- #1

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2. Homework Equations :

g = Gm/r

^{2}

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.

g

_{1}= g

_{3}= Gm/d

^{2}

g

_{2}= Gm/(d[tex]\sqrt{}2[/tex]

^{2})

g

_{y}= g

_{1}+ g

_{2y}

= Gm/d

^{2}+ g

_{2}sin 45

= Gm/d

^{2}+ Gm/(d[tex]\sqrt{}2[/tex])

^{2}

g

_{x}= g

_{3}+ g

_{2x}

= Gm/d

^{2}+ g

_{2}cos 45

= Gm/d

^{2}+ Gm(d[tex]\sqrt{}2[/tex])

^{2}

g

^{2}= g

_{x}

^{2}+ g

_{y}

^{2}

g = [tex]\sqrt{}(2Gm/d

^{2 + Gm/d^2 cos 45}[/SUP])[/tex]