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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? - Science and Technology 1

Sum

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

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Solution

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

\[F = \frac{GM_e M_s}{R^2}\]

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

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

\[ \Rightarrow M_s = \frac{(3 . 5 \times {10}^{22} ) \times (1 . 5 \times {10}^{11} )^2}{(6 . 7 \times {10}^{- 11} ) \times (6 \times {10}^{24} )} = 1 . 96 \times {10}^{30} kg\]

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