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Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 1024 kg and of the Sun = 2 × 1030 kg. The average distance between the two is 1.5 × 1011 m.

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Answer

Given,

Mass of the sun (m) = 2 × 1030 kg

Mass of the earth (M) = 6 × 1024 kg

G = 6.67 x 10-11 Nm2kg-2

Average distance R = 1.5 × 1011 m

According to the formula for gravitational force we know,

F = G MmR2\dfrac{\text{M}\text{m}}{\text{R}^2}

Substituting we get,

F = 6.67×10−11×6×1024×2×1030(1.5×1011)2\dfrac{6.67 \times 10^{-11}\times 6 \times 10^{24} \times 2 \times 10^{30} }{(1.5 \times 10^{11})^2} = 3.56 x 1022 N

Hence, magnitude of the gravitational force = 3.56 x 1022 N

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