Astrodynamics combines Newtonian physics of celestial mechanics, orbital mechanics, and ballistics into a science which can be applied to satellites, rockets, and spacecraft.

Orbital Elements

Mean Motion

Mean Motion (revs/day) required for a body to complete one orbit.

In it's simplest form mean motion can be expressed as `"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 `"revolutions"/"time"`, `"radians"/"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 `"revolutions"/"day"`

can be expressed as a function of orbital period as:

`n = "1 rev" / P` = `"360 deg" / P` = `(2pi " radians")/ P`

Orbital Period

`P = 1/n`, where `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

`mu = a^3/P^2`

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

Equations

  • vLength by vCalc