Astrodynamics Collection

Last modified by

MichaelBartmess

on

Oct 18, 2019, 1:17:52 AM

Created by

MichaelBartmess

on

Oct 18, 2019, 1:17:52 AM

Equations

Orbital Elements

Mean Motion

required for a body to complete one orbit.

In it's simplest form mean motion can be expressed as $mean_motion = n = \frac{rev}{P}$ $"mean_motion" = n = "rev"/ P$ ,where P is the period and rev is a representation of the time to complete one orbit.

The Orbit time can be expressed in units of $\frac{revolutions}{time}$ $"revolutions"/"time"$ , $\frac{radians}{time}$ $"radians"/"time"$ , $\frac{degrees}{time}$ $"degrees"/"time"$

In the two-line element sets used by the both the government sector and commercial industry to specify a satellite's orbit, mean motion is captured in units of $\frac{revolutions}{day}$ $"revolutions"/"day"$

Mean Motion can be expressed as a function of orbital period as:

$n = \frac{1 rev}{P}$ $n = "1 rev" / P$ = $\frac{360 deg}{P}$ $"360 deg" / P$ = $\frac{2 π radians}{P}$ $(2pi " radians")/ P$

Orbital Period

$P = \frac{1}{n}$ $P = 1/n$ , where $n$ $n$ is the mean motion.

Kepler's Laws

Kepler's 3rd Law

Kepler's 3rd law of planetary motion states, the square of the periodic time is proportional to the cube of the mean distance, or

μ = \frac{a^{3}}{P^{2}}

$mu = a^3/P^2$

where a is the semi-major axis or mean distance, P is the orbital period as above, and ? is a constant for any particular gravitational system.

Equations

Length Units Conversion KurtHeckman Use Equation

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Astrodynamics Collection

Orbital Elements

Mean Motion

Orbital Period

Kepler's Laws

Kepler's 3rd Law

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