The innermost satellite of Jupiter orbits the planet with a radius of $422 \times 10 ^ { 3 } \mathrm {~km}$ and a period of 1.77 days. What is the mass of Jupiter? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$
A) $1.33 \times 10 ^ { 27 } \mathrm {~kg}$
B) $1.50 \times 10 ^ { 27 } \mathrm {~kg}$
C) $3.08 \times 10 ^ { 27 } \mathrm { kq }$
D) $1.72 \times 10^{27} \mathrm {~kg}$
E) $1.89 \times 10 ^ { 27 } \mathrm {~kg}$

Question

Quizplus · Accepted Answer

Using Kepler's third law and the formula $ T^2 = \frac{4\pi^2}{GM}r^3 $, solving for $ M $ gives $ M = \frac{4\pi^2r^3}{GT^2} $. Substituting the given values, the mass of Jupiter is approximately $ 1.89 \times 10^{27} \mathrm{~kg} $.

The Innermost Satellite of Jupiter Orbits the Planet with a Radius