Concept:The passenger's weight equals the net gravitational pull of Earth and Moon, which changes with position as the spaceship travels at constant velocity.
Explanation:Let the Earth–Moon distance be
d and the spaceship's distance from Earth's centre be
r, so its distance from the Moon's centre is
d−r.
Since the spaceship moves at constant velocity,
r increases uniformly with time, so the graph mirrors the force variation with
r.
The net gravitational force on the passenger is:
Fnet=r2GMeM−(d−r)2GMmMAt Earth's surface (
t=0), the Moon's pull is negligible, so
Fnet=Mg.
As the ship moves away from Earth, Earth's pull weakens while the Moon's pull strengthens, so the net force decreases.
At the neutral point the two pulls cancel, giving
Fnet=0.
Since
Me≈81Mm, the neutral point lies much closer to the Moon (
r≈0.9d), so the zero occurs near
t=t0, not early in the journey.
After the neutral point, the Moon's pull dominates and the force magnitude rises; at the Moon's surface,
∣Fnet∣=Mg′.
Also,
g′<g, so the final weight
Mg′ is lower than the starting weight
Mg.
Thus the correct curve starts at
Mg, falls to zero near the Moon, and then rises to
Mg′.
This behaviour matches curve C.
Answer:C