Geosynchronous Orbits Video Lessons

Concept

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

###### FREE Expert Solution

Gravitational force:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{G}\mathbf{Mm}}{{\mathbf{R}}^{\mathbf{2}}}}$

Centripetal Force:

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

Velocity for a circular orbit:

$\overline{){\mathbf{v}}{\mathbf{=}}\frac{\mathbf{Circumfrence}}{\mathbf{T}}{\mathbf{=}}\frac{\mathbf{2}\mathbf{\pi R}}{\mathbf{T}}}$

m is the mass of a planet, M, the mass of the sun, R, the radius of the orbit, T, the time take to cover one revolution.

For the planet to remain in a uniform circular orbit, the gravitational force must equal the expression for centripetal force.

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###### Problem Details

Find an expression for the square of the orbital period.