J₂

J₂ is a coefficient reflecting the gravitational effect of a body's (planet's or moon's) oblateness (extra width making it flatter than a perfect sphere), typically the result of the body's rotation. J₂ is of interest for space flight navigation and is measured through tracing the flight of spacecraft: for example, an orbit that is not confined to the equatorial plane undergoes a J2 perturbation (a perturbation being a small change from the Keplerian orbit it has been following to another). J₂'s measure aids in modeling the composition of a body, thus measuring that of solar system planets is of interest. Cassini has been used for this with Saturn, and Juno similarly with Jupiter. A spherically-symmetric planet has a J₂ of 0 and more oblateness generally means a larger J₂.

J₂ is one coefficient in a standard type of model of gravitational potential of such a body: a zonal harmonic gravity model and in the case of Earth, it is often termed a geopotential model (which term is also sometimes borrowed for other bodies: for the general case, I use the term gravitational potential model). The word zonal indicates these are the coefficients that do not affect gravity's symmetry about the axis of rotation. The coefficients are called gravitational moments, and indicate the arrangement of mass other than that of a sphere of spherically-symmetric density. The generally-used set of coefficients presume the body is somewhat close to spherical and hydrostatic equilibrium, and its rotation is the major factor producing the moments. They are representations of the gravitational potential's spherical harmonic coefficients (those that are axis-symmetric around the axis of rotation), and are generally cited scaled to the body's size and radius so as to be dimensionless. The specific function represented by these coefficients quantifies the deviation of an equipotential surface (i.e., a mathematical surface around the body with the same gravitational potential) of the body from a spherical surface which has the same mean gravitational potential. In the case of Earth, the equipotential surface is a representation of sea level, i.e., the coefficients show how far sea level differs from spherical.

J₃ is a similar coefficient but reflects asymmetry across the equator, and is typically far less significant than J₂. Further coefficients (J coefficients, J₄, J₅, J₆, etc.) are symmetric across the equator if they are even-numbered. There are spherical harmonics corresponding to J₀ and J₁ but the values are coordinated and scaled so J₀ is taken as 1 (the coefficients are scaled to the total mass of the body) and J₁ is 0 (the coefficients are based on the body's center of mass). The moments corresponding to other (non-axis-symmetric) spherical harmonics can be significant and of interest but the terms used vary. Also, various other names are also used for the coefficients and models described above.

All the solar system planets and the Sun are oblate from to rotation, and have a significant J₂ coefficient. Jupiter and Saturn, with rotation periods of less than half an Earth-day, are the most oblate. A planet's J₂ value is also useful in modeling the behavior of its ring system. Determinations are improving with continuing measurement and analysis but here are some example determined values:

Determinations of the Sun's J₂ put it in the general area of 0.00000022.