Question

Calculate the mass of the sun from the radius of the earth's orbit (1.50×10¹¹ m), the earth's period in its orbit, and the gravitational constant G.

What is the density of the sun ? (The sun's radius is 6.96×10⁸ m). Notice how it compares with the density of the earth.

Answer 1

From Kepler's law,

the time period of the circular orbit is, T=365.24 days*86400 minutes = 31556736 s

GM=3*pi*V/T²

M=(3*pi*V/T²)/G

    But volume of the sphere is V=4/3*pi*r³

here radius of the earth's orbit, r=1.51011 m, pi value is 3.14 and gravitational constant G=6.674 10^-11 N.m²/kg²

then volume V=4/3*3.14*(1.51011 m)³

                      =14601437997.03 m³

M=(3*3.14*14601437997.03 m³/(31556736 s)²)/(6.67410^-11 N.m²/kg²)

=2.0610³⁰ kg

density of the sun = M/V

                            =2.0610³⁰ kg/ 14601437997.03 m³

                           = 1410 kg/m³

the density of the earth approximately=5500 kg/m³