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C2 2 (often appearing as C22 or C22, or in some cases it is written with the latter "2" as a superscript) is a coefficient reflecting the gravitational effect of a type of rotational asymmetry of an astronomical body, such as a planet or moon. It is often cited along with J2, the two capturing the most common and pronounced deviations from spherical symmetry found in rotating bodies. J2 is a measure of the body's oblateness, i.e., how much larger equator-to-equator diameter is than its pole-to-pole diameter. A non-zero C22 implies a lack of circular symmetry around the pole, elongation along some direction, which presumably results in a non-circular equator: in the simplest case, of a non-zero C22 with other coefficients zero, the equator is an ellipse centered on the rotational axis. This deformation is relatively stable despite rotation, just as a two-blade fan rotates stably around its axis. Tidal forces from a co-orbiting body can cause this type of non-circularity.
These two are coefficients of what I term a gravitational potential model, the coefficients being spherical harmonics. The common, more-complete model-type identifies its coefficients with a C and two numerical subscripts, and a simpler model-type that presumes circular symmetry identifies its coefficients with a J and one numerical subscript.
These coefficients are of interest for bodies in the study of their structure, and for their effect on orbits, for navigation of artificial satellites and space probes. They are often determined through careful monitoring of the timing and position of orbiting bodies and probes, the work often listed as radio science, when discussing the instruments and experiments of planetary space probes.