Question

at which point does the planet have the highest acceleration?
a. point d
b. point b
c. point c
d. point a

Explanation:

Step1: Recall Gravitational Acceleration

The acceleration of a planet in orbit is due to gravitational force from the sun. By Newton's law of gravitation, \( F = G\frac{Mm}{r^2} \), and by Newton's second law \( F = ma \), so \( a = G\frac{M}{r^2} \). Acceleration is inversely proportional to the square of the distance \( r \) from the sun.

Step2: Analyze Distance at Each Point

• Point A: Far from the sun (large \( r \)).
• Point B: Far from the sun (large \( r \)).
• Point D: Moderate distance from the sun.
• Point C: Closest to the sun (smallest \( r \)).

Since acceleration \( a \propto \frac{1}{r^2} \), the smallest \( r \) gives the largest \( a \). So at Point C, \( r \) is minimum, hence acceleration is maximum.

Answer:

C. Point C