ABSTRACT
J2 A dimensionless coefficient in the P2(cos θ) term of the Legendre polynomial expression of the gravitational potential of a planet, where θ is the colatitude (90◦-latitude). Assuming symmetry of mass distribution with respect to the rotational axis and to the equatorial plane and without considering the effect of rotation, the gravitational potential of a planet as a function of radial coordinate r and colatitude θ is
V =− GM r
+ J2GMa 2
( 3 2
cos2 θ − 1 2
)
+ higher order terms of 1 r
where G = 6.6725985× 10−11 m3 kg−1 s−2 is the gravitational constant, M is the total mass of the planet, and a is the equatorial radius. J2 is an important parameter in the gravitational and rotational dynamics of a planet because of its relation with the moments of inertia:
J2 = C − A Ma2
where C and A are the polar and equatorial moments of inertia, respectively, and a is the mean radius of the Earth. The value of J2 for the Earth is about 1.082626 × 10−3. Redistribution of mass in the Earth causes changes to the gravitational potential and hence J2.
