Gravity gradiometers for planetary geodesy: requirements and concept for a space instrument

The measurement of the gravitational field of Solar System bodies is becoming ever and ever crucial in the physical description of their composition, state and evolution. Indeed, many planetary processes at large scale are ruled by their internal structure, where surface and tectonic features are mainly the result of heat exchanges from the interior to the surface. Gravity field measurements are one of the observational methods to investigate those processes and to place constraints on the structure of the planetary interiors and on the formation and geologic evolution of a planet. The retrieval of the spherical harmonic coefficients used to describe the gravitational field of a body gives insights into e.g. its polar oblateness, moment of inertia and deviations from hydrostatic equilibrium. With geologic assumptions and other remote sensing data, significant geophysical parameters, related e.g. to crust and mantle density and thickness, core size and structure, mantle/core coupling can be obtained. These parameters are used in planetary models to address topics such as planets differentiation, thermal evolution, characteristics and composition of the interiors. Moreover, the internal structure can be further investigated (wherever possible) through seismometers on the surface, exploiting the analysis of seismic waves travelling through the interior (as performed by Apollo missions EASEP and ALSEP packages and currently by Mars Insight). Until now, the Radio-Tracking technique (RT), part of the Radio Science (RS) observations, jointly with POD (Precise Orbit Determination), has been de-facto the main technique for gathering this type of information. It has been implemented in several deep-space missions, such as Magellan (Venus), MRO (Mars), Cassini (Saturn), Messenger (Mercury), Juno (Jupiter), and, in the forthcoming future, BepiColombo (Mercury) and JUICE (Jupiter and its moons). Concerning scientific targets of interest, it needs to be highlighted that gravity field models are available (section 2), besides the Earth and the Moon, just for few planetary bodies such as the terrestrial planets Mercury, Venus and Mars. However, often such models are restricted only to large spatial resolutions, about one or more hundreds of kilometers, not enough to understand the geophysical processes that have driven formation and evolution of those bodies. The accuracy of these models is good enough as well but just for the lower part of the gravity field spectra, where a sufficient signal-to-noise ratio is achieved. Moreover, there is much more lack of data for the external planets, where only few gravity field parameters have been derived for some of the gaseous planets and their main moons. Any improvement on those targets, with a special attention to Venus, Mars and Galilean moons, would be very helpful in understanding their interior and the geophysical and geological processes that operated on them. To answer the need for higher space resolution and accuracy in planetary gravity fields, two different approaches can be pursued: 1. to improve the measurement performance of the instrumentation used for RS; in these experiments the gravity field to be studied is inferred by the orbit of a spacecraft (that can be considered a ‘proof mass’ falling in the overall external gravity field) and an accelerometer is used to measure the Non-Gravitational Perturbations (NGP) perturbing the spacecraft free-fall, i.e. its motion from a pure (in principle) geodesic of space-time. An improvement of the accelerometer performance and its integration within an enhanced tracking system used to measure the spacecraft position and velocity, are needed conditions to improve the performance of gravity field reconstruction. 2. to introduce innovative measurement concepts, allowing to overcome some of the bottlenecks of the current methods (non-continuous monitoring, field attenuation with the altitude, disturbances mitigation, etc. In a roadmap definition, one of the more promising is the gravity gradiometry technique, which would allow to directly sense the gravity field by measuring the gravity gradients, and not just indirectly, as for RT, through monitoring the spacecraft gravitational perturbations. Unlike the radio-tracking, spacebased gravity gradiometry has still to unfold its potentialities; indeed, the ESA’s GOCE mission is the first and unique till now that has flown a gravity gradiometer to explore Earth’s gravity in 2009-13. The planetary gradiometry still awaits achievements outside the Earth System. Satellite gradiometry refers to the measurement of acceleration differences, ideally in all three spatial directions, between the test-masses of an ensemble of accelerometers inside one satellite. The differentiation of gravity accelerations allows to highlight small-scale surface and sub-surface features, making such a technique, differently wrt RT, inherently sensitive to medium and large degrees (i.e. high resolutions) of the spherical harmonic representation of the gravity field. Therefore, the use of gradiometry would allow to improve the gravity field knowledge by measuring medium and large degrees, filling the gap above depicted and fostering the investigation on the structure and evolution of the planets. The activity of this PhD Thesis starts from the definition of the planetary gravity field state of the art and the identification of the needs of the scientific community to improve the planetary bodies knowledge. Based on this result, a selection of targets of interest will be operated. A review of the gravity field measurement techniques will be carried out, identifying advantages and drawbacks, pointing out innovative techniques such as gradiometry. On the basis of these activities, a series of numerical simulations will be implemented to produce the time series of gradiometric signals foreseen in a set of case studies. The choice of the case studies will be based on the preliminary studies about the science needs. The main outcome will be a set of requirements to be matched by a typical gradiometric instrument/mission, aiming at fulfilling the scientific needs. An important requirement would be, for instance, the typical instrument sensitivity and spectral band, as well as the expected acceleration or gravity gradient amplitude of a signal sensed with a reasonable signal-tonoise ratio. Different scenarios will be simulated on the basis of the science needs. In chapter 2 the gravity field is faced from the theoretical point of view and a snapshot of the current understanding of gravity field of planetary bodies is carried out. At last, science needs are identified and planetary bodies of interest are selected. In chapter 3 measurement techniques of the gravity field are described, focusing the attention on the gravitational gradiometry. Advantages and drawbacks are considered. Moreover, spaceborne, airborne and groundborne gradiometric instruments have been identified and analysed to identify the current state of the art. In chapter 4 gravity mission needs are identified in terms of science and mission requirements. Afterwards, a matlab code developed to compute the gravity gradient signal expected in some case studies is described and evaluated. At last, analysis of ways to increase the sensitivity of gradiometers is carried out. In chapter 5, based on analysis of previous chapters, an instrument concept is introduced and analysed to match the requirements identified. The basic performance are derived, discussed and compared to the signal that is expected to be measured according to the computation carried out with the matlab code. Future work foresees to further develop the concept and to further deep the analysis of the identified gradiometer configurations.