Answer
The mass of Jupiter: $M \simeq 1.9 \times {10^{27}}$ kg
Work Step by Step
We have
$T = 7.154$ days $ = 7.154 \times 24 \times 60 \times 60 = 618106$ s
$a = 1.07 \times {10^9}$ m
From Exercise 2 we obtain the mass of Jupiter:
$M = \left( {\frac{{4{\pi ^2}}}{G}} \right)\left( {\frac{{{a^3}}}{{{T^2}}}} \right)$,
where $G$ is the gravitational constant,
$G \simeq 6.673 \times {10^{ - 11}}$ ${m^3}k{g^{ - 1}}{s^{ - 2}}$
So,
$M = \left( {\frac{{4{\pi ^2}}}{{6.673 \times {{10}^{ - 11}}}}} \right)\frac{{{{\left( {1.07 \times {{10}^9}} \right)}^3}}}{{{{618106}^2}}} \simeq 1.9 \times {10^{27}}$ kg
