# How to calculate mass of the sun? Please tell in a simple methamatical way.

Dec 23, 2016

You can calculate the mass of the Sun from Newton's form of Kepler's 3rd law.

#### Explanation:

Newton's form of Kepler's 3rd law describes the orbit of a planet around the Sun. It relates the semi major axis distance of the orbit to the period of the orbit using the equation:

${p}^{2} \alpha \textcolor{w h i t e}{'} {a}^{3}$

That means:

${p}^{2} = \frac{4 {\pi}^{2}}{G M} {a}^{3}$

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.

Rearranging the equation gives:

$M = \frac{4 {\pi}^{2} {a}^{3}}{G {p}^{2}}$

Now for planet Earth:
$a = 1.496 \cdot {10}^{11} m$
$p = 3.154 \cdot {10}^{7} s$
and
$G = 6.67408 \cdot {10}^{- 11} {m}^{3} K {g}^{- 1} {s}^{- 2}$

Putting the values into the equation gives the mass of the Sun:
$M = 1.99 \cdot {10}^{30} K g$