Answer
$\frac{r_{max}}{r_{min}}=1.05$
Work Step by Step
- The mass of the moon $M_m$
- The mass of the planet $M_p$
- The maximum distance $r_{max}$ and the minimum distance $r_{min}$
- Gravitational constant $G$
The gravtiational force formula states that $$F=G\frac{m_1m_2}{r^2}$$
In other words, the gravitational force is inversely proportional with the distance between 2 objects.
Therefore, the maximum gravitational force exerted on the moon is when $r$ is minimum $$F_{max}=G\frac{M_mM_p}{r^2_{min}}$$
The minimum gravitational force exerted on the moon is when $r$ is maximum $$F_{min}=G\frac{M_mM_p}{r^2_{max}}$$
Since $F_{max}$ exceeds $F_{min}$ by $11\%$, we have $$F_{max}=1.11F_{min}$$ $$G\frac{M_mM_p}{r^2_{min}}=1.11G\frac{M_mM_p}{r^2_{max}}$$ $$\frac{1}{r^2_{min}}=\frac{1.11}{r^2_{max}}$$ $$\frac{r^2_{max}}{r^2_{min}}=1.11$$ $$\frac{r_{max}}{r_{min}}=\sqrt{1.11}=1.05$$
