Question

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

Answer 1

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 color(white)(')a^3`

That means:

`p^2=(4pi^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.

Rearranging the equation gives:

`M=(4pi^2a^3)/(Gp^2)`

Now for planet Earth:
`a=1.496*10^11m`
`p=3.154*10^7s`
and
`G=6.67408*10^(-11)m^3Kg^(-1)s^(-2)`

Putting the values into the equation gives the mass of the Sun:
`M=1.99*10^30Kg`