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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
Solution
Given: Mass of the earth (Me) = 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,
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.
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