Question

1.4.2 test (cst): computer-scored unit test
at which point does the planet have the highest acceleration?
a. point b
b. point c
c. point a
d. point d

Explanation:

Step1: Recall gravitational - force and acceleration relation

According to Newton's law of universal gravitation $F = G\frac{Mm}{r^{2}}$ and $F=ma$, so $a = G\frac{M}{r^{2}}$, where $a$ is acceleration, $G$ is the gravitational - constant, $M$ is the mass of the sun, $m$ is the mass of the planet, and $r$ is the distance between the sun and the planet.

Step2: Analyze the distance at each point

The closer the planet is to the sun, the smaller the value of $r$. From the diagram, point C is the closest to the sun. When $r$ is the smallest, according to $a = G\frac{M}{r^{2}}$, the acceleration $a$ is the largest.

Answer:

B. Point C