Question

two identical satellites are in orbit about the earth. one orbit has a radius r and the other 2r. the centripetal force on the satellite in the larger orbit is ____________ as that on the satellite in the smaller orbit.
the same
twice as great
four times as great
half as great
one fourth as great
attempts: 0 of 5 used

Explanation:

Step1: Recall centripetal - force formula

The centripetal force for a satellite in orbit around the Earth is given by $F = \frac{GMm}{r^{2}}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, $m$ is the mass of the satellite, and $r$ is the radius of the orbit.

Step2: Compare forces for two orbits

Let $F_1$ be the force on the satellite in the orbit of radius $r$ and $F_2$ be the force on the satellite in the orbit of radius $2r$. So $F_1=\frac{GMm}{r^{2}}$ and $F_2=\frac{GMm}{(2r)^{2}}=\frac{GMm}{4r^{2}}$.

Step3: Find the ratio of the forces

$\frac{F_2}{F_1}=\frac{\frac{GMm}{4r^{2}}}{\frac{GMm}{r^{2}}}=\frac{1}{4}$. So $F_2=\frac{1}{4}F_1$.

Answer:

one - fourth as great