Question

The mass of the earth is 6 × 10²⁴ kg. The distance between the earth and the sun is 1.5 × 10¹¹ m. If the gravitational force between the two is 3.5 × 10²² N, what is the mass of the sun? Use G = 6.7 × 10^–11 N m² kg^–2

Answer 1

Given: Mass of the earth (M_e) = 6 × 10²⁴ kg,

Gravitational force (F) = 3.5 × 10²² N,

Distance (R) = 1.5 × 10¹¹ m,

Gravitational constant (G) = 6.7 × 10^-11 Nm²/kg²

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

F = `("G""m"_1"m"_2)/"r"^2`

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

`=> 3.5 xx 10^22 = (6.7 xx 10^-11 xx 6 xx 10^24 xx "m"_2)/(1.5 xx 10^11)^2`

\[ \Rightarrow \text{m}_2 = \frac{(3 . 5 \times {10}^{22} ) \times (1 . 5 \times {10}^{11} )^2}{(6 . 7 \times {10}^{- 11} ) \times (6 \times {10}^{24} )}\]

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

= 1.96 × 10³⁰ kg

The mass of the Sun is 1.96 × 10³⁰ kg.