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The Juno spacecraft reached the mid‐point of its nominal mission in December 2018, after completing 17 perijove passes. Ten of these were dedicated to the determination of the gravity field of the planet, with the aim of constraining its interior structure. We provide an update on Jupiter's gravity field, its tidal response and spin axis motion over time. The analysis of the Doppler data collected during the perijove passes hints to a non‐static and/or non‐axially symmetric field, possibly related to several different physical mechanisms, such as normal modes or localized atmospheric or deeply‐rooted dynamics.

International audience; Jupiter’s atmosphere is rotating differentially, with zones and belts rotating at speeds that differ by up to 100 metres per second. Whether this is also true of the gas giant’s interior has been unknown1,2, limiting our ability to probe the structure and composition of the planet3,4. The discovery by the Juno spacecraft that Jupiter’s gravity field is north–south asymmetric5 and the determination of its non-zero odd gravitational harmonics J3, J5, J7 and J9 demonstrates that the observed zonal cloud flow must persist to a depth of about 3,000 kilometres from the cloud tops6. Here we report an analysis of Jupiter’s even gravitational harmonics J4, J6, J8 and J10 as observed by Juno5 and compared to the predictions of interior models. We find that the deep interior of the planet rotates nearly as a rigid body, with differential rotation decreasing by at least an order of magnitude compared to the atmosphere. Moreover, we find that the atmospheric zonal flow extends to more than 2,000 kilometres and to less than 3,500 kilometres, making it fully consistent with the constraints obtained independently from the odd gravitational harmonics. This depth corresponds to the point at which the electric conductivity becomes large and magnetic drag should suppress differential rotation7. Given that electric conductivity is dependent on planetary mass, we expect the outer, differentially rotating region to be at least three times deeper in Saturn and to be shallower in massive giant planets and brown dwarfs.

The International Astronomical Union (IAU) defines planet and satellite coordinate systems relative to their axis of rotation and the angle about that axis. The rotational elements of the bodies are the right ascension and declination of the rotation axis in the International Celestial Reference Frame and the rotation angle, W, measured easterly along the body's equator. The IAU specifies the location of the body's prime meridian by providing a value for W at epoch J2000. We provide new trigonometric series representations of the rotational elements of Mars and its satellites, Phobos and Deimos. The series for Mars are from a least squares fit to the rotation model used to orient the Martian gravity field. The series for the satellites are from a least squares fit to rotation models developed in accordance with IAU conventions from recent ephemerides.

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.

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 J_(2n) that are approximately proportional to q^n, 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, J_3, J_5, J_7, J_9 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.

In-spiraling supermassive black holes should emit gravitational waves, which would produce characteristic distortions in the time of arrival residuals from millisecond pulsars. Multiple national and regional consortia have constructed pulsar timing arrays by precise timing of different sets of millisecond pulsars. An essential aspect of precision timing is the transfer of the times of arrival to a (quasi-)inertial frame, conventionally the solar system barycenter. The barycenter is determined from the knowledge of the planetary masses and orbits, which has been refined over the past 50 years by multiple spacecraft. Within the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), uncertainties on the solar system barycenter are emerging as an important element of the NANOGrav noise budget. We describe what is known about the solar system barycenter, touch upon how uncertainties in it affect gravitational wave studies with pulsar timing arrays, and consider future trends in spacecraft navigation., Comment: Four pages, 3 figures; to appear in the proceedings of IAU Symposium 337: Pulsar Astrophysics - The Next 50 Years, eds. P. Weltevrede, B. B. P. Perera, L. Levin Preston & S. Sanidas; see also http://ssd.jpl.nasa.gov/ and arXiv:1801.02617

The modified Newtonian dynamics (MOND) is an attempt to modify the gravitation theory to solve the dark matter problem. This phenomenology is very successful at the galactic level. The main effect produced by MOND in the Solar System is called the external field effect parametrized by the parameter ${Q}_{2}$. We have used nine years of Cassini range and Doppler measurements to constrain ${Q}_{2}$. Our estimate of this parameter based on Cassini data is given by ${Q}_{2}=(3\ifmmode\pm\else\textpm\fi{}3)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}27}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}2}$, which shows no deviation from General Relativity and excludes a large part of the relativistic MOND theories. This limit can also be interpreted as a limit on an external tidal potential acting on the Solar System coming from the internal mass of our Galaxy (including dark matter) or from a new hypothetical body.

The radio signal from the Galileo probe to the orbiter experienced attenuation due to ammonia in Jupiter's atmosphere during the probe descent. A profile of the ammonia content as a function of depth in the atmosphere has been derived from the measurements of the attenuation. The derived ammonia abundance rises to a molar fraction of 700±100 parts per million for pressures greater than 7 bars, about 4 times that expected based on the solar abundance of nitrogen.

The method for measuring changes in the lengths of the three arms for the LISA gravitational-wave detector is described. Accurate phase measurements are required on signals with Doppler shifts of about 1 MHz for the two main arms of the interferometer, and up to 15 MHz for the third arm. This is accomplished by shifting the signal frequencies down to near 100 kHz, filtering and then timing zero crossings of the signals. The basic methods for correcting for the laser phase noise and for phase noise in the ultra-stable oscillators used to derive various radio frequencies are described briefly. The corrections are made on the spacecraft, before the data are telemetred to the ground.

High‐precision pulsar timing relies on a solar system ephemeris in order to convert times of arrival (TOAs) of pulses measured at an observatory to the solar system barycenter. Any error in the conversion to the barycentric TOAs leads to a systematic variation in the observed timing residuals; specifically, an incorrect planetary mass leads to a predominantly sinusoidal variation having a period and phase associated with the planet’s orbital motion about the Sun. By using an array of pulsars (PSRs J0437−4715, J1744−1134, J1857+0943, J1909−3744), the masses of the planetary systems from Mercury to Saturn have been determined. These masses are consistent with the best‐known masses determined by spacecraft observations, with the mass of the Jovian system, 9.547921(2)×10−4M⊙, being significantly more accurate than the mass determined from the Pioneer and Voyager spacecraft, and consistent with but less accurate than the value from the Galileo spacecraft. While spacecraft are likely to produce the most accurat...

The largest uncertainty in the ephemerides for the inner planets is in the orientation of the dynamical system to the celestial reference frame. A program of VLBI measurements of spacecraft in orbit about Venus and Mars has been performed to reduce the orientation uncertainty to 0.2 milliarcseconds.

The proposed Laser Interferometer Space Antenna (LISA) is designed to observe gravitational radiation from galactic binaries and massive black holes in other galaxies. LISA will observe waves in the frequency range 0.1 mHz to 1 Hz, which can never be observed on Earth due to background noise. The three LISA spacecraft will be located at the vertices of an equilateral triangle with side length 5 million km. The orbits are chosen so that the triangle formation trails the Earth by 20 degrees. Each spacecraft will contain two independent instruments containing a proof mass, laser and 30 cm diameter telescope for the transmission and reception of laser signals. Two independent Michelson interferometers will be formed, allowing both polarizations of gravitational waves to be detected. The observed signals will yield unique information about the formation of massive black holes and the nature of gravity in the high-field limit.

The effectualness of post-Newtonian wave forms and recently proposed P-approximants in extracting gravitational waves from inspiralling binaries of supermassive black holes is explored. Based on the extent of the overlaps of these approximate wave forms with the exact ones, we conclude that P-approximants are essential to reliably measure the parameters of supermassive binaries. The wave form from such a source depends on several parameters: The masses of the component bodies, their spins, eccentricity of the orbit, angles describing the orientation of the binary relative to the LISA detector, direction to the source, etc. Making a choice of search templates in such a multi-dimensional parameter space could be pretty complicated. We suggest a method based on the principal component analysis which could potentially simplify the search to a great extent by enabling us to choose templates in a parameter space of much smaller dimension than the physical parameter space.

Orbit determination results are presented for Magellan and Pioneer 12 utilizing same-beam interferometer (SBI) data, which is a new data type for planetary orbiter navigation. The orbit determination data employing this data type, based on orbit-to-orbit consistency, has been explained in terms of nominal error models. Results show the orbit determination accuracy for Pioneer 12 using Doppler plus SBI data to be better than the accuracy utilizing only Doppler data by 30 percent.

The potential for earth-based radiometric observations of a network of Mars surface landers to provide accurate determination of the Mars rotational orientation in inertial space is investigated. An error budget is presented for the carrier phase data type and related to system requirements for the surface landers. Differencing the carrier phase observations for a pair of Mars landers can provide extremely high precision due to common-mode error cancellation. Results of a covariance analysis are presented which show that Mars orientation can be determined to better than 10 milliarcsec, corresponding to decimeter distances at the planet surface. Recommendations on how to incorporate these concepts into future Mars missions, such as the Mars Environmental Survey, are discussed.

The instrumentation of a low‐temperature three‐mode gravitationa1 radiation antenna incorporating a low‐noise dc SQUID provided by IBM is described. The feedback circuitry necessary to maintain the linearity and dynamic range of the SQUID was found to drive the resonant system due to high coupling between the input coil and the feedback coil of the SQUID. In order for this type of planar thin‐film dc SQUID to be useful for gravitational radiation detectors and other applications requiring high Q input circuits, a solution to this feedback problem is needed. To this end, the nonlinear equations describing the dc SQUID with linear feedback are solved in terms of an isolated SQUID. The important feedback parameters for a high Q resonant system are found to be the slew rate of the electronics and the coupling constant ratio α2if/α2f, where α2if is the energy coupling efficiency between the feedback coil and input coil and α2f is the energy coupling efficiency between the feedback coil and the SQUID loop. Meth...

A vacuum heat treatment facility, with hot zone dimensions of 12 x 19 x 19 cm, has been designed and constructed at a cost substantially below that of a commercial unit. The design incorporates efficient water cooling and a resistive heating element. A vacuum pressure of 1.5 x 10 to the -8th torr at room temperature has been obtained after baking. The temperature limit is approximately 1900 C. This limit results from the choice of niobium as the hot zone material.

The mechanical and electrical quality factors of a 10-g niobium resonator were measured at 4.4 K and were found to be 8.1 x 10 to the 6th, and 3.8 x 10 to the 6th, respectively. The value for the electrical quality factor is high enough for a system operating at 50 mK at a sensitivity level of one phonon. The resonator's low damping properties make it suitable for use as a transducer for a cryogenic three-mode gravitational radiation detector. A practical design is given for the mounting of the resonator on a 2400-kg aluminum-bar detector. Projections are made for the sensitivity of a 2400-kg bar instrumented as a three-mode system with this resonator inductively coupled to a SQUID.