The magnitude of the gravitational field that would pull a particle at point P in the x -direction is the gravitational field multiplied by cos ⁡ ⁡ ( θ θ ) where θ θ is the angle adjacent to the x -axis. In this case, cos ⁡ ⁡ ( θ θ ) = p p 2 + R 2 . Hence, the magnitude of the gravitational field in the x -direction, E x is: E x = G M cos ⁡ ⁡ θ θ p 2 + R 2 Substituting in cos ⁡ ⁡ ( θ θ ) gives E x = G M p ( p 2 + R 2 ) 3 / 2 Suppose that this mass is evenly distributed in a ring centered at the origin and facing point P with the same radius R . Because all of the mass is located at the same angle with respect to the x -axis, and the distance between the points on the ring is the same distance as before, the gravitational field in the x -direction at point P due to the ring is the same as a point mass located at a point R units above the y -axis: E ring = G M p ( p 2 + R 2 ) 3 / 2