Answer
The mass of the star: $M \simeq 1.787 \times {10^{29}}$ kg
Work Step by Step
We have
$T = 9.5$ years $ = 9.5 \times 365 \times 24 \times 60 \times 60 \simeq 2.99 \times {10^8}$ s
$a = 3 \times {10^{11}}$ m
From Exercise 2 we obtain the mass of the star:
$M = \left( {\frac{{4{\pi ^2}}}{G}} \right)\left( {\frac{{{a^3}}}{{{T^2}}}} \right)$,
where $G$ is the gravitational constant,
$G \simeq 6.673 \times {10^{ - 11}}$ ${m^3}k{g^{ - 1}}{s^{ - 2}}$
So,
$M = \left( {\frac{{4{\pi ^2}}}{{6.673 \times {{10}^{ - 11}}}}} \right)\frac{{{{\left( {3 \times {{10}^{11}}} \right)}^3}}}{{{{\left( {2.99 \times {{10}^8}} \right)}^2}}} \simeq 1.787 \times {10^{29}}$ kg
