My Learning Cart
?
Categories
Account

A satellite is in a circular orbit around the Earth. If its speed is doubled, wh

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: A satellite is in a circular orbit around the Earth. If its speed is doubled, what will happen to its orbital radius?

Options:

  1. It will remain the same.
  2. It will double.
  3. It will increase by a factor of four.
  4. It will decrease by a factor of four.

Correct Answer: It will decrease by a factor of four.

Solution: 

If the speed of a satellite is doubled, the orbital radius will decrease by a factor of four, as orbital speed is inversely proportional to the square root of the radius.

A satellite is in a circular orbit around the Earth. If its speed is doubled, wh

Practice Questions

Q1
A satellite is in a circular orbit around the Earth. If its speed is doubled, what will happen to its orbital radius?
  1. It will remain the same.
  2. It will double.
  3. It will increase by a factor of four.
  4. It will decrease by a factor of four.

Questions & Step-by-Step Solutions

A satellite is in a circular orbit around the Earth. If its speed is doubled, what will happen to its orbital radius?
  • Step 1: Understand that a satellite in orbit has a specific speed that keeps it in a circular path around the Earth.
  • Step 2: Know that the gravitational force between the Earth and the satellite provides the necessary centripetal force for the orbit.
  • Step 3: Remember the formula for orbital speed: v = sqrt(G * M / r), where v is the orbital speed, G is the gravitational constant, M is the mass of the Earth, and r is the orbital radius.
  • Step 4: If the speed (v) is doubled, we can express this as 2v.
  • Step 5: Substitute 2v into the orbital speed formula: 2v = sqrt(G * M / r_new), where r_new is the new orbital radius.
  • Step 6: Square both sides of the equation to eliminate the square root: (2v)^2 = G * M / r_new.
  • Step 7: This simplifies to 4v^2 = G * M / r_new.
  • Step 8: Rearranging gives r_new = G * M / (4v^2).
  • Step 9: Compare this with the original radius formula r = G * M / v^2.
  • Step 10: Notice that r_new is 1/4 of the original radius (r), meaning the orbital radius decreases by a factor of four.
  • Orbital Mechanics – Understanding the relationship between orbital speed and radius in circular orbits, specifically how changes in speed affect the radius.
  • Gravitational Forces – Knowledge of how gravitational forces influence satellite motion and the principles governing orbital dynamics.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks