Paolo Teofilatto

On the Dynamics of Weak Stability Boundary Lunar Transfers

Recent studies demonstrate that lunar and solar gravitational assists can offer a good reduction of total variation of velocity ΔVneeded in lunar transfer trajectories. In particular the spacecraft, crossing regions of unstable equilibrium in the Earth—Moon—Sun system, can be guided by the Sun towards the lunar orbit with the energy needed to be captured ballistically by the Moon. The dynamics of these transfers, called weak stability boundary (WSB) transfers, will be studied here in some detail. The crucial Earth—Moon—Sun configurations allowing such transfers will be defined. The Suns gravitational effect and lunar gravitational capture will be analyzed in terms of variations of the Jacobi ‘constants’ in the Earth—Sun and Earth—Moon systems. Many examples will be presented, supporting the understanding of the dynamical mechanism of WSB transfers and analytical formulas will be obtained in the case of ‘quasi ballistic captures’.

High-Gain S-band Patch Antenna System for Earth-Observation CubeSat Satellites

A novel S-band circularly polarized patch antenna system suited for earth-observing CubeSats is presented. The antenna consists of four rectangular patches properly excited in order to have the maximum gain in the boresight direction and produce circular polarization. The antenna has a compact size, and its geometry and characteristics are compatible with any CubeSat standard structure. A 57-mm-wide square window allows to accommodate imaging system optics in its center leading to a very compact overall system. A prototype of the designed antenna system has been used to validate simulation results that showed a gain of 7.3 dBi. Experimental measurements confirm that the antenna achieves good impedance match at the desired frequency of 2450 MHz, a directivity of 8.3 dBi, and 60° 3-dB beamwidth, in good agreement with the simulation results.

Variable-Time-Domain Neighboring Optimal Guidance, Part 2: Application to Lunar Descent and Soft Landing

In recent years, several countries have shown an increasing interest toward both manned and automatic lunar missions. The development of a safe and reliable guidance algorithm for lunar landing and soft touchdown represents a very relevant issue for establishing a real connection between the Earth and the Moon surface. This paper applies a new, general-purpose neighboring optimal guidance algorithm, proposed in a companion paper and capable of driving a dynamical system along a specified nominal, optimal path, to lunar descent and soft landing. This new closed-loop guidance, termed variable-time-domain neighboring optimal guidance, avoids the usual numerical difficulties related to the occurrence of singularities for the gain matrices, and is exempt from the main drawbacks of similar algorithms proposed in the past. For lunar descent, the nominal trajectory is represented by the minimum-time path departing from the periselenium of a given elliptic orbit and arriving at the Moon with no residual velocity. Perturbations arising from the imperfect knowledge of the propulsive parameters and from errors in the initial conditions are considered. At specified, equally spaced times the state displacements from the nominal flight conditions are evaluated, and the guidance algorithm yields the necessary control corrections. Extensive robustness and Monte Carlo tests are performed, and definitely prove the effectiveness, robustness, and accuracy of the new guidance scheme at hand, also in comparison with the well-established linear tangent steering law.

Long-term effects on lunar orbiter

Abstract The motion of lunar satellites has been intensively studied in the past by interesting semi-analytical methods. However, the poor knowledge of the Moons gravity field makes those results incomplete. Subsequent lunar missions have allowed a more precise determination of the lunar gravity coefficients. Moreover, renewed scientific interest in the Moon has generated several more accurate models for the motion of a lunar orbiter. It is known that many zonal harmonic coefficients of the Moon have the same order of J 2 and must be included in a first-order perturbative theory. Despite of this, some success has been achieved in the study of long-term evolution of a lunar orbiter. In particular, “frozen” orbits have been found, that is orbits whose parameters have almost vanishing long period evolution. That is, these orbits can be regarded as equilibrium configurations of the orbital dynamics, and they are of interest for the general understanding of the free motion of an orbiter as well as reference orbits, taken in order to minimize the costs of a controlled spacecraft. However, stability of these equilibria has also to be checked with respect to other perturbations of the same order, such as the effects due to the Earth and, to a lesser degree, due to the Sun. We show that these perturbations, together with the effects induced by the lunar orbital plane motion, are rather relevant. We develop a picture analogous to the geometric approach to the motion of an Earth satellite under the influence of three poles ( J 2 , Moon and Sun). The presence of more poles of perturbations (due to the other harmonics) makes the picture more complex but similar. Interesting effects on the frozen orbits as well as on the general motion of the pole and eccentricity of a lunar orbiter are found.

Variable---Time---Domain Neighboring Optimal Guidance, Part 1: Algorithm Structure

This paper presents a general purpose neighboring optimal guidance algorithm that is capable of driving a dynamical system along a specified nominal, optimal path. This goal is achieved by minimizing the second differential of the objective function along the perturbed trajectory. This minimization principle leads to deriving all the corrective maneuvers, in the context of a closed-loop guidance scheme. Several time-varying gain matrices, referring to the nominal trajectory, are defined, computed offline, and stored in the onboard computer. Original analytical developments, based on optimal control theory, in conjunction with the use of a normalized time scale, constitute the theoretical foundation for three relevant features: (i) a new, efficient law for the real-time update of the time of flight (the so called time-to-go), (ii) a new termination criterion, and (iii) a new analytical formulation of the sweep method. This new guidance, termed variable–time–domain neighboring optimal guidance, is rather general, avoids the usual numerical difficulties related to the occurrence of singularities for the gain matrices, and is exempt from the main disadvantages of similar algorithms proposed in the past. For these reasons, the variable–time–domain neighboring optimal guidance has all the ingredients for being successfully applied to problems of practical interest.

Use of weak stability boundary trajectories for planetary capture

The consideration of transfers to the Weak Stability Boundary region represents one of the most advanced concepts when trying to reduce the propellant requirements to obtain an interplanetary goal. Deimos Space, under ESA contract, has developed a tool to simulate such transfers to inner planets, giant planets and natural moons of giant planets. The method is based on a three-step approach consisting on: selection of strategy, generation of initial solutions and numerical optimisation. The feasibility of building WSB transfer trajectories to Mercury, Venus and Mars has been proven. Instead of ∆V saving, the greatest advantage results from the increased flexibility in the selection of the final orbit with no ∆V penalty in most cases. The use of the Sun/Planet WSB region for the problem of giant planets capture does not introduce significant profit since the penalty in transfer time makes the mission unrealistic. Feasible missions to Jupiter and Saturn are obtained when using a double flyby strategy in Ganymede and Titan respectively. The capture by a natural moon of a giant planet incorporates a phase of energy reduction by moon flybys using resonant orbits linking at the end with the WSB region of the moon to achieve a ballistic capture.

Satellite constellations for continuous and early warning observation : A correlation-based approach

Recently, telecommunication and navigation corporations have shown a growing interest in low and medium Earth orbit constellations due to several operational advantages, such as reduced power requirements and signal time delays with respect to geostationary platforms. An increased imaging resolution of Earths surface is also associated with the use of low orbits rather than high altitude orbits. A large set of parameters is involved in defining constellation configurations, so usually some basic assumptions are taken. For instance, this occurs for Walker constellations, exhibiting a high degree of symmetry and suitability for coverage of large areas. Yet, for special purposes, such as continuous observation or early warning monitoring of a specific location, geometric hypotheses often seem inadequate or oversimplified. In this paper all satellites are placed in circular, repeating orbits with semimajor axis and inclination yielding maximum visibility of a preselected target location. Then, a correlation function is introduced as an effective tool to find all allowed time delays between two consecutive passes over the target. Some optimal constellation configurations (of 2, 4, 8 satellites) are deduced and discussed with reference to different kinds of local observation.

Preliminary aircraft design: lateral handling qualities

Abstract Handling qualities of airplanes can be improved by the use of an automatic control system (augmented stability control system), however, in the preliminary design phase it is sometimes better to implement suitable design changes. These changes can be performed according to iterative and trial–error procedures in order to get the required flight qualities. In the present paper a different approach to improve lateral handling qualities of aircraft is followed, based on necessary and sufficient conditions for the roots of the lateral characteristic equation to lie in prescribed region of the complex plane. As a result of this study, handling quality region of levels 1–3 can be visualized in the space of the physically relevant parameters. As an example, the vertical tail surface Sv and the dihedral angle Γ are chosen and the regions of levels 1–3 corresponding to some aircraft are shown in the ( S v , Γ ) plane.

On the Accessibility of the Moon

The large mass fraction of the Moon with respect to the Earth implies an extended sphere of influence which can be exploited in planning exploration missions either directed to our satellite or to other solar system bodies. The dynamical systems approach to mission design has shown the existence of novel trajectories in the Earth-Moon system, which can respond to widely different exploration goals such as low-energy lunar orbit insertion, reaching Mars from the Moon or bringing lunar resources to Earth. Within this framework the general topic of the accessibility of our satellite is discussed and examples of actual mission profiles are given.

Low ΔV Orbit Insertion in Interplanetary Missions

A key issue in interplanetary missions is the attempt to reduce as much as possible the on board propellant, which has a direct inpact on the payload weight and eventually on the cost of the mission. Then in the mission analysis one tries to to minimize the variation of velocity ΔV f needed for the spacecraft orbit insertion, and it is of interest to look for arrival conditions close to (temporary) ballistic capture of the spacecraft by the target planet (ΔV f ~ 0).