Giacomo Tommei

Innovative methods of correlation and orbit determination for space debris

We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm, based upon the admissible region, that is the set of the unknown quantities corresponding to possible orbits for a given observation for objects in Earth orbit (as opposed to both interplanetary orbits and ballistic ones). A similar method has already been successfully used in recent years for the asteroidal case. The second algorithm uses the integrals of the geocentric 2-body motion, which must have the same values at the times of the different observations for a common orbit to exist. We also discuss how to account for the perturbations of the 2-body motion, e.g., the J2 effect.

Correlation and orbit determination of space objects based on sparse optical data

While building up a catalog of Earth orbiting objects, if the available optical observations are sparse, not deliberate follow ups of specific objects, no orbit determination is possible without previous correlation of observations obtained at different times. This correlation step is the most computationally intensive, and becomes more and more difficult as the number of objects to be discovered increases. In this paper we tested two different algorithms (and the related prototype software) recently developed to solve the correlation problem for objects in geostationary orbit (GEO), including the accurate orbit determination by full least squares solutions with all six orbital elements. Because of the presence in the GEO region of a significant subpopulation of high area to mass objects, strongly affected by nongravitational perturbations, it was actually necessary to solve also for dynamical parameters describing these effects, that is to fit between 6 and 8 free parameters for each orbit. The validation was based upon a set of real data, acquired from the ESA Space Debris Telescope (ESASDT) at the Teide observatory (Canary Islands). We proved that it is possible to assemble a set of sparse observations into a set of objects with orbits, starting from a sparse time distribution of observations, which would be compatible with a survey capable of covering the region of interest in the sky just once per night. This could result in a significant reduction of the requirements for a future telescope network, with respect to what would have been required with the previously known algorithm for correlation and orbit determination.

Orbit determination of space objects based on sparse optical data

While building up a catalog of Earth orbiting objects, if the available optical observations are sparse, not deliberate follow ups of specific objects, no orbit determination is possible without previous correlation of observations obtained at different times. This correlation step is the most computationally intensive, and becomes more and more difficult as the number of objects to be discovered increases. In this paper we tested two different algorithms (and the related prototype software) recently developed to solve the correlation problem for objects in geostationary orbit (GEO), including the accurate orbit determination by full least squares solutions with all six orbital elements. Because of the presence in the GEO region of a significant subpopulation of high area to mass objects, strongly affected by nongravitational perturbations, it was actually necessary to solve also for dynamical parameters describing these effects, that is to fit between 6 and 8 free parameters for each orbit. The validation was based upon a set of real data, acquired from the ESA Space Debris Telescope (ESASDT) at the Teide observatory (Canary Islands). We proved that it is possible to assemble a set of sparse observations into a set of objects with orbits, starting from a sparse time distribution of observations, which would be compatible with a survey capable of covering the region of interest in the sky just once per night. This could result in a significant reduction of the requirements for a future telescope network, with respect to what would have been required with the previously known algorithm for correlation and orbit determination.

Light-time computations for the BepiColombo Radio Science Experiment

The Radio Science Experiment is one of the on board experiments of the Mercury ESA mission BepiColombo that will be launched in 2014. The goals of the experiment are to determine the gravity field of Mercury and its rotation state, to determine the orbit of Mercury, to constrain the possible theories of gravitation (for example by determining the post-Newtonian parameters), to provide the spacecraft position for geodesy experiments and to contribute to planetary ephemerides improvement. This is possible thanks to a new technology which allows to reach great accuracies in the observables range and range rate; it is well known that a similar level of accuracy requires studying a suitable model taking into account numerous relativistic effects. In this paper we deal with the modelling of the space-time coordinate transformations needed for the light-time computations and the numerical methods adopted to avoid rounding-off errors in such computations.

On the Juno radio science experiment: models, algorithms and sensitivity analysis

Juno is a NASA mission launched in 2011 with the goal of studying Jupiter. The probe will arrive to the planet in 2016 and will be placed for one year in a polar high-eccentric orbit to study the composition of the planet, the gravity and the magnetic field. The Italian Space Agency (ASI) provided the radio science instrument KaT (Ka-Band Translator) used for the gravity experiment, which has the goal of studying the Jupiters deep structure by mapping the planets gravity: such instrument takes advantage of synergies with a similar tool in development for BepiColombo, the ESA cornerstone mission to Mercury. The Celestial Mechanics Group of the University of Pisa, being part of the Juno Italian team, is developing an orbit determination and parameters estimation software for processing the real data independently from NASA software ODP. This paper has a twofold goal: first, to tell about the development of this software highlighting the models used, second, to perform a sensitivity analysis on the parameters of interest to the mission.

Relativistic models for the BepiColombo radioscience experiment

To test General Relativity with the tracking data of the BepiColombo Mercury orbiter we need relativistic models for the orbits of Mercury and of the Earth, for the light-time and for all the spatio-temporal reference frames involved, with accuracy corresponding to the measurements: 10 cm in range, 2 micron/s in range-rate, over 2 years. For the dynamics we start from the Lagrangian post-Newtonian (PN) formulation, using a relativistic equation for the solar system barycenter to avoid rank deficiency. In the determination of the PN parameters, the difficulty in disentangling the effects of β from the ones of the Sun’s oblateness is confirmed. We have found a consistent formulation for the preferred frame effects, although the center of mass is not an integral. For the identification of strong equivalence principle (SEP) violations we use a formulation containing both direct and indirect effects (through the modified position of the Sun in a barycentric frame). In the light-time equations, the Shapiro effect is modeled to PN order 1 but with an order 2 correction compatible with (Moyer 2003). The 1.5-PN order corrections containing the Sun’s velocity are not relevant at the required level of accuracy. To model the orbit of the probe, we use a mercury-centric reference frame with its own “Mercury Dynamic Time”: this is the largest and the only relativistic correction required, taking into account the major uncertainties introduced by non-gravitational perturbations. A delicate issue is the compatibility of our solution with the ephemerides for the other planets, and for the Moon, which cannot be improved by the BepiColombo data alone. Conversely, we plan to later export the BepiColombo measurements, as normal points, to contribute with their unprecedented accuracy to the global improvement of the planetary ephemerides.

Desaturation manoeuvres and precise orbit determination for the BepiColombo mission

This work analyses the consequences that the desaturation manoeuvres can have on the precise orbit determination corresponding to the Mercury Orbiter Radioscience Experiment (MORE) of the BepiColombo mission to Mercury. This is an ESA/JAXAjoint project with challenging objectives regarding geodesy, geophysics and fundamental physics. We will show how these manoeuvres affect the orbit of the s/c and the radio science measurements and how to include them in the orbit determination and parameter estimation procedure. The non-linear least-squares fit is applied on a set of observational arcs separated by intervals of time where the probe is not visible. With the current baseline of two ground stations, two manoeuvres are performed per day, one during the observing session and the other in the dark. To reach the scientific goals of the mission, they have to be treated as ‘solve for quantities’. We developed a specific methodology based on the deterministic propagation of the orbit, which is able to deal with these variables, by connecting subsequent observational arcs in a smooth way. The numerical simulations demonstrate that this constrained multi-arc strategy is able to determine all the manoeuvres together with the other parameters of interest at a high level of accuracy.

Constraining the Nordtvedt parameter with the BepiColombo Radioscience experiment

BepiColombo is a joint ESA/JAXA mission to Mercury with challenging objectives regarding geophysics, geodesy, and fundamental physics. The Mercury Orbiter Radioscience Experiment (MORE) is one of the on-board experiments, including three different but linked experiments: gravimetry, rotation, and relativity. The aim of the relativity experiment is the measurement of the post-Newtonian parameters. Thanks to accurate tracking between Earth and spacecraft, the results are expected to be very precise. However, the outcomes of the experiment strictly depend on our “knowledge” about solar system: ephemerides; number of bodies (planets, satellites, and asteroids); and their masses. In this paper we describe a semianalytic model used to perform a covariance analysis to quantify the effects on the relativity experiment, due to the uncertainties of Solar System bodies’ parameters. In particular, our attention is focused on the Nordtvedt parameter η used to parametrize the strong equivalence principle violation. After our analysis we estimated σ½η� ⪅ 4.5 × 10 −5 , which is about 1 order of magnitude larger than the “ideal” case where masses of planets and asteroids have no errors. The current value, obtained from ground-based experiments and lunar laser ranging measurements, is σ½η� ≈ 4.4 × 10 −4 . Therefore, we conclude that, even in the presence of uncertainties on Solar System parameters, the measurement of η by MORE can improve the current precision of about 1 order of magnitude.

Addressing some critical aspects of the BepiColombo MORE relativity experiment

The Mercury Orbiter Radio science Experiment (MORE) is one of the experiments on-board the ESA/JAXA BepiColombo mission to Mercury, to be launched in October 2018. Thanks to full on-board and on-ground instrumentation performing very precise tracking from the Earth, MORE will have the chance to determine with very high accuracy the Mercury-centric orbit of the spacecraft and the heliocentric orbit of Mercury. This will allow to undertake an accurate test of relativistic theories of gravitation (relativity experiment), which consists in improving the knowledge of some post-Newtonian and related parameters, whose value is predicted by General Relativity. This paper focuses on two critical aspects of the BepiColombo relativity experiment. First of all, we address the delicate issue of determining the orbits of Mercury and the Earth–Moon barycenter at the level of accuracy required by the purposes of the experiment and we discuss a strategy to cure the rank deficiencies that appear in the problem. Secondly, we introduce and discuss the role of the Solar Lense–Thirring effect in the Mercury orbit determination problem and in the relativistic parameters estimation.

Short arc orbit determination and imminent impactors in the Gaia era

Short-arc orbit determination is crucial when an asteroid is first discovered. In these cases usually the observations are so few that the differential correction procedure may not converge. We have developed an initial orbit computation method, based on the systematic ranging, an orbit determination techniques which systematically explores a raster in the topocentric range and range-rate space region inside the admissible region. We obtain a fully rigorous computation of the probability for the asteroid that could impact the Earth within few days from the discovery, without any a priori assumption. We test our method on the two past impactors 2008 TC3 and 2014 AA, on some very well known cases, and on two particular objects observed by the ESA Gaia mission.