Abstract

Fast and precise propagation of satellite orbits is required for mission design, orbit determination and payload data analysis. We present a method to improve the computational performance of numerical propagators and simultaneously maintain the accuracy level required by any particular application. This is achieved by determining the positional accuracy needed and the corresponding acceptable error in acceleration on the basis of the mission requirements, removing those perturbation forces whose effect is negligible compared to the accuracy requirement, implementing an efficient and precise algorithm for the harmonic synthesis of the geopotential gradient (i.e., the gravitational acceleration) and adjusting the tolerance of the numerical propagator to achieve the prescribed accuracy level with minimum cost. In particular, to achieve the optimum balance between accuracy and computational performance, the number of geopotential spherical harmonics to retain is adjusted during the integration on the basis of the accuracy requirement. The contribution of high-order harmonics decays rapidly with altitude, so the minimum expansion degree meeting the target accuracy decreases with height. The optimum degree for each altitude is determined by making the truncation error of the harmonic synthesis equal to the admissible acceleration error. This paper presents a detailed description of the technique and test cases highlighting its accuracy and efficiency.

Abstract

In nominal mission scenarios, geostationary satellites perform end-of-life orbit maneuvers to reach suitable disposal orbits, where they do not interfere with operational satellites. This research investigates the long-term orbit evolution of decommissioned geostationary satellite under the assumption that the disposal maneuver does not occur and the orbit evolves with no control. The dynamical model accounts for all the relevant harmonics of the terrestrial gravity field at the typical altitude of geostationary orbits, as well as solar radiation pressure and third-body perturbations caused by the Moon and the Sun. Orbit propagations are performed using two algorithms based on different equations of motion and numerical integration methods: (i) Gauss planetary equations for modified equinoctial elements with a Runge-Kutta numerical integration scheme based on 8-7th-order Dorman and Prince formulas; (ii) Cartesian state equations of motion in an Earth-fixed frame with a Runge-Kutta Fehlberg 7/8 integration scheme. The numerical results exhibit excellent agreement over integration times of decades. Some well-known phenomena emerge, such as the longitudinal drift due to the resonance between the orbital motion and Earth’s rotation, attributable to the J2 term of the geopotential. In addition, the third-body perturbation due to Sun and Moon causes two major effects: (a) a precession of the orbital plane, and (b) complex longitudinal dynamics. This study proposes an analytical approach for the prediction of the precessional motion and show its agreement with the (more accurate) orbit evolution obtained numerically. Moreover, long-term orbit propagations show that the above mentioned complex longitudinal dynamics persists over time scales of several decades. Frequent and unpredictable migrations toward different longitude regions occur, in contrast with the known effects due only to the perturbative action of J2

Abstract

The Tisserand graph (TG) is a graphical tool commonly employed in the preliminary design of gravity-assisted trajectories. The TG is a two-dimensional map showing essential orbital information regarding the Keplerian orbits resulting from the close passage by one or more  massive bodies, given the magnitude of the hyperbolic excess speed and the minimum allowed pericenter height for each passage. Contours of constant populate the TG. Intersections between contours allow to link consecutive flybys and build sequences of encounters en route to a selected destination. When the number of perturbing bodies is large and many excess velocity levels are considered, the identification of all the possible sequences of encounters through visual inspection of the TG  becomes a laborious task.  Besides, if the sequences are used as input for a numerical code for trajectory design and optimization, an automated examination of the TG is desirable.  This contribution describes an automatic technique to explore the TG and find all the encounter paths. The technique is based on a tree search method, and the intersections between contours are computed using the regula-falsi scheme.  The method is validated through comparisons with solutions available in the open literature. Examples are given of application to interplanetary mission scenarios, including the coupling with a trajectory optimizer.

Abstract

Orbit insertion at Saturn requires a large impulsive manoeuver due to the velocity difference between the spacecraft and the planet. This paper presents a strategy to reduce dramatically the hyperbolic excess speed at Saturn by means of deep-space electric propulsion. The interplanetary trajectory includes a gravity assist at Jupiter, combined with low-thrust maneuvers. The thrust arc from Earth to Jupiter lowers the launch energy requirement, while an ad hoc steering law applied after the Jupiter flyby reduces the hyperbolic excess speed upon arrival at Saturn. This lowers the orbit insertion impulse to the point where capture is possible even with a gravity assist with Titan. The control-law algorithm, the benefits to the mass budget and the main technological aspects are presented and discussed. The simple steering law is compared with a trajectory optimizer to evaluate the quality of the results and possibilities for improvement.

Abstract

An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

Abstract

A new method, based on singular value decomposition and QR factorization, has been developed and applied to the analysis of F-18 flutter flight test data. The method is capable of identifying the frequency and damping of the critical aircraft modes, those responsible for the flutter phenomenon. The procedure relies on the capability of singular value decomposition for the analysis, modeling, and prediction of data series with periodic features and also on its power to identify matrix rank. The analysis of simulated and real flutter flight test data demonstrates the effectiveness, robustness, noise-immunity, and the capability for automation of the method proposed under specific conditions.

Abstract

A technique for the aeroelastic solution of parachute decelerators is presented in this work. The methodology uses empirical aerodynamics, based on a filling-time inflation model and Ludtke’s area law, coupled to two explicit structural solution approaches. A mass-spring-damper technique allows solving the deployment of the system (when the grid is highly distorted) efficiently, and a finite element model is used for the accurate calculation of the structural loads and stresses during parachute opening and steady flight. The coupling strategy is staggered and the models share the same mesh. The methodology is intended for practical calculations of deceleration systems, and provides useful performance and structural data minimizing model complexity and computational cost. The suitability of the proposed technique is assessed by comparisons with reference test drop data.

Abstract

Lambert’s problem is the two-point boundary-value problem resulting from a two-body orbital transfer between two position vectors in a given time. It lies at the very heart of several fundamental astrodynamics and space engineering problems and, as such, it has attracted the interest of scientists over centuries. In this work, we revisit the solution of Lambert’s problem based on Levi-Civita regularization developed by Carles Simó in 1973. We offer an exhaustive derivation of the theory, including proofs of all the results and the formulae employed, and we extend the algorithm to deal with multi-revolution transfers. Then, after investigating a range of initial guess search techniques and testing different numerical methods to approximate the solution, we propose a procedure in which the initial guess is assigned very efficiently by querying a pre-defined interpolating table. Then, in order to achieve both speed and robustness, we combine Newton-Raphson with safety checks to avoid out of boundary deviations to approximate the solution. We validate the method through several tests and applications, and we assess its convergence and performance. The algorithm presents no singularities, converges in all realistic scenarios and its computational cost is comparable with state of the art algorithms.

Abstract

We present and discuss a solution to the growing demand for satellite telecommunication coverage in the high-latitude geographical regions (beyond 55◦N), where the signal from geostationary satellites is limited or unavailable. We focus on the dynamical issues associated to the design, the coverage, the maintenance and the disposal of a set of orbits selected for the purpose. Specifically, we identify a group of highly inclined, moderately eccentric geosynchronous orbits derived from the Tundra orbit (geosynchronous, eccentric and critically inclined). Continuous coverage can be guaranteed by a constellation of three satellites in equally spaced planes and suitably phased. By means of a highprecision model of the terrestrial gravity field and the relevant environmental perturbations, we study the evolution of these orbits. The effects of the different perturbations on the ground track (which is more important for coverage than the orbital elements themselves) are isolated and analyzed. The physical model and the numerical setup are optimized with respect to computing time and accuracy. We show that, in order to maintain the ground track unchanged, the key parameters are the orbital period and the argument of perigee. Furthermore, corrections to the right ascension of the ascending node are needed in order to preserve the relative orientation of the orbital planes. A station-keeping strategy that minimizes propellant consumption is then devised, and comparisons are made between the cost of a solution based on impulsive maneuvers and one with continuous thrust. Finally, the issue of end-of-life disposal is discussed.