 4, the force decreases by a factor of 4 squared (4^2).
Step 6: Calculate 4^2, which equals 16.
Step 7: Therefore, the gravitational force at 4R is 1/16 of the gravitational force at the surface of the Earth.
