Question

at which point does the satellite have the least gravitational potential energy?
a. point d
b. point c
c. point b
d. point a

Explanation:

Gravitational potential energy (GPE) in a gravitational field depends on the distance from the massive object (like the star here). The formula for gravitational potential energy (for a satellite - planet system) is \( U = -\frac{GMm}{r} \) (where \( G \) is gravitational constant, \( M \) is mass of the star, \( m \) is mass of satellite, \( r \) is the distance between them). As \( r \) decreases, the magnitude of \( U \) (since it's negative) increases in magnitude but the GPE (in the context of how close the satellite is to the star, lower distance means lower GPE? Wait, no—wait, the gravitational potential energy is lower (more negative) when the distance is smaller? Wait, no, let's think in terms of the system: when the satellite is closer to the star, the gravitational potential energy is lower (because to move it away, you have to do work against gravity, so at closer distances, the GPE is less (more negative). Wait, but the question is about "least" gravitational potential energy. So the smallest (most negative) value. So the closer the satellite is to the star (the red object), the lower (more negative) the GPE. Looking at the diagram, Point C is closest to the star. So among the options, Point C (Option B) is the closest. So the satellite at Point C has the least gravitational potential energy.

Answer:

B. Point C