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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 speed of the satellite is 7.9 km/s, what is the centripetal acceleration?

Options:

  1. 7.9 m/s²
  2. 9.8 m/s²
  3. 11.2 m/s²
  4. 14.0 m/s²

Correct Answer: 7.9 m/s²

Solution: 

Centripetal acceleration a_c = v²/r = (7.9 km/s)² / (7000 km) = 0.00063 km/s² = 6.3 m/s².

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 speed of the satellite is 7.9 km/s, what is the centripetal acceleration?
  1. 7.9 m/s²
  2. 9.8 m/s²
  3. 11.2 m/s²
  4. 14.0 m/s²

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 speed of the satellite is 7.9 km/s, what is the centripetal acceleration?
  • Step 1: Identify the formula for centripetal acceleration, which is a_c = v² / r.
  • Step 2: Note the values given: the speed (v) of the satellite is 7.9 km/s and the radius (r) of the orbit is 7000 km.
  • Step 3: Square the speed of the satellite: (7.9 km/s)² = 62.41 km²/s².
  • Step 4: Divide the squared speed by the radius: 62.41 km²/s² / 7000 km.
  • Step 5: Perform the division: 62.41 / 7000 = 0.0089142857 km/s².
  • Step 6: Convert the result from km/s² to m/s² by multiplying by 1000 (since 1 km = 1000 m): 0.0089142857 km/s² * 1000 = 8.9142857 m/s².
  • Step 7: Round the result to two decimal places: 8.91 m/s².
  • Centripetal Acceleration – Centripetal acceleration is the acceleration directed towards the center of a circular path, necessary for an object to maintain its circular motion.
  • Circular Motion – Understanding the principles of circular motion, including the relationship between speed, radius, and acceleration.
  • Unit Conversion – Converting units correctly, especially between kilometers and meters, to ensure accurate calculations.
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