Question

How to calculate the mass of the sun?

Answer 1

Answer:

To determine the mass of sun let’s use an approach called the orbital method. We can calculate the mass of the Sun by measuring the orbital speed and the radius of one of the planets, such is Jupiter. Jupiter orbits the sun at 13 km/s, the shape of Jupiter’s orbit is essentially circular with a radius of 780 million km.

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Answer 2

$\huge\bold\red{Question}$

How to calculate the mass of the sun?

$\huge\bold\green{Solution}$

$\sf{Newton’s\: form \:of \:Kepler’s \:3rd\: law\: describes\: the}$ $\sf{orbit\:of\:a\:planet \:around\: the\: Sun. \:From\: this \:law}$ $\sf{we\: can\: calculate\: the\: mass \:of \:the\:sun.}$

$\sf{\frac{p^2=4π^2}{GM a^3}}$

$\sf{P\: is\: the\: orbital\: period;}$

$\sf{G\: is\: the\: gravitation\: constant;}$

$\sf{M\: is \:the\: mass \:of \:the\: Sun;}$

$\sf{a \:is \:the\: orbit\: semi\: major \:axis\: distance.}$

Rearranging the equation gives:

$\sf{\frac{M=4π^2a^3}{Gp^2}}$

$\sf{Now \:for\: planet \:Earth: a = 1.496⋅1011 m}$

$\sf{p = 3.154⋅10^7s}$

$\sf{G=6.67408⋅10−11m3Kg−1s−2}$

Substitute all the values to the equation and thus gives the mass of the sun $\sf{M=1.99⋅10^{30}\:Kg}$