The speed of a satellite in a circular orbit of radius $R$ around the earth is $3.0 \mathrm{~km} / \mathrm{s}$. The speed of another satellite in a different circular orbit around the earth is one-half this value. What is the radius of that satellite's orbit?
A) $4 R$
B) $2 R$
C) $\sqrt{2} R$
D) $R / \sqrt{2}$
E) $R / 2$
F) $R / 4$
G) Some other multiple of $R$ (specify)

Question

Quizplus · Accepted Answer

The speed of a satellite in orbit is proportional to the square root of the inverse of the radius of the orbit ($v \propto \sqrt{1/R}$). If the speed of the second satellite is half that of the first ($v_2 = 0.5v_1$), then its orbital radius must be four times larger ($R_2 = 4R_1$) to maintain this relationship, as $(0.5)^2 = 1/4$, inversely relating speed to radius.

The Speed of a Satellite in a Circular Orbit of Radius