Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

The ratio $\frac{F_1}{F_2}$ is 2
Let $M_s$ be the mass of the star. Let $M$ be the mass of planet 1. Let $R$ be the distance from the star to planet 1. We can write an expression for the gravitational force of the star on planet 1. $F_1 = \frac{G~M_s~M}{R^2}$ Note that the mass of planet 2 is $2M$ and the distance from the star to planet 2 is $2R$. We can write an expression for the gravitational force of the star on planet 2. $F_2 = \frac{G~M_s~(2M)}{(2R)^2}$ $F_2 = \frac{G~M_s~M}{2~R^2}$ $F_2 = \frac{F_1}{2}$ We can divide $F_1$ by $F_2$. $\frac{F_1}{F_2} = \frac{F_1}{(F_1/2)} = 2$ The ratio $\frac{F_1}{F_2}$ is 2.