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A satellite is in a circular orbit around the Earth. If its orbital radius is 4R

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Question: 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?

Options:

  1. 1/4
  2. 1/16
  3. 1/8
  4. 1/2

Correct Answer: 1/16

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.

A satellite is in a circular orbit around the Earth. If its orbital radius is 4R

Practice Questions

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. 1/4
  2. 1/16
  3. 1/8
  4. 1/2

Questions & Step-by-Step Solutions

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?
  • 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.
  • Gravitational Force – Understanding how gravitational force varies with distance from the center of a mass, specifically following the inverse square law.
  • Orbital Mechanics – Knowledge of how satellites behave in circular orbits and the relationship between orbital radius and gravitational force.
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