# Homework Help: Gravitational field for 2 particles

1. Oct 9, 2008

### Symstar

1. The problem statement, all variables and given/known data
Two identical particles, each of mass m, are located on the x axis at x = +x0 and x = -x0.

Determine a formula for the gravitational field due to these two particles for points on the y axis; that is, write $$\vec{g}$$ as a function of y, m, x0, and so on.
Express your answers in terms of the variables y, m, x0, and appropriate constants. Answer in the form gx,gy.

2. Relevant equations
$$\vec{g}=\frac{\vec{F}}{m}$$
$$\vec{g}=\frac{GM}{r^2}\hat{r}$$

3. The attempt at a solution
I'm really at a loss as to how to approach this problem. I would assume that, graphically, the y axis will be between the two particles and that we are trying to find the components of g in terms of the point on the y axis.

I suppose that in this frame we have a triangle with our particles on two corners and our point on the y axis at the third corner.

I'm still very unsure as to how gravitational fields work in cases like this, but here's what I attempted:

$$\vec{g}=\frac{\vec{F_1}}{m} + \frac{\vec{F_2}}{m}$$
$$\vec{g}=\frac{mG}{r^2_1}\hat{r_1} + \frac{mG}{r^2_2}\hat{r_2}$$
$$r^2_1=-x^2_0+y^2$$
$$r^2_2=x^2_0+y^2$$
$$\vec{g}=\frac{mG}{-x^2_0+y^2}\hat{r_1} + \frac{mG}{x^2_0+y^2}\hat{r_2}$$

At this point, assuming I haven't made a mistake (I doubt that I haven't) I don't know what to do. Could someone give me a hand and some explaining, please?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 9, 2008

### nasu

You are on the right track, kind of.

Correction:
r1^2= xo^2+y^2=r2^2

Then find the x and y components for each one of the two forces (or gravitational fields).