Question

1. doubling the distance between the center of an orbiting satellite and the center of earth will result in what change in the gravitational attraction of earth for the satellite? (a) one - half as much (b) one - fourth as much (c) twice as much (d) four times as much (e) none of the above

Explanation:

Step1: Recall gravitational - force formula

The gravitational force formula is $F = G\frac{Mm}{r^{2}}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, $m$ is the mass of the satellite, and $r$ is the distance between the center of the Earth and the center of the satellite.

Step2: Consider the new distance

Let the initial distance be $r_1 = r$ and the new distance $r_2 = 2r$. The initial gravitational force $F_1=G\frac{Mm}{r^{2}}$, and the new gravitational force $F_2 = G\frac{Mm}{(2r)^{2}}$.

Step3: Simplify the new - force expression

$F_2=G\frac{Mm}{4r^{2}}=\frac{1}{4}\times G\frac{Mm}{r^{2}}$. Since $F_1 = G\frac{Mm}{r^{2}}$, we have $F_2=\frac{1}{4}F_1$.

Answer:

B. One - fourth as much