Gravitational Force:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{{\mathbf{GM}}_{\mathbf{1}}{\mathbf{M}}_{\mathbf{2}}}{{\mathbf{R}}^{\mathbf{2}}}}$

Centripetal Force:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{m}{\mathbf{v}}^{\mathbf{2}}}{\mathbf{R}}}$

Velocity:

$\overline{){\mathbf{v}}{\mathbf{=}}\frac{\mathbf{d}\mathbf{i}\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{c}\mathbf{e}\mathbf{,}\mathbf{}\mathbf{d}}{\mathbf{t}}}$

Distance covered in one revolution:

d = 2πR

The velocity of the object:

v = d/T = 2πR/T

v^{2} = 4π^{2}R^{2}/T^{2}

The potential energy U of an object of mass m that is separated by a distance R from an object of mass M is given by U= -GMm/R

Find an expression for the square of the orbital period.

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