Mithra Is an Unknown Planet That Has Two Moons $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

Multiple Choice

$\begin{array} { | c | c | c | c | c | } \hline & \text { Mass } & \text { Radius } & \text { Orbital radius } & \text { Orbital period } \\\hline \text { Moon A } & 4.0 \times 10 ^ { 20 } \mathrm {~kg} & \text { unknown } & 2.0 \times 10 ^ { 8 } \mathrm {~m} & 4.0 \times 10 ^ { 6 } \mathrm {~s} \\\hline \text { Moon B } & 1.5 \times 10 ^ { 20 } \mathrm {~kg} & 2.0 \times 10 ^ { 5 } \mathrm {~m} & 3.0 \times 10 ^ { 8 } \mathrm {~m} & \text { unknown } \\\hline\end{array}$
Mithra is an unknown planet that has two moons, A and B , in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $1.6 \times 10 ^ { 13 } \mathrm {~N}$
B) $4.4 \times 10 ^ { 13 } \mathrm {~N}$
C) $2.0 \times 10 ^ { 14 } \mathrm {~N}$
D) $1.0 \times 10 ^ { 14 } \mathrm {~N}$
E) $4.0 \times 10 ^ { 14 } \mathrm {~N}$