Answer to Question #142830 in Physics for Kiara

Question

A research satellite orbits the Sun. A second research satellite is 2× the mass of the first research satellite and orbits the Sun at 1/3 the distance of the first research satellite. How does the force of gravity on the first research satellite from the Sun (Fg1) compare to the force of gravity on the second research satellite from the Sun(Fg2)?
(a) Fg2 =29Fg1
(b) Fg2 =23Fg1
(c) Fg2 = 6Fg1
(d) Fg2 = 18Fg1

Answer 1

The force of gravity on the first research satellite from the Sun is

$$F_1=G\frac{Mm_1}{R_1^2},$$

for the second one it is

$$F_2=G\frac{Mm_2}{R_2^2}=G\frac{M(2m_1)}{(R_1/3)^2}.$$

The ratio is

$$\frac{F_2}{F_1}=\frac{G\frac{M(2m_1)}{(R_1/3)^2}}{G\frac{Mm_1}{R_1^2}}=\frac29.\\\space\\ F_2=\frac29F_1.$$