An Algorithm to Estimate the Power Spectral Density From Allan Deviation.

Complex architectures for wireless communications, digital electronics, and space-based navigation interlink several oscillator-based devices such as clocks, transponders, and synthesizers. Estimators characterizing their stability are critical for addressing the impact of random fluctuations (noise) on the overall system performance. Manufacturers typically specify this as an Allan/Hadamard Variance (AVAR/HVAR) profile in the time domain. However, stochastic processes constituting the noise are more thoroughly described in the frequency domain by the power spectral density function (PSD). Both are second-moment measures of the time series, but it is only possible to translate unambiguously from the PSD to the AVAR/HVAR, not vice versa, except in the case of a single noise type, a rather unrealistic case. This note presents an analytical method to generate an approximated PSD expressed as a set of power-laws defined in specific intervals in the frequency domain, starting from an AVAR/HVAR expressed as a set of power-laws in the time domain. The proposed algorithm is straightforward to implement, applicable to all noise types (and combinations thereof), and can be self-validated by reconstructing the corresponding AVAR/HVAR by direct computation. Coupling with well-established algorithms relying on the PSD for power-law noise generation, the ensuing method encompasses the capability for generating multicolored noise in end-to-end simulations, as demonstrated hereby for NASA's deep space atomic clock. We also report on the limitations of the algorithm and analytical expressions of the continuous version of the algorithm.

Jupiter Science Enabled by ESA's Jupiter Icy Moons Explorer.

ESA's Jupiter Icy Moons Explorer (JUICE) will provide a detailed investigation of the Jovian system in the 2030s, combining a suite of state-of-the-art instruments with an orbital tour tailored to maximise observing opportunities. We review the Jupiter science enabled by the JUICE mission, building on the legacy of discoveries from the Galileo, Cassini, and Juno missions, alongside ground- and space-based observatories. We focus on remote sensing of the climate, meteorology, and chemistry of the atmosphere and auroras from the cloud-forming weather layer, through the upper troposphere, into the stratosphere and ionosphere. The Jupiter orbital tour provides a wealth of opportunities for atmospheric and auroral science: global perspectives with its near-equatorial and inclined phases, sampling all phase angles from dayside to nightside, and investigating phenomena evolving on timescales from minutes to months. The remote sensing payload spans far-UV spectroscopy (50-210 nm), visible imaging (340-1080 nm), visible/near-infrared spectroscopy (0.49-5.56 µm), and sub-millimetre sounding (near 530-625 GHz and 1067-1275 GHz). This is coupled to radio, stellar, and solar occultation opportunities to explore the atmosphere at high vertical resolution; and radio and plasma wave measurements of electric discharges in the Jovian atmosphere and auroras. Cross-disciplinary scientific investigations enable JUICE to explore coupling processes in giant planet atmospheres, to show how the atmosphere is connected to (i) the deep circulation and composition of the hydrogen-dominated interior; and (ii) to the currents and charged particle environments of the external magnetosphere. JUICE will provide a comprehensive characterisation of the atmosphere and auroras of this archetypal giant planet.

Juno spacecraft gravity measurements provide evidence for normal modes of Jupiter.

The Juno spacecraft has been collecting data to shed light on the planet's origin and characterize its interior structure. The onboard gravity science experiment based on X-band and Ka-band dual-frequency Doppler tracking precisely measured Jupiter's zonal gravitational field. Here, we analyze 22 Juno's gravity passes to investigate the gravity field. Our analysis provides evidence of new gravity field features, which perturb its otherwise axially symmetric structure with a time-variable component. We show that normal modes of the planet could explain the anomalous signatures present in the Doppler data better than other alternative explanations, such as localized density anomalies and non-axisymmetric components of the static gravity field. We explain Juno data by p-modes having an amplitude spectrum with a peak radial velocity of 10-50 cm/s at 900-1200 µHz (compatible with ground-based observations) and provide upper bounds on lower frequency f-modes (radial velocity smaller than 1 cm/s). The new Juno results could open the possibility of exploring the interior structure of the gas giants through measurements of the time-variable gravity or with onboard instrumentation devoted to the observation of normal modes, which could drive spacecraft operations of future missions.

The depth of Jupiter's Great Red Spot constrained by Juno gravity overflights.

Jupiter's Great Red Spot (GRS) is the largest atmospheric vortex in the Solar System and has been observed for at least two centuries. It has been unclear how deep the vortex extends beneath its visible cloud tops. We examined the gravity signature of the GRS using data from 12 encounters of the Juno spacecraft with the planet, including two direct overflights of the vortex. Localized density anomalies due to the presence of the GRS caused a shift in the spacecraft line-of-sight velocity. Using two different approaches to infer the GRS depth, which yielded consistent results, we conclude that the GRS is contained within the upper 500 kilometers of Jupiter's atmosphere.

The tides of Titan.

We have detected in Cassini spacecraft data the signature of the periodic tidal stresses within Titan, driven by the eccentricity (e = 0.028) of its 16-day orbit around Saturn. Precise measurements of the acceleration of Cassini during six close flybys between 2006 and 2011 have revealed that Titan responds to the variable tidal field exerted by Saturn with periodic changes of its quadrupole gravity, at about 4% of the static value. Two independent determinations of the corresponding degree-2 Love number yield k(2) = 0.589 ± 0.150 and k(2) = 0.637 ± 0.224 (2σ). Such a large response to the tidal field requires that Titan's interior be deformable over time scales of the orbital period, in a way that is consistent with a global ocean at depth.

Gravity field, shape, and moment of inertia of Titan.

Precise radio tracking of the spacecraft Cassini has provided a determination of Titan's mass and gravity harmonics to degree 3. The quadrupole field is consistent with a hydrostatically relaxed body shaped by tidal and rotational effects. The inferred moment of inertia factor is about 0.34, implying incomplete differentiation, either in the sense of imperfect separation of rock from ice or a core in which a large amount of water remains chemically bound in silicates. The equilibrium figure is a triaxial ellipsoid whose semi-axes a, b, and c differ by 410 meters (a-c) and 103 meters (b-c). The nonhydrostatic geoid height variations (up to 19 meters) are small compared to the observed topographic anomalies of hundreds of meters, suggesting a high degree of compensation appropriate to a body that has warm ice at depth.

Titan's rotation reveals an internal ocean and changing zonal winds.

Cassini radar observations of Saturn's moon Titan over several years show that its rotational period is changing and is different from its orbital period. The present-day rotation period difference from synchronous spin leads to a shift of approximately 0.36 degrees per year in apparent longitude and is consistent with seasonal exchange of angular momentum between the surface and Titan's dense superrotating atmosphere, but only if Titan's crust is decoupled from the core by an internal water ocean like that on Europa.