Question

According to the law of universal gravitation, any two objects are attracted to each other. The strength of the gravitational force depends on the masses of the objects and their distance from each other.

Many stars have planets around them. If there were no gravity attracting a planet to its star, the planet's motion would carry it away from the star. However, when this motion is balanced by the gravitational attraction to the star, the planet orbits the star.

Two solar systems each have a planet the same distance from the star. The planets have the same mass, but Planet A orbits a more massive star than Planet B.



Which of the following statements is true about the planets?
A.
Planet A has a longer year than Planet B.
B.
Planet B will keep orbiting its star longer than Planet A.
C.
Planet B is more attracted to its star than Planet A.
D.
Planet A orbits its star faster than Planet B.

Answer 1

D. Planet A orbits its star faster than Planet B.

Reason: For a circular orbit v = sqrt(GM/r), so at the same orbital radius r a larger star mass M gives a larger orbital speed. (Equivalently the orbital period T = 2π√(r^3/GM) is shorter for the more massive star.)