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Areostationary Relay Satellites are the most robust candidates to meet the coming set of Mars science missions. Areostationary satellites combine both the continuous coverage over the same Mars localization and the return of engineering and scientific instrument data in almost real time needed for the tele-robotic exploration. We present a procedure to minimize the total required impulses magnitudes in the major mission phases for an areostationary satellite. This mission design optimization problem involves two main problems. First, the determination of the launch and arrival dates for an optimal minimum energy Earth-Mars transfer trajectory. Second, the optimal minimum thrust manoeuvres to capture the spacecraft from the hyperbolic arrival trajectory to Mars and place it in the areostationary orbit. 1. IntroductionAn areostationary satellite would orbit Mars in an areoequatorial circular orbit with a semi-major axis of as = 20428 km to remain over a fixed point on the Martian surface with respect to the rotating Mars with a period of P=88775.244 s (Montabone, 2020). The purpose of this work is to analyse the elliptic heliocentric transfer and the hyperbolic areocentric orbits to achieve the final areostationary position with the minimal impulses cost. To this end, first the elliptic trajectory optimization using genetic metaheuristic algorithms is performed. Then, an analysis of accuracy of the matched solutions for the elliptic and the hyperbolic orbits using an iterative procedure at the Mars influence sphere is accomplished. Finally, the Mars arrival manoeuvres needed to capture the probe and to place it in an areostationary orbit are optimized. 2. Earth to Mars elliptic transfer optimizationIn this minimum-energy problem, we search a solution minimizing the equation:where the characteristic energy at the boundary of the sphere of influence of the Earth, C3= V2∞E, and the Mars arrival velocity V∞M are weighted according to WC3 and W∞M, respectively. The minimum C in equation (1) tends to give lower values of the total impulsive manoeuvres required, first to give to the space vehicle an orbital velocity greater than the parabolic Earth escape velocity, and after, at the Mars arriving hyperbolic orbit, to reduce the hyperbolic excess velocity to capture the probe. Determining the optimal elliptic orbital transfer parameters by minimizing C by exhaustive search or analytical methods is infeasible as for each Earth departure date and Mars arrival date combination the Lambert's problem needs to be solved:being and the heliocentric Earth and Mars position vectors and the areocentric vector position of the spacecraft in an ecliptic reference system. Genetic algorithms are metaheuristic algorithms that explore different solutions amongst a defined population, finding a possible minimum solution. Lambert's problem shall be solved for each member of the population following the procedure in Gooding (1988), having the orbital elements of the spacecraft's orbit once the solution is achieved. Table 1 shows different simulation scenarios to compare genetic algorithms performance minimizing the cost function C. Figure 1 shows an optimal transfer for launch on 20th July 2020 and arrival on 1st February 2021. 3. Accuracy analysis for the conic matching procedureTo match the heliocentric and the areocentric orbits, the following model is used:The function f corresponds to the Lambert's problem (2), g and h are given in Battin (1999). Then, the following iterative method is implemented:that converges when the following condition is met:which is equivalent to:Simulations are performed introducing different initial inclination conditions. The method converges, after 3 iterations, to the objective values of the periapsis radius and the inclination of the hyperbolic orbit. 4. Mars arrival optimizationFinally, we present the procedure for minimizing the total impulse needed to capture the probe and to place it in an areostationary orbit:where is the capture manoeuvre to avoid the probe leaving its sphere of influence on a flyby trajectory; and are the Hoffman transfer maneuvers from the capture orbit to target the areostationary orbit; and is the inclination correction manoeuvre to reach the final zero desired inclination.5. Summary and ConclusionsOptimal dates which provide minimum hyperbolic excess velocity at Earth and the Mars arrival velocity are determined to obtain the optimal transfer orbit from Earth to Mars. Then, an iterative procedure is proposed to match the heliocentric and areocentric orbits at Mars sphere of influence which converges to the objective values to position the spacecraft in the areostationary orbit. Optimal Mars arrival manoeuvres are obtained when hyperbolic periapsis is fixed to be the semi-major axis of the areostationary orbit with the minimum inclination constrained by the areocentric declination of the arrival velocity direction V∞M. AcknowledgementsPart of this research has been funded by the Government of Spain (Project ESP2016-79135-R). References Montabone, L. et al, Observing Mars from Areostationary Orbit: Benefits and Applications, 2020, MEPAG Gooding, R.H., On the solution of Lambert's orbital boundary-value problem, 1988, Royal Aerospace Establishment Battin, R.H., An Introduction to the Mathematics and Methods of Astrodynamics, 1999, AAIA Educational Series

We present a qualitative analysis in a phase space to determine the longitudinal equilibrium positions on the planetary stationary orbits by applying an analytical model that considers linear gravitational perturbations. We discuss how these longitudes are related with the orientation of the planetary principal inertia axes with respect to their Prime Meridians, and then we use this determination to derive their positions with respect to the International Celestial Reference Frame. Finally, a numerical analysis of the non-linear effects of the gravitational fields on the equilibrium point locations is developed and their correlation with gravity field anomalies shown.

S ATELLITES in areostationary orbit are considered efficient candidates for meeting the telecommunications needs of the foreseen science missions to Mars. An areostationary satellite, in analogy to a geostationary satellite around the Earth, would orbit Mars in a circular areoequatorial orbit with a period of a Martian day (sol) to remain at a fixed point with respect to the Martian surface. A design for aMars areostationary relay satellite (MARSAT) to provide a continuous coverage of a specific region ofMars has been proposed in [1–8]. An areostationary satellite must have a semimajor axis of as 20428 km to be at rest with respect to the rotating Mars with a period of P 1 sol 88775.244 s. Stationary position also requires zero eccentricity and inclination. However, natural perturbations tend to shift an areostationary satellite from its nominal station point, and station-keeping orbital maneuvers are necessary to keep the satellite within a predefined box over one place on Mars. East/west tangential maneuvers are used to control the satellite longitude evolution, due to the drift caused by the perturbing terms of theMars potential and to the nonzero eccentricity because of the solar radiation pressure (SRP) effects. The north/south normal maneuvers have to control the oscillations in latitude due to solar and Phobos and Deimos gravitational perturbations on the inclination of the satellite’s orbit. Detailed theories for the main effects on the geostationary orbit are well known and can be found in the literature, for instance, [9–12]. For areostationary satellites, only the parabolic evolution of themean longitude l caused by the tangential acceleration due to the tesseral harmonics of Mars’s potential, as well as the characterization of the two stable longitudes at 17.92°W, 167.83°E and the two unstable longitudes at 75.34°E, 105.55°W have been described in [13–15]. The oscillations in longitude due to the evolution of the mean eccentricity vector, caused by the SRP, and the annual maneuvers for the east/west station keeping to control the satellite longitude evolution have been analyzed and evaluated in [15]. Temporal patterns of solar eclipses on areostationary satellites to model SRP properly are given in [16]. In this note, a strategy for the inclination maneuvers to correct the solar and Phobos and Deimos perturbations for an areostationary satellite is presented.

In this work we present an analysis of several sets of parameters connecting Earth–Mars reference systems by applying an eclipse model to available observations of Phobos eclipses on Mars. Results for the involved parameters needed for the eclipse prediction in our parametrization which better fit the observations are presented. As the comparison is limited to individual eclipse data this may not be an accuracy criterion in general.

This paper deals with an inverse problem concerning the determination of the MetNet Precursor Mission landing site coordinates on Mars using Phobos eclipses detection. The main difficulties are that this problem corresponds to the inversion of a multievaluated and nonlinear function which models the latitudinal and longitudinal Phobos shadow motion across the Mars surface and the use of experimental data involving measurement errors. We consider two different algorithms for the inverse problem: the Levenberg-Marquardt algorithm and the block relaxation method, and we perform numerical tests in order to compare the results obtained. We show the efficiency of an algorithm which employs a recursive least squares estimator based on a coordinate relaxation method. The precision in coordinate determination has been analyzed for different uncertainty values of the observed contact times and for different number of observed eclipses. The numerical results for the planned MetNet Precursor Mission show how, within a landing site band of delta phi = +/- 5 degrees around the equator, a maximum difference of 40 x 60 m between the true position and the solution is attainable with 1 s uncertainties in eclipse time observations.

La Misión ExoMars16 es la primera misión del programa ExoMars de la ESA, cuyo lanzamiento se realizó el día 14 de marzo de 2016 estando prevista su llegada a Marte en octubre de 2016. Esta misión consta del módulo orbital Gas Tracer Orbiter y del módulo de descenso Schiaparelli. Este último está equipado con tecnología experimental entre la que se encuentra el Sensor de Irradiación Solar (SIS) desarrollado por el Instituto Nacional de Técnica Aeroespacial, incluido dentro del experimento para la caracterización del entorno atmosférico sobre la superficie marciana DREAMS. El principal objetivo del sensor SIS es la medición del espectro solar en la superficie de Marte, la transparencia atmosférica y la concentración de polvo para, combinado con los datos del sensor de campos eléctricos MicroARES, estudiar los mecanismos que inician las tormentas de polvo marcianas. El objetivo de este trabajo es caracterizar la visibilidad del Sol desde el módulo Schiaparelli y establecer un cronograma de observaciones solares para SIS en el tiempo de vida previsto para el módulo sobre la superficie de Marte de 2 a 8 soles. Para establecer el cronograma de observaciones solares se ha calculado la posición del Sol vista desde SIS, determinando el TU de los ortos y ocasos, así como el origen del Local True Solar Time (LTST) en el lugar de amartizaje. Para el cálculo de las coordenadas locales, azimut y altura, se ha realizado una simulación de Montecarlo de 1000 posiciones aleatorias dentro de la elipse de amartizaje prevista por la ESA. Por último, se establece el cronograma de visibilidad del Sol más probable, así como para los puntos característicos de la elipse, que acotan los márgenes de error de dicha determinación. Esto permite planificar adecuadamente las observaciones de radiación solar con SIS. El Sol estará visible durante aproximadamente 12 horas y 26 minutos cada sol.

We have generated predictions for observing Phobos transits during the period 2012–2014 using the Mars Science Laboratory. We describe how the detections of Phobos eclipses can be used as an alternative procedure to determine the coordinates of the rover. We present a numerical simulation to analyse the sensitivity of the precise observed contact times to the coordinate determination. The numerical results show that after four days of eclipse observations for 1 min each day, within the 25 × 20 km2 landing site ellipse, the position of the lander can be determined to within an ellipse of 40 × 60 m2 for uncertainties of 1 s in eclipse time observations. A 20 × 15 m2 ellipse is estimated if a 0.1-s time precision can be gathered.

Mars MetNet Precursor is a mission for Martian atmospheric measurement studies. In this work, we present an areographic temporal pattern description of Phobos solar eclipses for the establishment of an observational strategy to detect such events with the Mars MetNet Precursor Lander. The two-dimensional shadow motion model on the surface of Mars has been obtained by combining the latitude and longitude cycles firstly derived. In order to check the developed algorithm and the implemented parameters to predict the location of Phobos penumbral footprint at a given time, we compare the predictions for the observed eclipses from the surface of Mars made by Spirit and Opportunity. Overall differences are less than 0.1 s, showing how the parameterization model fits Mars Prime Meridian position. Finally, the temporal occurrence of solar eclipses for the MetNet lifetime mission is characterized and the results are applied to set up a predefined operational strategy at regular time intervals for the eclipse data acquisition with MetNet instrumentation.

The orbital information given in the form of Ultra-Rapid Orbits (IGA and IGU), Rapid Orbits (IGR), and Final Orbits (IGS), as well as the Earth rotational parameters and the clock offset provided by the International GNSS Service plays an important role in supporting the Global Navigation Satellite Systems GPS and GLONASS. In this paper, we compare the observables, the force models, the adjustment methods and the numerical integration procedures applied by the different International GNSS Service Analysis Centers for the orbital parameter determination.

Until now, several heuristics for scheduling parameter sweep applications in environments such as cluster and grid have been introduced. Cloud computing has revolutionized the way applications are executed in distributed environments, as now it is the infrastructure which is adapted to the application and not vice versa. In the present contribution an astronomy application from the next mission to Planet Mars with Finnish-Russian-Spanish flag is ported on to a cloud environment, resulting in a parameter sweep profile. The number of needed executions and the deadline provided required a big quantity of computing resources in a short term and punctual situations. For this reason, we introduce and validate a model for an optimal execution on a public cloud infrastructure by means of time, cost and a metric involving both.