Right Ascension Precession

The Right Ascension Precession calculator estimates the rate of precession of the right ascension of the ascending node (RAAN) due to Earth oblateness (J2) based on the orbital parameters.

INSTRUCTION: Choose units and enter the following:

• (i) Orbital Inclination
• (a) Semi-Major Axis
• (e) Eccentricity of Orbit

Right Ascension Precession (Ω_J2): The calculator returns the precession in degrees per day. 

The Math / Science

The Precession of Right Ascension due to J2 equation computes and approximation of the rate of change of an orbit's right ascension of the ascending node (RAAN) 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 formula for RAAN precession is:

`dotOmega_"J2" = (-2.06474 *10^14 * cos(i) ) / (a^(7/2) *  (1-e^2)^2)`

 where:

• `dotOmega_"J2"` = precession rate of the RAAN
• a = the orbit's semi-major axis
• e = the eccentricity of the orbit
• i = the orbit inclination 

[mcb]

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.

SEE ALSO

• J2 Perturbation Force
• Non-spherical Earth Perturbation - RAAN (combined coefficients)
• J2 (constant)
• Earth Rotation Rate