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 = `(Gm_1m_2)/r^2`

Where I 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`

⇒ m₂ = `((3.5 xx 10^22) xx (1.5 xx 10^11)^2)/((6.7 xx 10^(−11)) xx (6 xx 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.