If an astronaut who is orbiting the planet at a radius of 3R wants to move their orbit to a radius of 2R, what direction should they fire their thrusters? (and how is your answer supported by the given graph of U(r) ?)
If an astronaut who is orbiting the planet at a radius of 3R wants to move their orbit to a radius of 2R, what direction should they fire their thrusters? (and how is your answer supported by the given graph of U(r) ?)
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Transcribed Image Text:**Gravitational Potential Energy and Orbital Mechanics**
**Questions 3 and 4** refer to the universal gravitational potential energy function \( U(r) \) for a planet with mass \( M \) and radius \( R \), as shown in the figure below.
**Diagram Explanation:**
The diagram illustrates the gravitational potential energy \( U(r) \) as a function of the distance \( r \) from the center of a planet. The curve shows that the potential energy becomes less negative as the distance increases. At the planet's surface, the distance is \( R \).
**3.**
If a projectile is launched from the surface of the planet with a speed equal to the planet's escape speed, how much mechanical energy does it have when it reaches a distance \( r = \infty \)?
**4.**
If an astronaut who is orbiting the planet at a radius of \( 3R \) wants to move their orbit to a radius of \( 2R \), what direction should they fire their thrusters? (And how is your answer supported by the given graph of \( U(r) \)?)
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