### Q.13:- How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5 × 10^{8} km.

**Answer:-**

Orbital radius of the Earth around the Sun, *r* = 1.5 × 10^{11} 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} Nm^{2} kg^{–2}

Thus, mass of the Sun can be calculated using the relation,

*M* = 4π^{2}*r*^{3} / G*T*^{2}

= 4 × 3.14^{2} × (1.5 × 10^{11})^{3} / [ 6.67 × 10^{-11} × (365.25 × 24 × 60 × 60)^{2}]

= 2 × 10^{30} kg

Hence, the mass of the Sun is 2 × 10^{30} kg.