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/RWhat is the kinetic energy K of the satellite?Express your answer in terms of the potential energy.

###### FREE Expert Solution

Gravitational Force:

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

Centripetal Force:

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

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

M1 = M

M= m

-U = (GMm/R)

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###### 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

What is the kinetic energy K of the satellite?