Juno, the angular momentum of Jupiter and the Lense–Thirring effect

Abstract

Abstract The recently approved Juno mission will orbit Jupiter for 1 year in a highly eccentric ( r min = 1.06 R Jup , r max = 39 R Jup ) polar orbit ( i = 90 ° ) to accurately map, among other things, the jovian magnetic and gravitational fields. Such an orbital configuration yields an ideal situation, in principle, to attempt a measurement of the general relativistic Lense–Thirring effect through the Juno’s node Ω which would be displaced by about 570 m over the mission’s duration. Conversely, by assuming the validity of general relativity, the proposed test can be viewed as a direct, dynamical measurement of the Jupiter’s angular momentum S which would give important information concerning the internal structure and formation of the giant planet. The long-period orbital perturbations due to the zonal harmonic coefficients J l , l = 2 , 3 , 4 , 6 of the multipolar expansion of the jovian gravitational potential accounting for its departures from spherical symmetry are, in principle, a major source of systematic bias. While the Lense–Thirring node rate is independent of the inclination i, the node zonal perturbations vanish for i = 90 . In reality, the orbit injection errors will induce departures δ i from the ideal polar geometry, so that, according to a conservative analytical analysis, the zonal perturbations may come into play at an unacceptably high level, in spite of the expected improvements in the low-degree zonals by Juno. A linear combination of Ω, the periJove ω and the mean anomaly M cancels out the impact of J 2 and J 6 . A two orders of magnitude improvement in the uncanceled J 3 and J 4 would be needed to reduce their bias on the relativistic signal to the percent level; it does not seem unrealistic because the expected level of improvement in such zonals is three orders of magnitude. More favorable conclusions are obtained by looking at single Doppler range-rate measurements taken around the closest approaches to Jupiter; numerical simulations of the classical and gravito-magnetic signals for this kind of observable show that a 0.2–5% accuracy would be a realistic goal.