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 Jupiter's deep structure by mapping the planet's 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.Comment: Accepted for publication in MONTHLY NOTICES of the Royal Astronomical Society 2014 October 31. Received 2014 July 28; in original form 2013 October

Superfici algebriche rigate con massimo numero di nodi

In questa tesi mi propongo di studiare le superfici algebriche nodali rigate non razionali che abbiano il numero massimo di nodi. Il lavoro si articola in tre capitoli. Nel primo, si discute il problema della risoluzione delle superfici normali insieme a quello della contrazione delle curve nodali e, in base a questi risultati, si da la definizione di nodo. Il secondo capitolo serve a preparare il terreno per affrontare il problema centrale: si descrive il codice associato a una famiglia di curve nodali di una superficie liscia e, nel caso di una superficie rigata non razionale, si determina il rivestimento associato a questo codice. Infine, nel terzo ed ultimo capitolo, si risolve il problema centrale del lavoro, determinando il massimo numero di nodi che può avere una superficie nodale rigata non razionale e caratterizzando le superfici nodali rigate non razionali con massimo numero di nodi

Chaotic quasi-collision trajectories in the 3-centre problem

We study a particular kind of chaotic dynamics for the planar 3-centre problem on small negative energy level sets. We know that chaotic motions exist, if we make the assumption that one of the centres is far away from the other two (see Bolotin and Negrini, J. Diff. Eq. 190 (2003), 539--558): this result has been obtained by the use of the Poincar\'e-Melnikov theory. Here we change the assumption on the third centre: we do not make any hypothesis on its position, and we obtain a perturbation of the 2-centre problem by assuming its intensity to be very small. Then, for a dense subset of possible positions of the perturbing centre on the real plane, we prove the existence of uniformly hyperbolic invariant sets of periodic and chaotic almost collision orbits by the use of a general result of Bolotin and MacKay (see Cel. Mech. & Dyn. Astr. 77 (2000), 49--75). To apply it, we must preliminarily construct chains of collision arcs in a proper way. We succeed in doing that by the classical regularisation of the 2-centre problem and the use of the periodic orbits of the regularised problem passing through the third centre.Comment: 22 pages, 6 figure

The Impact Trajectory of Asteroid 2008 TC3

Asteroid 2008 TC3 was the rst asteroid ever discovered before reaching Earth. By using the almost 900 astrometric observations acquired prior to impact we estimate the trajectory of 2008 TC3 and the ground-track of the impact location as a function of altitude. For a reference altitude of 100 km the impact location 3- formal uncertainty is a 1.4 km 0.15 km ellipse with a semimajor axis azimuth of 105. We analyze the contribution of modeling errors and nd that the second-order zonal harmonics of the Earth gravity eld moves the ground-track by more than 1 km and the location along the ground-track by more than 2 km. Non-zonal and higher order harmonics only change the impact prediction by less than 20 m. The contribution of the atmospheric drag to the trajectory of 2008 TC3 is at the numerical integration error level, a few meters, down to an altitude of 50 km. Integrating forward to lower altitudes and ignoring the break-up of 2008 TC3, the atmospheric drag causes an along-track error that can be as large as a few kilometers at sea level. The locations of the recovered meteorites is consistent with the computed ground-track

Gravimetry, rotation and angular momentum of Jupiter from the Juno Radio Science experiment

Juno is a NASA space mission to Jupiter, arriving at the planet in July 2016. Through accurate Doppler tracking in X and Ka-band, the Radio Science experiment will allow to map Jupiter's gravity field, crucial for the study of the interior structure of the planet. In this paper we describe the results of numerical simulations of this experiment, performed with the ORBIT14 orbit determination software, developed by the Department of Mathematics of the University of Pisa and by the spin-off Space Dynamics Services srl. Our analysis included the determination of Jupiter's gravity field, the Love numbers, the direction of the rotation axis and the angular momentum magnitude, the latter by measuring the Lense-Thirring effect on the spacecraft. As far as the gravity field is concerned, the spherical harmonics coefficients of Jupiter's gravitational potential are highly correlated and the accuracy in the determination of the zonal coefficients of degree ℓ is degraded for ℓ>15ℓ>15. We explore the possibility of using a local model, introducing ring-shaped mascons, so as to determine the gravity field of the portion of the spherical surface bounded by latitudes 6°N and 35°N, the latitude belt observed during Juno's pericenter passes. Finally, the determination of Jupiter's angular momentum magnitude turned out to be compromised by the impossibility of separating the effects of the Lense-Thirring acceleration and of a change in Jupiter's rotation axis direction

End-of-life disposal trajectories for libration point and highly elliptical orbit missions

Libration Point Orbits (LPOs) and Highly EllipticalOrbits (HEOs) are often selected for astrophysics and solar terrestrial missions as they offer vantage points for the observation of the Earth, the Sun and the Universe. Orbits around L1and L2 are relatively inexpensive to be reached from the Earth and ensure a nearly constant geometry for observation and telecoms, in addition to advantages for thermal system design. On the other hand, HEOs about the Earth guarantee long dwelling times at an altitude outside the Earth’s radiation belt; therefore, long periods of uninterrupted scientific observation are possible with nearly no background noise from radiations. No guidelines currently exist for LPO and HEO missions’ end-of-life; however, as current and future missions are planned to be placed on these orbits, it is a critical aspect to clear these regions at the end of operations. Orbits about the Libration point or Earth-centred orbits with very high apogee lie in a highly perturbed environment due to the chaotic behaviour of the multi-body dynamics1; moreover, due to their challenging mission requirements, they are characterised by large-size spacecraft. Therefore, the uncontrolled s/c on manifold trajectories could re-enter to Earth or cross the protected regions. Finally, the end-of-life phase can enhance the science return of the mission and the operational knowledge base. In this paper, a detailed analysis of possible disposal strategies for LPO and HEO missions is presented as a result of an ESA/GSP study. End-of-life disposal options are proposed, which exploit the multi-body dynamics in the Earth environment and in the Sun–Earth system perturbed by the effects of solar radiation, the Earth potential and atmospheric drag. The options analysed are Earth re-entry, or injection into a graveyard orbit for HEOs, while spacecraft on LPOs can be disposed through an Earth re-entry, or can be injected onto trajectories towards a Moon impact, or towards the inner or the outer solar system, by means of delta-v manoeuvres or the enhancement of solar radiation pressure with some deployable light reflective surfaces. On the base of the operational cost, complexity and demanding delta-v manoeuvres, some disposal options were preliminary analysed and later discarded such as the HEO disposal through transfer to a LPO or disposal through Moon capture 2. The paper presents the dynamical models considered for each disposal design: in the case of HEOs the long term variation of the orbit is propagated through semi-analytical techniques 2, considering the interaction of the luni/solar perturbations with the zonal harmonics of the Earth’s gravity field. In the case of LPOs the Circular Restricted Three Body Problem 4 (CR3BP) or the full-body dynamics is employed for the Earth re-entry option and the transfer towards the inner or the outer solar system, while the coupled restricted three-body problem 5 is used for the Moon disposal option. The approach to design the transfer trajectories is presented. In order to perform a parametric study, different starting dates and conditions for the disposal are considered, while the manoeuvre is optimised considering the constraints on the available fuel at the end-of-life. Five ESA missions are selected as scenarios: Herschel, GAIA, SOHO as LPOs, and INTEGRAL and XMM-Newton as HEOs. For each mission the disposal strategies are analysed, in terms of optimal window for the disposal manoeuvre, manoeuvre sequences, time of flight and disposal characteristics, such as re-entry conditions or the hyperbolic excess velocity at arrival in case of a Moon impact. In a second step, a high accuracy approach is used for validating the optimised trajectories. Finally, a trade-off is made considering technical feasibility (in terms of the available on-board resources and ∆vrequirements), as well as the sustainability context and the collision probability in the protected regions. General recommendations will be drawn in terms of system requirements and mission planning

End-of-life disposal trajectories for libration point and highly elliptical orbit missions

In this paper a preliminary analysis of the possible disposal strategies for Lagrange Point Orbits (LPO) and Highly Elliptical Obits (HEO) is presented. Five ESA missions currently (or in the future) operating on LPO and HEO are selected, namely, Hershel, GAIA, SOHO as LPO, and Integral and XMM-Newton as HEO. LPO disposal options comprehend disposal through Earth re-entry, disposal towards the Moon, disposal towards the Sun or a planet; while for HEO disposal the proposed options are end-of-life disposal through Moon capture, disposal through Earth re-entry or graveyard orbit, or LPO targeting from HEO. For each strategy the design methodology is presented and results are shown in terms of Av requirements and disposal parameters. ©2013 by the International Astronautical Federation. All rights reserved