J2

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Constant / Last modified by eng on 2017/09/11 02:08
J_2 = 1.08262668 X 10^-3 = (2 epsilon_E) / 3 - (R_"Earth"^3 * omega_"Earth"^2) / (3G*M_"Earth")
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The J_2 constant is the Earth's second dynamic form factor used in computing the J_2 perturbation of the inverse square formulation of the gravitational effect on the force due to a perfect spherical body of uniform density.

The MATH AND SCIENCE

This factor can be calculated as:

J_2 = (2 epsilon_E/3) -  (R_E^3 omega_E^2) / (3 G M_E)

where

• epsilon_E is the central body's oblateness (in this case Earth's oblateness)
• R_E is the central body's equatorial radius (in this case the Earth's mean equatorial radius)
• omega_E is the central body's rotational rate (in this case Earth's rotation rate is 7.292115 X 10^-5 rad/sec
• G is the universal gravitational constant
• M_E is the mass of the central body (in this case the Earth's mass)

REFERENCE

Equation section of Nodal Precession article