Question

Earth II is a planet in a distant solar system which is
earth-like, but a little smaller than our earth. In the distance
future, Earth II has been settled by bold travelers from our home
planet. Very far from Earth II (effectively at R=∞), a spacecraft
has run out of fuel and its kinetic energy is zero. If only the
gravitational force of Earth II were to act on the spacecraft
(i.e., neglect the forces from the sun and other solar system
objects), the spacecraft would eventually crash into Earth II. The
mass of Earth II is Me=4.600×10^{24} kg and its
radius is Re=5.850×10^{6} m . Neglect air
resistance throughout this problem, since the spacecraft is
primarily moving through the near vacuum of space.

Part A

Find the speed se of the spacecraft when it eventually crashes into Earth II.

Part B

Now find the spacecraft's speed when its distance from the center of Earth II is 12.5 times the radius of Earth II, i.e. R=αRe, where α = 12.5.

Part C

Now find the spacecraft's speed when its distance from the center of Earth II is 125 times the radius of Earth II, i.e R=αRe, where α = 125.

Answer #1

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measured in the fixed frame of reference, in which the
sun, Planet A, and Planet X are at rest. (We neglect any motion of
the planets with respect to each other and the sun during this
short time.)
a....

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