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A satellite is in a circular orbit around the Earth. If the radius of the orbit

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Question: A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the gravitational acceleration is 9.8 m/s², what is the speed of the satellite?

Options:

  1. 5.5 km/s
  2. 7.9 km/s
  3. 9.8 km/s
  4. 11.2 km/s

Correct Answer: 7.9 km/s

Solution: 

Speed (v) = √(g*r) = √(9.8 m/s² * 7000 * 1000 m) = 7.9 km/s.

A satellite is in a circular orbit around the Earth. If the radius of the orbit

Practice Questions

Q1
A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the gravitational acceleration is 9.8 m/s², what is the speed of the satellite?
  1. 5.5 km/s
  2. 7.9 km/s
  3. 9.8 km/s
  4. 11.2 km/s

Questions & Step-by-Step Solutions

A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the gravitational acceleration is 9.8 m/s², what is the speed of the satellite?
  • Step 1: Understand that the satellite is in a circular orbit around the Earth.
  • Step 2: Identify the radius of the orbit, which is given as 7000 km.
  • Step 3: Convert the radius from kilometers to meters because the gravitational acceleration is in meters per second squared. 7000 km = 7000 * 1000 m = 7,000,000 m.
  • Step 4: Note the gravitational acceleration (g) is given as 9.8 m/s².
  • Step 5: Use the formula for the speed (v) of a satellite in orbit: v = √(g * r).
  • Step 6: Substitute the values into the formula: v = √(9.8 m/s² * 7,000,000 m).
  • Step 7: Calculate the product inside the square root: 9.8 * 7,000,000 = 68,600,000.
  • Step 8: Take the square root of 68,600,000 to find the speed: √(68,600,000) ≈ 8,287.5 m/s.
  • Step 9: Convert the speed from meters per second to kilometers per second: 8,287.5 m/s = 8.3 km/s.
  • Circular Orbit Dynamics – Understanding the relationship between gravitational acceleration, radius of orbit, and orbital speed.
  • Units Conversion – Converting kilometers to meters to ensure consistency in calculations.
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