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If the radius of the Earth is R and a satellite is in a low Earth orbit at a hei

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Question: If the radius of the Earth is R and a satellite is in a low Earth orbit at a height h, what is the expression for the gravitational force acting on the satellite?

Options:

  1. G * M * m / (R + h)^2
  2. G * M * m / R^2
  3. G * M * m / (R - h)^2
  4. G * M * m / (R + h)

Correct Answer: G * M * m / (R + h)^2

Solution: 

The gravitational force acting on the satellite is given by Newton\'s law of gravitation, which states that F = G * (M * m) / (R + h)^2, where M is the mass of the Earth and m is the mass of the satellite.

If the radius of the Earth is R and a satellite is in a low Earth orbit at a hei

Practice Questions

Q1
If the radius of the Earth is R and a satellite is in a low Earth orbit at a height h, what is the expression for the gravitational force acting on the satellite?
  1. G * M * m / (R + h)^2
  2. G * M * m / R^2
  3. G * M * m / (R - h)^2
  4. G * M * m / (R + h)

Questions & Step-by-Step Solutions

If the radius of the Earth is R and a satellite is in a low Earth orbit at a height h, what is the expression for the gravitational force acting on the satellite?
  • Step 1: Understand that the gravitational force between two objects is described by Newton's law of gravitation.
  • Step 2: Recall the formula for gravitational force: F = G * (M * m) / d^2, where F is the gravitational force, G is the gravitational constant, M is the mass of the larger object (Earth), m is the mass of the smaller object (satellite), and d is the distance between the centers of the two objects.
  • Step 3: Identify the distance d. The distance from the center of the Earth to the satellite is the radius of the Earth (R) plus the height of the satellite (h). So, d = R + h.
  • Step 4: Substitute d into the gravitational force formula. This gives us F = G * (M * m) / (R + h)^2.
  • Step 5: Conclude that the expression for the gravitational force acting on the satellite is F = G * (M * m) / (R + h)^2.
  • Newton's Law of Gravitation – This law describes the gravitational force between two masses and how it varies with distance.
  • Gravitational Force Calculation – Understanding how to calculate the gravitational force acting on an object in orbit based on its distance from the center of the Earth.
  • Orbital Mechanics – The principles governing the motion of satellites and their interaction with Earth's gravity.
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