In Another Solar System, a Planet Has a Moon That $4.0 \times 10 ^ { 5 } \mathrm {~m}$

Multiple Choice

In another solar system, a planet has a moon that is $4.0 \times 10 ^ { 5 } \mathrm {~m}$ in diameter. Measurements reveal that this moon takes $3.0 \times 10 ^ { 5 }$ s to make each orbit of diameter $1.8 \times 10 ^ { 8 } \mathrm {~m}$ What is the mass of the planet? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A) $2.4 \times 10 ^ { 24 } \mathrm {~kg}$
B) $3.4 \times 10 ^ { 24 } \mathrm {~kg}$
C) $4.8 \times 10 ^ { 24 } \mathrm {~kg}$
D) $1.2 \times 10 ^ { 24 } \mathrm {~kg}$
E) $1.7 \times 10 ^ { 24 } \mathrm {~kg}$