# Gravitational Field

1. Three objects of equal mass are located at three corners of a square of edge length d. Find the magnitude and direction of the gravitational field at the fourth corner due to these objects. (Use the following as necessary: G, d, and m.)

2. Homework Equations :

g = Gm/r2

3. My attempt at the solution: I labeled the masses as 1, 2, and 3, where 1 and 3 are adjacent to the fourth corner and 2 is in the opposite corner from the fourth.

g1 = g3 = Gm/d2
g2 = Gm/(d$$\sqrt{}2$$2)

gy = g1 + g2y

= Gm/d2 + g2 sin 45

= Gm/d2 + Gm/(d$$\sqrt{}2$$)2

gx = g3 + g2x

= Gm/d2 + g2 cos 45

= Gm/d2 + Gm(d$$\sqrt{}2$$)2

g2 = gx2 + gy2

g = $$\sqrt{}(2Gm/d2 + Gm/d^2 cos 45[/SUP])$$

## The Attempt at a Solution

your calculations for the x and y components of g are wrong. use the correct values of
sin and cos

$$\sin(45)=\cos(45)=\frac{1}{\sqrt{2}}$$

reworkout that