Mithra Is an Unknown Planet That Has Two Moons $( G = 6.67 \times$

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 mass of Mithra? $( G = 6.67 \times$ $\left. 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $1 \times 10 ^ { 23 } \mathrm {~kg}$
B) $1 \times 10 ^ { 22 } \mathrm {~kg}$
C) $1 \times 10 ^ { 24 } \mathrm {~kg}$
D) $3 \times 10 ^ { 22 } \mathrm {~kg}$
E) $3 \times 10 ^ { 23 } \mathrm {~kg}$