# Gravitationtrouble setting up equation

1. Oct 1, 2007

### Saladsamurai

My problem lies in setting this up.

A particle of mass M is split into two pieces, M and M-m, and are set some distance apart.

What ratio of m/M maximizes the magnitude of the gravitational attraction.

I will definately be needing $$F_g=\frac{Gm_1m_2}{r^2}$$

I know that after making appropriate substitutions I get.

$$F_g=\frac{GM(M-m)}{r^2}$$
but my problem is in how to compare what happens as m-->M?

Any thoughts in the set up?

Thanks,
Casey

2. Oct 1, 2007

### nrqed

You mean that the pieces are m and M-m!!
basically, you have to optimize the product m(M-m) as a function of m. Just take the derivative with respect to m and set the derivative equal to zero. That will give you the optimum m and then you may calculate the ratio m/M.

Last edited: Oct 1, 2007
3. Oct 1, 2007

### Saladsamurai

AWWWW!! I knew that! I wrote out the product wrong! Thanks nrqed

Casey!

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