Non-spherical Earth Perturbation - RAAN

Not Reviewed
Equation / Last modified by Administrator on 2015/08/11 07:05
MichaelBartmess.Non-spherical Earth Perturbation - RAAN

This equation computes the rate of change of the right ascension of the ascending node  (RAAN) of an orbit where the rate of change (`dotOmega_"J2"`) in deg/day results from the `J_2` geopotential coefficients derived from the geopotential function of the Earth.  The inputs to this equation are:

  • the mean motion of the orbit (n) in deg/day
  • the Earth equatorial radius (`R_E`) in kilometers
  • the orbit's semi-major axis (a) in kilometers
  • the eccentricity of the orbit, (e)
  • the orbit inclination (i)




The earth is not a sphere.  In fact, the Earth is neither a homogeneous mass nor a sphere.  Consequently, the several attributes of the Earth's shape and composition have noticeable affects on a satellite's orbit.  The bulge at the equator, the flattening at the poles, and the slight pear shape of the Earth are important contributors to the perturbation of an orbit due to a non-spherical Earth.