Universal Law of Gravitation Video Lessons

Concept

# Problem: 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/RFind an expression for the square of the orbital period.

###### FREE Expert Solution

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:

Distance covered in one revolution:

d = 2πR

The velocity of the object:

v = d/T = 2πR/T

v2 = 4π2R2/T2

###### Problem Details

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.