Question

select the correct answer. in the diagram, planets a, b, and c have the same mass. which of these statements is true about the motion of these planets? a. planet a will take the longest time to complete an orbit, while planet c will take the shortest time. b. planet a will take the shortest time to complete an orbit, while planet c will take the longest time. c. the combined gravity of planets a and c will cause planet b to take the longest time to orbit. d. all the planets will take the same amount of time to complete one orbit.

Explanation:

Step1: Recall Kepler's third law

The square of the orbital - period ($T$) of a planet is proportional to the cube of the semi - major axis ($a$) of its orbit, i.e., $T^{2}\propto a^{3}$.

Step2: Analyze the distances of the planets

Planet A is closest to the star, so it has the smallest semi - major axis. Planet C is the farthest from the star, so it has the largest semi - major axis.

Step3: Determine the orbital times

Based on Kepler's third law, the planet with the smallest semi - major axis will have the shortest orbital period and the planet with the largest semi - major axis will have the longest orbital period. So planet A will take the shortest time to complete an orbit and planet C will take the longest time.

Answer:

B. Planet A will take the shortest time to complete an orbit, while planet C will take the longest time