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Question
If the ratio of the orbital distance of two planets `"d"_1/"d"_2` = 2, what is the ratio of gravitational field experienced by these two planets?
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Solution
The gravitational field experienced by planets 1
E1 = `"GM"/"d"_1^2`
The gravitational field experienced by planet 2
E2 = `"GM"/"d"_2^2`
The ratio of their orbital distance `"d"_1/"d"_2` = 2
∴ d1 = 2d2
The ratio of the gravitational field of two planets.
`"E"_1/"E"_2 = ("GM")/(2"d"_2)^2 xx "d"_2^2/"GM" = "GM"/(4"d"_2^2) xx "d"_2^2/"GM"`
`"E"_1/"E"_2 = 1/4`
∴ E2 = 4E1
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