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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:
Referenced by: Legendre Polynomials Love Number Laplace Radius (r_{L}) |