Question

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 22n what is the mass of the sun

Answer 1

the mass of the earth, m = 6 × 10²⁴ kg 
Assume the mass of the sun is M 
distance between earth and sun , r = 1.5 × 10¹¹ m
force between sun and earth , F = 3.5 × 10²²  N

   use gravitational force formula,
                                              F = GMm/r²
3.5 × 10²² = 6.67 × 10⁻¹¹ × 6 × 10²⁴ M/(1.5 × 10¹¹)² 
3.5 × 10²² × 2.25 × 10²²/(6.67 × 6 × 10¹³) = M
M = 0.196 × 10³¹ kg 

hence, mass of the sun is 1.96 × 10³⁰ kg 

Answer 2

Let the mass of the sun be M kg.

Given conditions ⇒
Mass of the Earth (m) = 6 × 10²⁴ kg.
Distance between the Earth and the Sun(r) = 1.5 × 10¹¹ m.
Force of Attraction between the sun and the Earth(F) = 3.5 × 10²² N.
Constant of the Gravitation(G) = 6.67 × 10⁻¹¹ Nm² kg⁻².

Using the Formula,
F = G m M/r²
∴ M = Fr²/G m
⇒ M = 3.5 × 10²² ×  (1.5 × 10¹¹)²/6.67 × 10⁻¹¹ × 6 × 10²⁴
⇒ M = 0.196 × 10³¹
∴ M = 1.96 × 10³⁰
or M ≈ 2 × 10³⁰ kg.

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


Hope it helps.