The mass of the earth is 6 × 10^{24} kg. The distance between the earth and the sun is 1.5 × 10^{11} m. If the gravitational force between the two is 3.5 × 10^{22} N, what is the mass of the sun? Use G = 6.7 × 10^{–11 }N m^{2} kg^{–2}

#### Solution

**Given:** Mass of the earth (M_{e}) = 6 × 10^{24} kg,

Gravitational force (F) = 3.5 × 10^{22} N,

Distance (R) = 1.5 × 10^{11} m,

Gravitational constant (G) = 6.7 × 10^{-11} Nm^{2}/kg^{2}

The gravitational force between the Sun and the Earth can be found out using the formula,

where, Me and Ms are the masses of the Earth and the Sun, respectively. Using all the given values, we have

\[3 . 5 \times {10}^{22} = (6 . 7 \times {10}^{- 11} )\frac{(6 \times {10}^{24} ) \times M_s}{(1 . 5 \times {10}^{11} )^2}\]

\[ \Rightarrow M_s = \frac{(3 . 5 \times {10}^{22} ) \times (1 . 5 \times {10}^{11} )^2}{(6 . 7 \times {10}^{- 11} ) \times (6 \times {10}^{24} )}\]

`= (7.88 xx 10^44)/(40.2 xx 10^13)`

**= 1.96 × 10 ^{30} kg**

The mass of the Sun is **1.96 × 10 ^{30} kg**.