Three objects of equal mass are located at three conrners of a square, find the gravitatinal field.?

Question

I want to see the theory in finding gravitational field.

Thanks in advance, I appericate it.

Sorry I made a mistake. Find the gravitational field at the fourth corner of the sqaure.

Answer 1

The theory of this is similar to finding the resultant electric field due to three charges of the the same magnitude placed at the corners of a square.

E =F/q
F =kq1q2/r²

g =F/m
F =Gm1m2/r²
Gravitational force are always attractive while Electrical force may sometimes be repulsive.

To compute for the resultant g, you do it similarly with the computation of E using vector addition.

E = E1 + E2 + E3

g = g1 + g2 + g3

And my answer is g = (√2 + ½ ) Gm/r²

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Answer 2

Vector addition:
The net gravitational field will be directed toward the center mass and will equal (mG/s²)*(½+√2) where s is the length of a side of the square.
The gravitational field is such that any mass M placed at that point will have a force on it of M*(the expression above)