Non-spherical Earth Perturbation - RAAN (combined coefficients)

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Equation / Last modified by eng on 2017/09/09 23:03
MichaelBartmess.Non-spherical Earth Perturbation - RAAN (combined coefficients)

This equation computes and approximation of 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 affects of the `J_2` geopotential coefficients derived from the geopotential function of the Earth.  The inputs to this equation are:

  • 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.