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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Questions 3 and 4 below refer to the universal gravitational potential energy function U(r) for a
planet with mass M and radius R, which is shown in the figure below.
R
3.
If a projectile is launched from the surface of
the planet with a speed equal to the planets
escape speed, how much mechanical energy
does it have when it reaches a distance
r = ∞ ?
(n
I
I
I
Distance from center of planet, r
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) ?)
Transcribed Image Text:Questions 3 and 4 below refer to the universal gravitational potential energy function U(r) for a planet with mass M and radius R, which is shown in the figure below. R 3. If a projectile is launched from the surface of the planet with a speed equal to the planets escape speed, how much mechanical energy does it have when it reaches a distance r = ∞ ? (n I I I Distance from center of planet, r 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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