Marco Zannoni

Jupiter gravity field estimated from the first two Juno orbits

The combination of the Doppler data from the first two Juno science orbits provides an improved estimate of the gravity field of Jupiter, crucial for interior modeling of giant planets. The low-degree spherical harmonic coefficients, especially J4 and J6, are determined with accuracies better than previously published by a factor of 5 or more. In addition, the independent estimates of the Jovian gravity field, obtained by the orbits separately, agree within uncertainties, pointing to a good stability of the solution. The degree 2 sectoral and tesseral coefficients, C2,1, S2,1, C2,2, and S2,2, were determined to be statistically zero as expected for a fluid planet in equilibrium.

Measurement of Jupiter’s asymmetric gravity field

The gravity harmonics of a fluid, rotating planet can be decomposed into static components arising from solid-body rotation and dynamic components arising from flows. In the absence of internal dynamics, the gravity field is axially and hemispherically symmetric and is dominated by even zonal gravity harmonics J2n that are approximately proportional to qn, where q is the ratio between centrifugal acceleration and gravity at the planet’s equator. Any asymmetry in the gravity field is attributed to differential rotation and deep atmospheric flows. The odd harmonics, J3, J5, J7, J9 and higher, are a measure of the depth of the winds in the different zones of the atmosphere. Here we report measurements of Jupiter’s gravity harmonics (both even and odd) through precise Doppler tracking of the Juno spacecraft in its polar orbit around Jupiter. We find a north–south asymmetry, which is a signature of atmospheric and interior flows. Analysis of the harmonics, described in two accompanying papers, provides the vertical profile of the winds and precise constraints for the depth of Jupiter’s dynamical atmosphere.

Numerical Error in Interplanetary Orbit Determination Software

The core of every orbit determination process is the comparison between the measured observables and their predicted values, computed using the adopted mathematical models, and the minimization, in a least-squares sense, of their differences, known as residuals. In interplanetary orbit determination, Doppler observables, obtained by measuring the average frequency shift of the received carrier signal over a certain count time, are compared against their predicted values, usually computed by differencing two round-trip light times. This formulation is known to be sensitive to roundoff errors, caused by the use of finite arithmetic in the computation, giving rise to an additional noise in the residuals called numerical noise, which degrades the accuracy of the orbit determination solution. This paper presents a mathematical model for the expected numerical errors in two- and three-way Doppler observables computed using the differenced light-time formulation. The model was validated by comparing its predicti...