Question

1. the diagram below represents two satellites of equal mass, a and b, in circular orbits around a planet. compared to the magnitude of the gravitational force of attraction between satellite a and the planet, the magnitude of the gravitational force of attraction between satellite b and the planet is 1. half as great 2. twice as great 3. one - fourth as great 4. four times as great

Explanation:

Step1: Recall gravitational force formula

Newton's law: $F = G\frac{Mm}{r^2}$, where $r$ = distance from planet.

Step2: Identify distances for A and B

$r_A = R$, $r_B = 2R$. Masses $M$ (planet), $m$ (satellites) are equal.

Step3: Calculate force ratio $F_B/F_A$

$F_A = G\frac{Mm}{R^2}$, $F_B = G\frac{Mm}{(2R)^2} = G\frac{Mm}{4R^2}$. So $F_B = \frac{1}{4}F_A$.

Answer:

1. one-fourth as great