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Question
Solve the following problem.
Find the gravitational force between the Sun and the Earth.
Given Mass of the Sun = 1.99 × 1030 kg
Mass of the Earth = 5.98 × 1024 kg
The average distance between the Earth and the Sun = 1.5 × 1011 m.
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Solution
Given: MS = 1.99 × 1030 kg, ME = 5.98 × 1024 kg, R = 1.5 × 1011 m
To find: Gravitational force between the Sun and the Earth (F)
Formula: F = `("Gm"_1"m"_2)/"r"^2`
Calculation: As, we know, G = 6.67 × 10–11 N m2/kg2
From formula,
F = `("GM"_"s""M"_"E")/"R"^2`
`= (6.67 xx 10^-11 xx 1.99 xx 10^30 xx 5.98 xx 10^24)/(1.5 xx 10^11)^2`
∴ F = `(6.67 xx 1.99 xx 5.98)/2.25 xx 10^21`
= antilog{(log(6.67) + log(1.99) + log(5.98) - log(2.25)} × 1021
= antilog{(0.8241) + (0.2989) + (0.7767) - (0.3522)} × 1021
= antilog{1.5475} × 1021
= 35.28 × 1021
= 3.5 × 1022 N
The gravitational force between the Sun and the Earth is = 3.5 × 1022 N.
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