Question

How to calculate the mass of the sun?

Answer 1

Step 1: Kepler’s third law

According to Newton’s form of Kepler’s third law, the orbital period of a celestial body is given as,

$p^2=\frac{4{\mathrm{\pi }}^2}{GM}{a}^3$

Where, $p$ is the orbital period,
$G$ is the gravitation constant,
$M$ is the mass of the Sun,
$a$ is the orbit semi-major axis distance.

Upon rearranging the equation we get,

$M=\frac{4{\mathrm{\pi }}^2{\mathrm{a}}^3}{GM}$

Step 2: Calculate the Mass

Now for planet Earth:

$a=1.496\times {10}^{11}m$

$p=3.154\times {10}^{7}s$

$G=6.67\times 10{}^{-11}{m}^{3}k{g}^{-1}{s}^{-2}$

Upon substituting the values we get,

$M=\frac{4\times 3.{14}^2\times 1.496\times {10}^{11}}{6.67\times {10}^{-11}\times 3.154\times {10}^7}$

$=1.99\times {10}^{30}kg$

Hence, the mass of the sun is $1.99\times {10}^{30}kg$.