Low- and high-order gravitational harmonics of rigidly rotating Jupiter

The Juno Orbiter has provided improved estimates of the even gravitational harmonics J(2) to J(8) of Jupiter. To compute higher-order moments, new methods such as the concentric Maclaurin spheroids (CMS) method have been developed, which surpass the commonly used theory of figures (ToF) method in accuracy. This progress raises the question whether ToF can still provide a useful service for deriving the internal structure of giant planets in the solar system. In this paper, I apply both the ToF and the CMS method to compare results for polytropic Jupiter and for the physical equation of state H/He-REOS. 3-based models. An accuracy in the computed values of J(2) and J(4) of 0.1% is found to be sufficient in order to obtain the core mass safely within 0:5 M-circle plus numerical accuracy and the atmospheric metallicity within about 0.0004. ToF to the fourth order provides that accuracy, while ToF to the third order does not for J(4). Furthermore, I find that the assumption of rigid rotation yields J(6) and J(8) values in agreement with the current Juno estimates, and that higher-order terms (J(10) to J(18)) deviate by about 10% from predictions by polytropic models. This work suggests that ToF4 can still be applied to infer the deep internal structure of giant planets, and that the zonal winds on Jupiter reach less deep than 0.9 R-J.