A planet orbiting a star with a mass one-quarter that of the Sun has an orbital radius of 1/25 AU.If Earth's orbital velocity is 30 km/s,what is the orbital velocity of this planet?
A) 15 km/s
B) 30 km/s
C) 60 km/s
D) 75 km/s

Question

Quizplus · Accepted Answer

The orbital velocity (v) of a planet is given by v = sqrt(GM/r), where G is the gravitational constant, M is the mass of the star, and r is the orbital radius. Since the star's mass is one-quarter of the Sun's, and the orbital radius is 1/25 AU, the velocity is v = sqrt((1/4) * GM_sun / (1/25) AU) = sqrt(25/4) * v_earth = (5/2) * 30 km/s = 75 km/s.

A Planet Orbiting a Star with a Mass One-Quarter That