Measurement of Jupiter’s asymmetric gravity field

Abstract

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 equator1. 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 atmosphere2,3. 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 papers4,5, provides the vertical profile of the winds and precise constraints for the depth of Jupiter’s dynamical atmosphere.

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Figure 1: Zonal gravity harmonic coefficients J2–J12.
Figure 2: 3σ uncertainty ellipses of J3J5 and J7J9.
Figure 3: Gravity disturbances due to atmospheric dynamics.

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Acknowledgements

This research was carried out at the Sapienza University of Rome, University of Bologna and University of Pisa under the sponsorship of the Italian Space Agency; at the Jet Propulsion Laboratory, California Institute of Technology under a NASA contract; by the Southwest Research Institute under a NASA contract. Support was provided also by the Israeli Space Agency (Y.K. and E.G.) and the Centre National d'Études Spatiales (T.G. and Y.M.). All authors acknowledge support from the Juno Project.

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Authors

Contributions

L.I. and W.M.F. led the experiment and supervised the data analysis. L.I. wrote most of the manuscript. D.D. and M.P. carried out the gravity data analysis. Y.K. and E.G. provided models of the asymmetric and tesseral gravity field. Y.K., E.G., T.G., W.B.H. and D.J.S. carried out consistency checks with interior models and provided theoretical support. D.R.B. planned and supervised the data collection. P.R. designed and coded the orbit determination filter used in this analysis. L.G.C., P.T. and M.Z. provided the media calibrations. J.D.A., A.M., R.P. and D.S. advised on the data analysis. H.C., R.H., J.I.L., Y.M., B.M. and S.W. helped in the definition of the scientific objectives of the measurements. J.E.P.C., S.M.L. and S.J.B. supervised the planning and execution of the gravity experiment.

Corresponding author

Correspondence to L. Iess.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks J. Fortney and N. Nettelmann for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Range-rate residuals.

Two-way range-rate residuals (integrated over 60?s) for the Ka-band perijove passes PJ3 and PJ6 are shown. The root-mean-square value of the residuals is 0.015?mm s−1 for both passes. The measured range rate was obtained from the radio-science open-loop receiver.

Extended Data Figure 2 Frequency stability.

The Allan deviation of relative frequency shift for the Ka-band perijove passes PJ3 and PJ6 is shown. The slopes are roughly consistent with white noise (dashed line).

Extended Data Figure 3 Gravity harmonic signatures.

Range-rate signals from the J3, J5, J7 and J9 gravity harmonics for PJ3 and PJ6 are shown. The smaller signal in PJ6 is due to a less favourable projection of the spacecraft velocity along the Earth–Jupiter line of sight (the angle between Juno’s orbit normal and the line of sight was 19.2° in PJ3 and 15.1° in PJ6). By comparison, the range-rate noise at 60?s is 0.015?mm s−1 in both passes.

Extended Data Figure 4 Io torus effects on the estimation of J3–J5.

Shown are estimation biases on J3 and J5 due to calibration errors of the Io torus path delay variation (cyan dots) in a Monte Carlo (MC) simulation of passes PJ3 and PJ6 of the Juno gravity experiment. The calibration errors are compared to the estimated 3σ uncertainty ellipses of the target solution (black), obtained without the Io torus, and the solutions obtained using only X- (red) and Ka-band (blue) data. The estimation bias on J3 is about 3σ if X-band data are used. Ka-band data or dual-link calibration reduce the bias to less than 1σ.

Extended Data Figure 5 Io torus effects on the estimation of J2J4.

Shown are estimation biases on J2 and J4 from the Monte Carlo simulation, as in Fig. 1. The estimation bias on J2 and J4 is larger than 4σ if X-band data are used, while using Ka-band or plasma-calibrated data reduces it to less than 1σ.

Extended Data Table 1 Characteristics of perijove passes PJ3 and PJ6 used in the gravity solution
Extended Data Table 2 Consider analysis covariances (3σ)

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Iess, L., Folkner, W., Durante, D. et al. Measurement of Jupiter’s asymmetric gravity field. Nature 555, 220–222 (2018). https://doi.org/10.1038/nature25776

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