### J_{2}

(geopotential coefficient regarding a planet's oblateness)

**J**_{2} is one coefficient in a standard type of model of
Gravitational potential of a planet called a **Geopotential Model**.
The coefficients are called **Gravitational Moments**,
and indicate gravitational mass arranged other than
that of a uniformly-dense sphere.
J_{2} specifically reflects
a planet's **Oblateness** (flattening) due to rotation.

J_{2} is of interest for space flight navigation and is
measured by observing the flight of spacecraft near a mass. Its
measure aids in modeling the composition of a planet, thus measuring
that of Solar System planets is of interest. Cassini has been
used for this with Saturn and Juno will be so-used with Jupiter.

All the solar system planets and the Sun are oblate from to
rotation, and have a significant J_{2} coefficient.
Jupiter and Saturn, with rotation periods of less
than half an Earth-day, are the most oblate.

It is also useful in modeling the behavior of rings.

The **J Coefficients** (J_{0} through infinity) are
gravitational-potential
Spherical Harmonics coefficients, specifically those that are
symmetric around the planet's pole. These are generally the most
significant coefficients for large rotating bodies (planets and
stars), J_{2} being the most significant.
They are termed **Gravity Harmonics** or **Gravitational Harmonics**,
making up a **Gravity Spectrum** or **Gravitational Spectrum** of the body.

J_{3} is a similar coefficient but reflects asymmetry across the
equator, thus is typically far less significant than J_{2}.
Further coefficients (J_{4}, J_{5}, J_{6}, etc.)
generally are symmetric across the equator if they are even-numbered.

For Earth:

- ν = GM = 398600.440 km
^{3}s^{-2}
- J
_{2} = 1.7555 x 10^{10} km^{5}s^{-2}
- J
_{3} = -2.619 x 10^{11} km^{6}s^{-2}

(*gravity,coefficient,model,measure*)
http://en.wikipedia.org/wiki/Geopotential_model

**Referenced by:**

Legendre Polynomials

Love Number

Laplace Radius (r_{L})

index