Lunar orbits for telecommunication and navigation services

Orbits that are frozen in an averaged model,including the effect of a disturbing body laying on the equatorial plane of the primary body and the influence of the oblateness of the primary body,have been applied to probes orbiting the Moon.In this scenario,the main disturbing body is represented by the Earth,which is characterized by a certain obliquity with respect to the equatorial plane of the Moon.As a consequence of this,and of the perturbing effects that are not included in the averaged model,such solutions are not perfectly frozen.However,the orbit eccentricity,inclination,and argument of pericenter present limited variations and can be set to guarantee the fulfillment of requirements useful for lunar telecommunication missions and navigation services.Taking advantage of this,a practical case of a Moon-based mission was investigated to propose useful solutions for potential near-future applications.

Optimal interplanetary trajectories for Sun-facing ideal diffractive sails

A diffractive sail is a solar sail whose exposed surface is covered by an advanced diffractive metamaterial film with engineered optical properties. This study examines the optimal performance of a diffractive solar sail with a Sun-facing attitude in a typical orbit-to-orbit heliocentric transfer. A Sun-facing attitude, which can be passively maintained through the suitable design of the sail shape, is obtained when the sail nominal plane is perpendicular to the Sun–spacecraft line. Unlike an ideal reflective sail, a Sun-facing diffractive sail generates a large transverse thrust component that can be effectively exploited to change the orbital angular momentum. Using a recent thrust model, this study determines the optimal control law of a Sun-facing ideal diffractive sail and simulates the minimum transfer times for a set of interplanetary mission scenarios. It also quantifies the performance difference between Sun-facing diffractive sail and reflective sail. A case study presents the results of a potential mission to the asteroid 16 Psyche.

Application of homotopy perturbation method to the radial thrust problem

The dynamics of a spacecraft propelled by a continuous radial thrust resembles that of a nonlinear oscillator.This is analyzed in this work with a novel method that combines the definition of a suitable homotopy with a classical perturbation approach,in which the low thrust is assumed to be a perturbation of the nominal Keplerian motion.The homotopy perturbation method provides the analytical(approximate)solution of the dynamical equations in polar form to estimate the corresponding spacecraft propelled trajectory with a short computational time.The accuracy of the analytical results was tested in an orbital-targeting mission scenario.

Optimal circle-to-rectilinear orbit transfer with circumferential thrust

This paper investigates the optimal transfer trajectories from a circular parking orbit towards the apocenter of a rectilinear ellipse,where the spacecraft reaches a quasi-stationary condition relative to an inertial reference frame.The spacecraft is equipped with a propulsion system that provides a circumferential continuous propulsive acceleration,that is,an acceleration whose direction is perpendicular to the primary body-spacecraft line.The performance index to minimize is the total flight time,and an indirect method is used to analyze the transfer trajectories.In this context,the optimal transfer performance is obtained as a function of the spacecraft propulsive acceleration magnitude through an interpolation procedure of numerical simulations.The results obtained with a continuous thrust propulsion system are also compared with those derived from a multi-impulse transfer.Finally,the paper investigates a heliocentric mission scenario in which the spacecraft minimizes the flight time required to reach a rectilinear ellipse with a given value of the aphelion radius.

Smart dust option for geomagnetic tail exploration

In-situ measurements are necessary for a long-term analysis of the spatial structure of the geomagnetic tail.This type of mission requires the use of a propellantless propulsion system,such as a classical solar sail,to continuously rotate the design orbit apse line such that it remains parallel to the Sun-Earth direction.To reduce the mission costs,this paper suggests the employment of Sun-pointing smart dusts,which are here investigated in terms of propulsive acceleration level necessary to guarantee a mission’s feasibility.A Sun-pointing smart dust can be thought of as a millimeter-scale solar sail,whose geometric configuration allows it to passively maintain an alignment with the Sun-spacecraft line.The smart dust external surface is coated with an electrochromic reflective film in such a way that it may change,within some limits,its propulsive acceleration magnitude.A suitable control law is necessary for the smart dust to enable an artificial precession of its Earth-centred orbit,similar to what happens in the GeoSail mission.This paper analyzes the required control law using an optimal approach.In particular,the proposed mathematical model provides a set of approximate equations that allow a simple and effective tradeoff analysis between the propulsive requirements,in terms of the smart dust acceleration,and the characteristics of the design orbit.

Comparison between direct and indirect approach to solar sail circle-to-circle orbit raising optimization

This paper deals with the optimization of the transfer trajectory of a solar sail-based spacecraft between circular and coplanar heliocentric orbits.The problem is addressed using both a direct and an indirect approach,while an ideal and an optical force model are used to describe the propulsive acceleration of a flat solar sail.In the direct approach,the total flight time is partitioned into arcs of equal duration,within which the sail attitude is assumed to be constant with respect to an orbital reference frame,and a nonlinear programming solver is used to optimize the transfer trajectory.The aim of the paper is to compare the performance of the two(direct and indirect)approaches in term of optimal(minimum)flight time.In this context,the simulation results show that a direct transcription method using a small number of arcs is sufficient to obtain a good estimate of the global minimum flight time obtained through the classical calculus of variation.

Spiral trajectories induced by radial thrust with applications to generalized sails

In this study,new analytical solutions to the equations of motion of a propelled spacecraft are investigated using a shape-based approach.There is an assumption that the spacecraft travels a two-dimensional spiral trajectory in which the orbital radius is proportional to an assigned power of the spacecraft angular coordinate.The exact solution to the equations of motion is obtained as a function of time in the case of a purely radial thrust,and the propulsive acceleration magnitude necessary for the spacecraft to track the prescribed spiral trajectory is found in a closed form.The analytical results are then specialized to the case of a generalized sail,that is,a propulsion system capable of providing an outward radial propulsive acceleration,the magnitude of which depends on a given power of the Sun-spacecraft distance.In particular,the conditions for an outward radial thrust and the required sail performance are quantified and thoroughly discussed.It is worth noting that these propulsion systems provide a purely radial thrust when their orientation is Sun-facing.This is an important advantage from an engineering point of view because,depending on the particular propulsion system,a Sun-facing attitude can be stable or obtainable in a passive way.A case study is finally presented,where the generalized sail is assumed to start the spiral trajectory from the Earth’s heliocentric orbit.The main outcome is that the required sail performance is in principle achievable on the basis of many results available in the literature.

Analytical solution to logarithmic spiral trajectories with circumferential thrust and mission applications

This study made use of a shape-based method to analyze the orbital dynamics of a spacecraft subject to a continuous propulsive acceleration acting along the circumferential direction.Under the assumption of a logarithmic spiral trajectory,an exact solution to the equations of motion exists,which allows the spacecraft state variables and flight time to be expressed as a function of the angular coordinate.There is also a case characterized by specific initial conditions in which the time evolution of the state variables may be analytically determined.In this context,the presented solution is used to analyze circle-to-circle trajectories,where the combination of two impulsive maneuvers and a logarithmic spiral path are used to accomplish the transfer.The determined results are then applied to the achievement of the Earth–Mars and the Earth–Venus transfers using actual data from a recent thruster developed by NASA.

Optimal solar sail transfers to circular Earth-synchronous displaced orbits

The aim of this paper is to evaluate the minimum flight time of a solar sail-based spacecraft towards Earth-synchronous(heliocentric)circular displaced orbits.These are special displaced non-Keplerian orbits characterized by a period of one year,which makes them suitable for the observation of Earth’s polar regions.The solar sail is modeled as a flat and purely reflective film with medium-low performance,that is,with a characteristic acceleration less than one millimeter per second squared.Starting from a circular parking orbit of radius equal to one astronomical unit,the optimal steering law is sought by considering the characteristic acceleration that is required for the maintenance of the target Earth-synchronous displaced orbit.The indirect approach used for the calculation of the optimal transfer trajectory allows the minimum flight time to be correlated with several Earth-synchronous displaced orbits,each one being characterized by given values of Earth-spacecraft distance and displacement over the ecliptic.The proposed mathematical model is validated by comparison with results available in the literature,in which a piecewise-constant steering law is used to find the optimal flight time for a transfer towards a one-year Type I non-Keplerian orbit.