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Question
What is meant by the superposition of the gravitational field?
Solution
The total gravitational field at a point due to all the masses is given by the vector sum of the gravitational field due to the individual masses. This principle is known as the superposition of gravitational fields.
`vec"E"_"total" = vec"E"_1 + vec"E"_2 + ... vec"E"_"n"`
= `-"Gm"_1/"r"_1^2 hat"r"_1 - "Gm"_2/"r"_2^2 hat"r"_2 - "Gm"_"n"/"r"_"n"^2 hat"r"_"n"`
`vec"E"_"total" = -sum_("i" = 1)^"n" ("Gm"_"i")/("r"_"i"^2) hat"r"_"i"`
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