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

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Dec 25, 2016

Answer:

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#

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