Gravitationtrouble setting up equation

[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 definitely 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

 

[nrqed]

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 definitely 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

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.

 

[Saladsamurai]

You mean that the pieces afre 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 an dthen you may calculate the ratio m/M.

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

Casey!