Wind-induced odd gravitational harmonics of Jupiter

While the rotational distortion of Jupiter makes a major contribution to its lowermost order even zonal gravitational coefficients J(n) with n a parts per thousand yen 2, the component of the zonal winds with equatorial antisymmetry, if sufficiently deep, produces a gravitational signature contained in the odd zonal gravitational coefficients J(n) with n a parts per thousand yen 3. Based on a non-spherical model of a polytropic Jupiter with index unity, we compute Jupiter's odd gravitational coefficients J(3), J(5), J(7), aEuro broken vertical bar, J(11) induced by the equatorially antisymmetric zonal winds that are assumed to be deep. It is found that the lowermost odd gravitational coefficients J(3), J(5) and J(7) are of the same order of magnitude with J(3) = -1.6562 x 10(-6), J(5) = 1.5778 x 10(-6) and J(7) = -0.7432 x 10(-6), and are within the accuracy of high-precision gravitational measurements to be carried out by the Juno spacecraft.