Search Results (22)

Hohmann transfer is the classical approach used in astrodynamics to analyze the optimal bi-impulsive transfer, from the point of view of the total velocity change, between two circular, coplanar orbits of assigned radius. The Hohmann transfer is characterized by an elliptical trajectory tangent to both circular orbits at the points where the transfer begins or ends and can be used to simply model, in a Kepler problem, a possible optimal transfer of a spacecraft equipped with a high-thrust propulsion system. Recent literature has proposed a sort of extension of the Hohmann transfer to a heliocentric mission scenario, where the total velocity change is reduced compared to the classical result by employing a photonic solar sail operating along the deep-space transfer trajectory. The study of this so-called augmented Hohmann transfer, where the spacecraft uses both two tangential impulses (one at the beginning and one at the end of the flight) provided by a high-thrust propulsion system and the propulsive acceleration (during the flight) provided by a low-thrust propulsion system, is extended in this paper by considering a more general case where the spacecraft moves around a generic primary body and uses, along the transfer, a freely orientable propulsive acceleration vector with constant and assigned magnitude. This scenario is consistent, for example, with the use of a typical electric thruster instead of the photonic solar sail considered in recent literature. In particular, the paper studies the impact of the continuous-thrust propulsion system on the transfer performance between the two circular orbits, analyzing the variation of the total velocity change as a function of the propulsive acceleration magnitude. The procedure, which uses an optimal approach to performance estimation, can be used both in a heliocentric and planetocentric mission scenario and can also be employed to analyze the performance of a spacecraft equipped with a multimode propulsion system. Full article

This paper studies the performance of an interplanetary CubeSat equipped with a continuous-thrust primary propulsion system in a heliocentric mission scenario, which models a nodal flyby with a potential near-Earth asteroid. In particular, the mathematical model discussed in this work considers a small array of (commercial) miniaturized electric thrusters installed onboard a typical CubeSat, whose power-generation system is based on the use of classic solar panels. The paper also discusses the impact of the size of thrusters’ array on the nominal performance of the transfer mission by analyzing the trajectory of the CubeSat from an optimization point of view. In this context, the propulsive characteristics of a commercial electric thruster which corresponds to a iodine-fueled gridded ion-propulsion system are considered in this study, while the proposed procedure can be easily extended to a generic continuous-thrust propulsion system whose variation in thrust magnitude and specific impulse as a function of the input electric power is a known analytic function. Using an indirect approach, the paper illustrates the optimal guidance law, which allows the interplanetary CubeSat to reach a given solar distance, with the minimum flight time, by starting from a circular (ecliptic) parking orbit of assigned radius. The mission scenario is purely two-dimensional and models a rapid nodal flyby with a near-Earth asteroid whose nodal distance coincides with the solar distance to be reached. Full article

A refractive sail is a special type of solar sail concept, whose membrane exposed to the Sun’s rays is covered with an advanced engineered film made of micro-prisms. Unlike the well-known reflective solar sail, an ideally flat refractive sail is able to generate a nonzero thrust component along the sail’s nominal plane even when the Sun’s rays strike that plane perpendicularly, that is, when the solar sail attitude is Sun-facing. This particular property of the refractive sail allows heliocentric orbital transfers between orbits with different values of the semilatus rectum while maintaining a Sun-facing attitude throughout the duration of the flight. In this case, the sail control is achieved by rotating the structure around the Sun–spacecraft line, thus reducing the size of the control vector to a single (scalar) parameter. A gradient-index solar sail (GIS) is a special type of refractive sail, in which the membrane film design is optimized though a transformation optics-based method. In this case, the membrane film is designed to achieve a desired refractive index distribution with the aid of a waveguide array to increase the sail efficiency. This paper analyzes the optimal transfer performance of a GIS with a Sun-facing attitude (SFGIS) in a series of typical heliocentric mission scenarios. In addition, this paper studies the attitude control of the Sun-facing GIS using a simplified mathematical model, in order to investigate the effective ability of the solar sail to follow the (optimal) variation law of the rotation angle around the radial direction. Full article

A diffractive solar sail is an elegant concept for a propellantless spacecraft propulsion system that uses a large, thin, lightweight surface covered with a metamaterial film to convert solar radiation pressure into a net propulsive acceleration. The latter can be used to perform a typical orbit transfer both in a heliocentric and in a planetocentric mission scenario. In this sense, the diffractive sail, proposed by Swartzlander a few years ago, can be considered a sort of evolution of the more conventional reflective solar sail, which generally uses a metallized film to reflect the incident photons, studied in the scientific literature starting from the pioneering works of Tsander and Tsiolkovsky in the first decades of the last century. In the context of a diffractive sail, the use of a metamaterial film with a Littrow transmission grating allows for the propulsive acceleration magnitude to be reduced to zero (and then, the spacecraft to be inserted in a coasting arc during the transfer) without resorting to a sail attitude that is almost edgewise to the Sun, as in the case of a classical reflective solar sail. The aim of this work is to study the optimal (i.e., the rapid) transfer performance of a spacecraft propelled by a diffractive sail with a Littrow transmission grating (DSLT) in a three-dimensional heliocentric mission scenario, in which the space vehicle transfers between two assigned Keplerian orbits. Accordingly, this paper extends and generalizes the results recently obtained by the author in the context of a simplified, two-dimensional, heliocentric mission scenario. In particular, this work illustrates an analytical model of the thrust vector that can be used to study the performance of a DSLT-based spacecraft in a three-dimensional optimization context. The simplified thrust model is employed to simulate the rapid transfer in a set of heliocentric mission scenarios as a typical interplanetary transfer toward a terrestrial planet and a rendezvous with a periodic comet. Full article

This paper analyzes the performance of an interplanetary CubeSat equipped with a hybrid propulsion system (HPS), which combines two different types of thrusters in the same deep space vehicle, in a heliocentric transfer between two assigned (Keplerian) orbits. More precisely, the propulsion system of the CubeSat considered in this work consists of a combination of a (low-performance) photonic solar sail and a more conventional solar electric thruster. In particular, the characteristics of the solar electric thruster are modeled using a recent mathematical approach that describes the performance of the miniaturized engine that will be installed on board the proposed ESA’s M-ARGO CubeSat. The latter will hopefully be the first interplanetary CubeSat to complete a heliocentric transfer towards a near-Earth asteroid using its own propulsion system. In order to simplify the design of the CubeSat attitude control subsystem, we assume that the orientation of the photonic solar sail is kept Sun-facing, i.e., the sail reference plane is perpendicular to the Sun-CubeSat line. That specific condition can be obtained, passively, by using an appropriate design of the shape of the sail reflective surface. The performance of an HPS-based CubeSat is analyzed by optimizing the transfer trajectory in a three-dimensional heliocentric transfer between two closed orbits of given characteristics. In particular, the CubeSat transfer towards the near-Earth asteroid 99942 Apophis is studied in detail. Full article

The Electric Solar Wind Sail (E-sail) deflects charged particles from the solar wind through an artificial electric field to generate thrust in interplanetary space. The structure of a spacecraft equipped with a typical E-sail essentially consists in a number of long conducting tethers deployed from a main central body, which contains the classical spacecraft subsystems. During flight, the reference plane that formally contains the conducting tethers, i.e., the sail nominal plane, is inclined with respect to the direction of propagation of the solar wind (approximately coinciding with the Sun–spacecraft direction in a preliminary trajectory analysis) in such a way as to vary both the direction and the module of the thrust vector provided by the propellantless propulsion system. The generation of a sail pitch angle different from zero (i.e., a non-zero angle between the Sun–spacecraft line and the direction perpendicular to the sail nominal plane) allows a transverse component of the thrust vector to be obtained. From the perspective of attitude control system design, a small value of the sail pitch angle could improve the effectiveness of the E-sail attitude maneuver at the expense, however, of a worsening of the orbital transfer performance. The aim of this paper is to investigate the effects of a constraint on the maximum value of the sail pitch angle, on the performance of a spacecraft equipped with an E-sail propulsion system in a typical interplanetary mission scenario. During flight, the E-sail propulsion system is considered to be always on so that the entire transfer can be considered a single propelled arc. A heliocentric orbit-to-orbit transfer without ephemeris constraints is analyzed, while the performance analysis is conducted in a parametric form as a function of both the maximum admissible sail pitch angle and the propulsion system’s characteristic acceleration value. Full article

The recent technology advancements in miniaturizing the primary components of spacecraft allow the classic CubeSats to be considered as a valid option in the design of a deep space scientific mission, not just to support a main typical interplanetary spacecraft. In this context, the proposed ESA M-ARGO mission, whose launch is currently planned in 2026, will use the electric thruster installed onboard of a 12U CubeSat to transfer the small satellite from the Sun–Earth second Lagrangian point to the orbit of a small and rapidly spinning asteroid. Starting from the surrogate model of the M-ARGO propulsion system proposed in the recent literature, this paper analyzes a simplified thrust vector model that can be used to study the heliocentric optimal transfer trajectory with a classical indirect approach. This simplified thrust model is a variation of the surrogate one used to complete the preliminary design of the trajectory of the M-ARGO mission, and it allows to calculate, in an analytical form, the typical Euler–Lagrange equations without singularities. The thrust model is then used to study the performance of a M-ARGO-type CubeSat (MTC) in a different scenario (compared to that of the real mission), in which the small satellite moves along a circular heliocentric orbit in the context of a classic phasing maneuver. In this regard, the work discusses a simplified study of the optimal constrained MTC transfer towards one of the two Sun–Earth triangular Lagrangian points. Therefore, the contributions of this paper are essentially two: the first is the simplified thrust model that can be used to analyze the heliocentric trajectory of a MTC; the second is a novel mission application of a CubeSat, equipped with an electric thruster, moving along a circular heliocentric orbit in a phasing maneuver. Full article

This paper discusses the optimal control law, in a three-dimensional (3D) heliocentric orbit transfer, of a spacecraft whose primary propulsion system is a Solar Wind Ion Focusing Thruster (SWIFT). A SWIFT is an interesting concept of a propellantless thruster, proposed ten years ago by Gemmer and Mazzoleni, which deflects, collects, and accelerates the charged particles of solar wind to generate thrust in the interplanetary space. To this end, the SWIFT uses a large conical structure made of thin metallic wires, which is positively charged with the aid of an electron gun. In this sense, a SWIFT can be considered as a sort of evolution of the Janhunen’s E-Sail, which also uses a (nominally flat) mesh of electrically charged tethers to deflect the solar wind stream. In the recent literature, the optimal performance of a SWIFT-based vehicle has been studied by assuming a coplanar orbit transfer and a two-dimensional scenario. The mathematical model proposed in this paper extends that result by discussing the optimal guidance laws in the general context of a 3D heliocentric transfer. In this regard, a number of different forms of the spacecraft state vectors are considered. The validity of the obtained optimal control law is tested in a simplified Earth–Venus and Earth–Mars transfer by comparing the simulation results with the literature data in terms of minimum flight time. Full article

In astrodynamics, orbit cranking is usually referred to as an interplanetary transfer strategy that exploits multiple gravity-assist maneuvers to change both the inclination and eccentricity of the spacecraft osculating orbit without changing the specific mechanical energy, that is, the semimajor axis. In the context of a solar sail-based mission, however, the concept of orbit cranking is typically referred to as a suitable guidance law that is able to (optimally) change the orbital inclination of a circular orbit of an assigned radius in a general heliocentric three-dimensional scenario. In fact, varying the orbital inclination is a challenging maneuver from the point of view of the velocity change, so orbit cranking is an interesting mission application for a propellantless propulsion system. The aim of this paper is to analyze the performance of a spacecraft equipped with an Electric Solar Wind Sail in a cranking maneuver of a heliocentric circular orbit. The maneuver performance is calculated in an optimal framework considering spacecraft dynamics described by modified equinoctial orbital elements. In this context, the paper presents an analytical version of the three-dimensional optimal guidance laws obtained by using the classical Pontryagin’s maximum principle. The set of (analytical) optimal control laws is a new contribution to the Electric Solar Wind Sail-related literature. Full article

A solar sail is a propellantless propulsion system that allows a spacecraft to use solar radiation pressure as a propulsive source for planetary and deep space missions that would be difficult, or even unfeasible, to accomplish with more conventional thrusters, either chemical or electric. A challenging application for these fascinating propulsion systems is a heliocentric mission that requires a displaced non-Keplerian orbit (DNKO), that is, a solar sail-induced closed trajectory in which the orbital plane does not contain the Sun’s center of mass. In fact, thanks to the pioneering work of McInnes, it is known that a solar sail is able to reach and maintain a family of heliocentric DNKOs of given characteristics. The aim of this paper is to analyze the properties of Mars-synchronous circular DNKOs, which have an orbital period matching that of the planet for remote sensing applications. In fact, those specific displaced orbits allow a scientific probe to continuously observe the high-latitude regions of Mars from a quasi-stationary position relative to the planet. In this context, this paper also analyzes the optimal (i.e., the minimum-time) heliocentric transfer trajectory from the Earth to circular DNKOs in two special mission scenarios taken as a reference. Full article

Solar sails are propellantless propulsion systems that extract momentum from solar radiation pressure. They consist of a large ultrathin membrane, typically aluminized, that reflects incident photons from the Sun to generate thrust for space navigation. The purpose of this study is to investigate the optimal performance of a solar sail-based spacecraft in performing two-dimensional heliocentric transfers to inertial points on the ecliptic that lie within an assigned annular region centered in the Sun. Similar to ESA’s Comet Interceptor mission, this type of transfer concept could prove useful for intercepting a potential celestial body, such as a long-period comet, that is passing close to Earth’s orbit. Specifically, it is assumed that the solar sail transfer occurs entirely in the ecliptic plane and, in analogy with recent studies, the flyby points explored are between $0.85\mathrm{au}$ and $1.35\mathrm{au}$ from the Sun. The heliocentric dynamics of the solar sail is described using the classical two-body model, assuming the spacecraft starts from Earth orbit (assumed circular), and an ideal force model to express the sail thrust vector. Finally, no constraint is imposed on the arrival velocity at flyby. Numerical simulation results show that solar sails are an attractive option to realize these specific heliocentric transfers. Full article

Recent literature indicates that the diffractive sail concept is an interesting alternative to the more conventional reflective solar sail, which converts solar radiation pressure into a (deep space) thrust using a thin, lightweight highly reflective membrane, usually metalized. In particular, a diffractive sail, which uses a metamaterial-based membrane to diffract incoming solar rays, is able to generate a steerable thrust vector even when the sail nominal plane is perpendicular to the Sun–spacecraft line. This paper analyzes the optimal transfer performance of a diffractive-sail-based spacecraft in a challenging heliocentric scenario that is consistent with the proposed Solar Polar Imager mission concept. In this case, the spacecraft must reach a near-circular (heliocentric) orbit with a high orbital inclination with respect to the Ecliptic in order to observe and monitor the Sun’s polar regions. Such a specific heliocentric scenario, because of the high velocity change it requires, is a mission application particularly suited for a propellantless propulsion system such as the classical solar sail. However, as shown in this work, the same transfer can be accomplished using a diffractive sail as the primary propulsion system. The main contribution of this paper is the analysis of the spacecraft transfer trajectory using a near-optimal strategy by dividing the entire flight into an approach phase to a circular orbit of the same radius as the desired final orbit but with a smaller inclination, and a subsequent cranking phase until the desired (orbital) inclination is reached. The numerical simulations show that the proposed strategy is sufficiently simple to implement and can provide solutions that differ by only a few percentage points from the optimal results obtainable with a classical indirect approach. Full article

There are plans to set up a space-based gravitational wave observatory that will use an ultra-large-scale laser interferometer in space to detect medium- and low-frequency gravitational waves. Both heliocentric and geocentric formations adopt the method of launching three satellites with one rocket, which has high requirements in terms of the carrying capacity of the rocket. Therefore, a proper transfer design is a prerequisite for achieving space-based gravitational wave detection. In this paper, the transfer orbit for three satellites of the Taiji mission is designed based on the two-impulse transfer model. Moreover, the influence on orbit design of the position of the formation relative to Earth, the initial phase angle of the formation, and the initial time of transfer is analyzed. The Earth-leading and -trailing transfers show opposite patterns in the above three aspects. A smaller velocity increment is required if a proper initial time is selected. After taking into account the stability of the formation, C3, the required velocity increment, transfer time, and the distance to Earth, 20° is determined to be the optimal initial trailing/leading angle. Full article

The transfer between two circular, coplanar Keplerian orbits of a spacecraft equipped with a continuous thrust propulsion system is usually studied in an optimal framework by maximizing a given performance index. Using an indirect approach, the optimal trajectory and the maximum value of the performance index are obtained by numerically solving a two-point boundary value problem (TPBVP). In this context, the computation time required by the numerical solution of the TPBVP depends on the guess of unknown initial costates. The aim of this paper is to describe an analytical procedure to accurately approximate the initial costate variables in a coplanar, circle-to-circle, minimum-time transfer. In particular, this method considers a freely steerable propulsive acceleration vector, whose magnitude varies over a finite range with a sufficiently low maximum value. The effectiveness of the analytical method is tested in a set of both geocentric and heliocentric (simplified) mission scenarios, which model the classical LEO-GEO or interplanetary transfers toward Venus, Mars, Jupiter, and comet 29P/Schwassmann–Wachmann 1. Full article

The aim of this paper is to analyze the performance of a state-feedback guidance law, which is obtained through a classical sliding mode control approach, in a two-dimensional circle-to-circle orbit transfer of a spacecraft equipped with a continuous-thrust propulsion system. The paper shows that such an inherently robust control technique can be effectively used to obtain possible transfer trajectories even when the spacecraft equations of motion are affected by perturbations. The problem of the guidance law design is first addressed in the simplified case of an unperturbed system, where it is shown how the state-feedback control may be effectively used to obtain simple mathematical relationships and graphs that allow the designer to determine possible transfer trajectories that depend on a few control parameters. It is also shown that a suitable combination of the controller parameters may be exploited to obtain trade-off solutions between the flight time and the transfer velocity change. The simplified control strategy is then used to investigate a typical heliocentric orbit raising/lowering in the presence of bounded disturbances and measurement errors. Full article