Silvano Sgubini

On radiative and conductive heat transfer in spacecraft

Abstract The “radiative” boundary condition in a heat conduction problem relates the heat flux in a point of the wall to the temperatures in all the other points of the surface system. That is, this condition is of a “functional” type. This “functional” can be solved in discrete terms by using the conventional technique of dividing the body in small discrete elements or “nodes”. This paper instead presents an approach on a continuous scheme, by which the functional is solved in terms of “spacewise harmonics” of the temperature inside the body; the heat conduction problem is thus reduced to an ordinary form differential system whose unknowns are these “harmonics”. An interative linearized procedure to solve this system is also suggested, by which “exact” solutions are obtained. The merits of these solutions, with respect to practical discrete element computations, are in the better spacewise resolution and in the consequent more accurate treatment of both radiation and conduction. The application of the procedure is, however, limited to particular geometries. It is relevant to note that among these possible geometries many are included of practical interest, like hollow cylinders and polygons, cubic boxes etc. A numerical example completes the work.

Elastic waves propagation in bounded periodic structures

Abstract Large space structures are mostly designed and constructed by repetitive lattice grids. Continuum models have been proposed in the literature as a simple means for the structural analysis of lattices. However continuum models hide some typical properties of the modular structures, such as their filtering effects. This paper investigates the differences between continuum and periodic models of a modular structure from the point of view of the elastic wave propagation. The analysis reveals that only for small wave numbers the models are equivalent, otherwise the dispersive behavior strongly differs and the continuum models become no longer effective.

Ground-based orbit determination for spacecraft formations

Spacecraft formations offer interesting challenges to orbit determination, especially for ground-based tracking. In fact, the limited distances between spacecraft and the possible ambiguity of the observables gathered from the ground have an impact on the solution process. The paper aims to apply the filtering techniques on a refined dynamical model, which can include the main perturbation effects - due to the oblateness of the Earth and, at the lower altitudes, the air drag - on spacecraft trajectories, representing them in series with a remarkably limited number of terms even in eccentric case. The idea is to focus on theoretically expected behavior rather than dealing with an enriched but heavier state including parameters directly related to the perturbing effects. In such a way, it could be possible to obtain a good estimate even with limited spacecraft tracking information. This is an important asset in navigating a formation from the Earth, due to the needed partition of ground station resources among different platforms belonging to the formation, and to the possible ambiguity among the measurements, which further reduce the available data. The specific nature of the dynamic model calls for an estimator with a flexible and “open” architecture, easily allowing for changes and additions in the model itself. Therefore, the estimator selected for testing the approach has been the Unscented Kalman Filter, versatile enough to allow for increasing model accuracy without the need for tedious computation of the Jacobian. This approach is also intended to offer a different way to investigate special perturbed configurations, via the semi-analytical and almost exact representation of the trajectories. In such a perspective, one of the first application, which is shortly outlined in the paper, will be the analysis of spacecraft formations under the J2 effect. In fact, recent studies identified a set of almost periodic relative configurations among the spacecraft. This set (sometimes referred as the special or magical inclinations one) has been recently identified by means of numeric search, and has also received some (partial) explanation. Due to the interest in control effort reduction, it is deemed that a better understanding of this special dynamics, possibly provided by means of a selected modeling approach, can be of some interest

Efficient techniques for relative motion analysis between eccentric orbits under J2 effect

Accurate orbital propagation is required in order to correctly estimate (in design phase) and carry out (during operations) the control actions needed to maintain relative geometry among formations spacecraft. Such an accurate propagation could be easily obtained by numerical methods, but their relevant computation cost would neither allow for general trade-offs during design nor match the onboard capabilities once spacecraft are in space. The interest for analytic, closed form solution is clear, as it would save on computation resources and allows for both speed and portability advantages. This paper proposes a special writing of the equations of motion which does provide a closed form solution for orbits including the oblateness effect. Such a representation is far more realistic than the approximate Keplerian one for LEO and medium altitude formations environment, and has indeed a remarkable appeal. The approach, originated from previous literature, is to express the variables of interest (radius, node, inclination, anomaly) as a series, which can be limited to the desired accuracy level in terms of eccentricity. The authors worked on this approach for several years, including currently available symbolic mathematics to allow for exact computation of the parameters of interest at every desired time. The more important contribution is a correct writing of the formulation in terms of relative dynamics, i.e. in terms of differences in the orbital parameters of the platforms, which is actually what is required in the spacecraft formation case. The paper details this special writing of the equation of motion and provides the analytical solution for eccentricities up to 0.2; i.e., remarkably extending the range of orbits previously considered in literature. These solutions are validated with respect to standard numerical propagators that end up with taking orders of magnitude longer to provide the same accuracy. Their quite high efficiency in terms of computational resources needed make them a suitable solution for inclusion in the onboard software, or a performing option for trade-off analysis during design phase.

A fast approach for relative orbital determination in spacecraft formations

The design and operation of spacecraft formation-flying missions require a suitable knowledge of the relative dynamics of the platforms belonging to the formations. The perturbed, non-Keplerian, orbital environment can be easily faced by numerical approaches, like Cowell integration. However, that solution is accurate but quite slow to obtain, and indeed more appealing in the design phase. Instead, in a number of applications, above all from the operation point of view, a faster propagation would have a strong interest. This paper proposes a special writing of the equations of motion which does provide a closed form solution for orbits including the oblateness, i.e. a more realistic representation than the Keplerian one for higher LEO and medium altitude formations environment. The idea, which originated from previous literature, is to express the variables of interest (radius, node, inclination, etc) as a series, which can be limited to the desired accuracy level in terms of eccentricity. The adoption of symbolic mathematics currently allows for exact computation of the parameters of interest at every time. More important, the paper offers this formulation in terms of relative dynamics, i.e. in terms of differences in the orbital parameters of the platforms. Such a writing, which is the novelty of the paper, is actually what is required in the spacecraft formation case. The strong advantage of the proposed formulation is the quick availability of the solution, orders of magnitude faster than numerical integrators of similar accuracy. In such a way the future behavior of the platforms belonging to the formation can be easily computed, and these data are available for on-line control strategy evaluation as well as for payload operation schedule. The paper details this special writing of the equation of motion, provides the solutions for eccentricities up to 0.01 while validating the solutions with respect to standard, accurate numerical propagators.

Technological requirements for a passively attitude stabilized solar orbiter

The paper represents an intermediate issue of a research project targeting a possible low cost probe to investigate the Sun. The proposed design involves a passively attitude stabilized, conical shaped spacecraft which continuously keeps its rotation axis directed towards the Sun. The mission analysis is here pursued with particular emphasis to thermal aspects. A simulation code has been arranged especially to solve the thermal field of the problem along the orbit. Equilibrium temperature is obtained as function of the distance from the Sun, and several test cases, including different characteristics for material absorptance and emission as well as for the solar cell distribution on the probe surface, have been investigated