Question

How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5×108 km.

Answer 1

Orbital radius of the Earth around the Sun, r = 1.5 × 1011 m
Time taken by the Earth to complete one revolution around the Sun, T = 1 year = 365.25 days
= 365.25 × 24 × 60 × 60 s

Universal gravitational constant, G = 6.67 × 10–11 Nm2 kg–2
Thus, mass of the Sun can be calculated using the relation,

$M = \frac{4π^2r^3}{ GT^2}$

$= \frac{4 × (3.14)2 × (1.5 × 10^11 )^3 }{6.67 × 10^-11 × (365.25 × 24 ×60 ×60 )^2}$

= $\frac{133.24 × 10 }{6.64 × 10^4} = 2.0 × 10^{30}$ kg

Hence, the mass of the Sun is 2 × 1030 kg.