Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle

Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.     

Time-optimal trajectories to circumsolar space using solar electric propulsion

The aim of this paper is to explore the capabilities of a solar electric propelled spacecraft on a mission towards circumsolar space. Using an indirect approach, the paper investigates minimum time of transfer (direct) trajectories from an initial heliocentric parking orbit to a desired final heliocentric target orbit, with a low perihelion radius and a high orbital inclination. The simulation results are then collected into graphs and tables for a trade-off analysis of the main mission parameters. Finally, a comparison of the performance between a solar electric and a (photonic) solar sail based spacecraft is discussed.     

Solar sail optimal control with solar irradiance fluctuations

The optimization of a solar sail-based orbital transfer amounts to searching for the control law that minimizes the flight time. In this context, the optimal trajectory is usually determined assuming constant solar properties. However, the total solar irradiance undergoes both long-term (solar cycles) and short-term variations, and recent analyses have shown that this may have an impact on solar sailing for missions requiring an accurate thrust modulation. In this regard, the paper discusses a strategy to overcome such an issue by suitably adjusting the thrust vector in order to track a reference, optimal, transfer trajectory. In particular, the sail propulsive acceleration magnitude is modified by means of a set of electrochromic material panels, which change their optical properties on application of a suitable electric voltage. The proposed control law is validated with a set of numerical simulations that involve a classical Earth-Mars, orbit-to-orbit, heliocentric transfer.     

Optimal solar sail trajectory approximation with finite Fourier series

The heliocentric transfer of a solar sail-based spacecraft is usually studied from an optimal perspective, by looking for the control law that minimizes the total flight time. The optimal control problem can be solved either with an indirect approach, whose solution is difficult to obtain due to its sensitivity to an initial guess of the costates, or with a direct method, which requires a good estimate of a feasible (guess) trajectory. This work presents a procedure to generate an approximate optimal trajectory through a finite Fourier series. The minimum time problem is solved using a nonlinear programming solver, in which the optimization parameters are the coefficients of the Fourier series and the positions of the spacecraft along the initial and target orbits. Suitable constraints are enforced on the direction and magnitude of the sail propulsive acceleration vector in order to obtain feasible solutions. A comparison with the numerical results from an indirect approach shows that the proposed method provides a good approximation of the optimal trajectory with a small computational effort.     

Spinning solar sail orbit steering via spin rate control

The orbit of a solar sail can be controlled by changing the attitude of the spacecraft. In this study, we consider the spinning solar power sail IKAROS (Interplanetary Kite-craft Accelerated by Radiation Of the Sun), which is managed by Japan Aerospace Exploration Agency (JAXA). The IKAROS attitude, i.e., the direction of its spin-axis, is nominally controlled by the rhumb-line control method. By utilizing the solar radiation torque, however, we are able to change the direction of the spin-axis by only controlling its spin rate. With this spin rate control, we can also control indirectly the solar sail’s trajectory. The main objective of this study is to construct the orbit control strategy of the solar sail via the spin-rate control method. We evaluate this strategy in terms of its propellant consumption compared to the rhumb-line control method. Finally, we present the actual flight attitude data of IKAROS and the change of its trajectory.     

Drag force on solar sails due to absorption of solar radiation

We consider a special relativistic effect, known as the Poynting–Robertson effect, on various types of trajectories of solar sails. Since this effect occurs at order v^?/c, where v^? is the transversal speed relative to the sun, it can dominate over other special relativistic effects, which occur at order v²/c². While solar radiation can be used to propel the solar sail, the absorbed portion of it also gives rise to a drag force in the transversal direction. For escape trajectories, this diminishes the cruising velocity, which can have a cumulative effect on the heliocentric distance. For a solar sail directly facing the sun in a bound orbit, the Poynting–Robertson effect decreases its orbital speed, thereby causing it to slowly spiral towards the sun. We also consider this effect for non-Keplerian orbits in which the solar sail is tilted in the azimuthal direction. While in principle the drag force could be counter-balanced by an extremely small tilt of the solar sail in the polar direction, periodic adjustments are more feasible.     

Dynamical analysis of a spinning solar sail

This paper discusses the orbit and attitude dynamics of a solar sail, and gives the sufficient conditions of a stable orbit and attitude coupled system. The stability of the coupled system is determined by the orbit stability and attitude stability. Based on the sufficient conditions, a spin-stabilized solar sail of cone configuration is proposed to evolve in the heliocentric displaced orbit. For this kind of configuration, the attitude is always stable by spinning itself. The orbit stability depends on the orbit parameters of the heliocentric displaced orbit, the ratio of the orbit radius to displaced distance and orbit angular velocity. If the center of mass and center of pressure overlap, it can be proved that the coupled system is stable when the orbit parameters are chosen in the stable region. When the center of mass and center of pressure offset exists, the stability of the coupled system can not be judged. A numerical example is given and the result shows that both the orbit and attitude are stable for the case.     

Extrasolar space exploration by a solar sail accelerated via thermal desorption of coating

For extrasolar space exploration it might be very convenient to take advantage of space environmental effects such as solar radiation heating to accelerate a solar sail coated by materials that undergo thermal desorption at a particular temperature. Thermal desorption can provide additional thrust as heating liberates atoms, embedded on the surface of the solar sail. We are considering orbital dynamics of a solar sail coated with materials that undergo thermal desorption at a specific temperature, as a result of heating by solar radiation at a particular heliocentric distance, and focus on two scenarios that only differ in the way the sail approaches the Sun. For each scenario once the perihelion is reached, the sail coat undergoes thermal desorption. When the desorption process ends, the sail then escapes the Solar System having the conventional acceleration due to solar radiation pressure. We study the dependence of a cruise speed of a solar sail on perihelion of the orbit where the solar sail is deployed. The following scenarios are considered and analyzed: (1) Hohmann transfer plus thermal desorption. In this scenario the sail would be carried as a payload to the perihelion with a conventional propulsion system by a Hohmann transfer from Earth’s orbit to an orbit very close to the Sun and then be deployed. Our calculations show that the cruise speed of the solar sail varies from 173?km/s to 325?km/s that corresponds to perihelion 0.3?AU and 0.1 AU, respectively. (2) Elliptical transfer plus Slingshot plus thermal desorption. In this scenario the transfer occurs from Earth’s orbit to Jupiter’s orbit; then a Jupiter’s fly-by leads to the orbit close to the Sun, where the sail is deployed and thermal desorption comes active. In this case the cruise speed of the solar sail varies from 187?km/s to 331?km/s depending on the perihelion of the orbit. Our study analyses and compares the different scenarios in which thermal desorption comes beside traditional propulsion systems for extrasolar space exploration.     

Paths not taken – The Gossamer roadmap’s other options

Highly efficient low-thrust propulsion is increasingly applied beyond commercial use, also in mainstream and flagship science missions, in combination with gravity assist propulsion. Another recent development is the growth of small spacecraft solutions, not in size but in numbers and individual capabilities.Just over ten years ago, the DLR-ESTEC Gossamer Roadmap to Solar Sailing was set up to guide technology developments towards a propellant-less and highly efficient class of spacecraft for solar system exploration and applications missions: small spacecraft solar sails designed for carefree handling and equipped with carried application modules.Soon, in three dedicated Gossamer Roadmap Science Working Groups it initiated studies of missions uniquely feasible with solar sails such as Displaced L₁ (DL1) space weather advance warning and monitoring, Solar Polar Orbiter (SPO) delivery to very high inclination heliocentric orbit, and multiple Near-Earth Asteroid (NEA) rendezvous (MNR). Together, they demonstrate the capability of near-term solar sails to achieve at least in the inner solar system almost any kind of heliocentric orbit within 10 years, from the Earth-co-orbital to the extremely inclined, eccentric and even retrograde. Noted as part of the MNR study, sail-propelled head-on retrograde kinetic impactors (RKI) go to this extreme to achieve the highest possible specific kinetic energy for the deflection of hazardous asteroids.At DLR, the experience gained in the development of deployable membrane structures leading up to the successful ground deployment test of a (20 m)², i.e., 20 m by 20 m square solar sail at DLR Cologne in 1999 was revitalized and directed towards a 3-step small spacecraft development line from as-soon-as-possible sail deployment demonstration (Gossamer-1) via in-flight evaluation of sail attitude control actuators (Gossamer-2) to an envisaged proving-the-principle flight in the Earth-Moon system (Gossamer-3). First, it turned the concept of solar sail deployment on its head by introducing four separable Boom Sail Deployment Units (BSDU) to be discarded after deployment, enabling lightweight 3-axis stabilized sailcraft. By 2015, this effort culminated in the ground-qualified technology of the DLR Gossamer-1 deployment demonstrator Engineering Qualification Model (EQM). For mission types using separable payloads, such as SPO, MNR and RKI, design concepts can be derived from the BSDU characteristic of DLR Gossamer solar sail technology which share elements with the separation systems of asteroid nanolanders like MASCOT. These nano-spacecraft are an ideal match for solar sails in micro-spacecraft format whose launch configurations are compatible with ESPA and ASAP secondary payload platforms.Like any roadmap, this one contained much more than the planned route from departure to destination and the much shorter distance actually travelled. It is full of lanes, narrow and wide, detours and shortcuts, options and decision branches. Some became the path taken on which we previously reported. More were explored along the originally planned path or as new sidings in search of better options when circumstance changed and the project had to take another turn. But none were dead ends, they just faced the inevitable changes when roadmaps face realities and they were no longer part of the road ahead. To us, they were valuable lessons learned or options up our sleeves. But for future sailors they may be on their road ahead.     

A torus-shaped solar sail accelerated via thermal desorption of coating

A torus-shaped sail consists of a reflective membrane attached to an inflatable torus-shaped rim. The sail’s deployment from its stowed configuration is initiated by introducing inflation pressure into the toroidal rim with an attached circular flat membrane coated by heat-sensitive materials that undergo thermal desorption (TD) from a solid to a gas phase. Our study of the deployment and acceleration of the sail is split into three steps: at a particular heliocentric distance a torus-shaped sail is deployed by a gas inflated into the toroidal rim and the membrane is kept flat by the pressure of the gas; under heating by solar radiation, the membrane coat undergoes TD and the sail is accelerated via TD of coating and solar radiation pressure (SRP); when TD ends, the sail utilizes thrust only from SRP. We study the stability of the torus-shaped sail and deflection and vibration of the flat membrane due to the acceleration by TD and SRP.