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A satellite is in a circular orbit around the Earth. What is the relationship be

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Question: A satellite is in a circular orbit around the Earth. What is the relationship between its orbital speed (v) and the radius of the orbit (r)?

Options:

  1. v = sqrt(G * M / r)
  2. v = G * M / r
  3. v = r / G * M
  4. v = G * r / M

Correct Answer: v = sqrt(G * M / r)

Solution: 

The orbital speed of a satellite is given by v = sqrt(G * M / r), where M is the mass of the Earth.

A satellite is in a circular orbit around the Earth. What is the relationship be

Practice Questions

Q1
A satellite is in a circular orbit around the Earth. What is the relationship between its orbital speed (v) and the radius of the orbit (r)?
  1. v = sqrt(G * M / r)
  2. v = G * M / r
  3. v = r / G * M
  4. v = G * r / M

Questions & Step-by-Step Solutions

A satellite is in a circular orbit around the Earth. What is the relationship between its orbital speed (v) and the radius of the orbit (r)?
  • Step 1: Understand that a satellite moves in a circular path around the Earth.
  • Step 2: Know that the speed of the satellite is called its orbital speed (v).
  • Step 3: Recognize that the radius of the orbit (r) is the distance from the center of the Earth to the satellite.
  • Step 4: Learn that the gravitational force between the Earth and the satellite keeps it in orbit.
  • Step 5: The formula for the orbital speed (v) is derived from the balance of gravitational force and the required centripetal force for circular motion.
  • Step 6: The formula is v = sqrt(G * M / r), where G is the gravitational constant and M is the mass of the Earth.
  • Step 7: This formula shows that as the radius (r) increases, the orbital speed (v) decreases.
  • Orbital Mechanics – The relationship between the orbital speed of a satellite and the radius of its orbit, derived from gravitational principles.
  • Gravitational Force – Understanding how gravitational force affects the motion of satellites in orbit.
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