# Non-spherical Earth Perturbation - RAAN

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dotOmega_"J2" =
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ID
MichaelBartmess.Non-spherical Earth Perturbation - RAAN
UUID
aa7aa8ee-ed25-11e3-b7aa-bc764e2038f2

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)

# Notes

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.