New periodic orbits in the solar sail three-body problem

We identify displaced periodic orbits in the circular restricted three-body problem, wher the third (small) body is a solar sail. In particular, we consider solar sail orbits in the earth-sun system which are high above the exliptic plane. It is shown that periodic orbits about surfaces of artificial equilibria are naturally present at linear order. Using the method of Lindstedt-Poincare, we construct nth order approximations to periodic solutions of the nonlinear equations of motion. In the second part of the paper we generalize to the solar sail elliptical restricted three-body problem. A numerical continuation, with the eccentricity, e, as the varying parameter, is used to find periodic orbits above the ecliptic, starting from a known orbit at e=0 and continuing to the requied eccentricity of e=0.0167. The stability of these periodic orbits is investigated

On orbit validation of solar sailing control laws with thin-film spacecraft

Many innovative approaches to solar sail mission and trajectory design have been proposed over the years, but very few ever have the opportunity to be validated on orbit with real spacecraft. Thin- Film Spacecraft/Lander/Rovers (TF-SL Rs) are a new class of very low cost, low mass space vehicle which are ideal for inexpensively and quickly testing in flight new approaches to solar sailing. This paper describes using TF- SLR based micro solar sails to implement a generic solar sail test bed on orbit. TF -SLRs are high area- to-mass ratio (A/m) spacecraft developed for very low cost consumer and scientific deep space missions. Typically based on a 5 μm or thinner metalised substrate, they include an integrated avionics and payload system -on-chip (SoC) die bonded to the substrate with passive components and solar cells printed or deposited by Metal Organic Chemical Vapour Deposition (MOCVD). The avionics include UHF/S- band transceivers, processors, storage, sensors and attitude control provided by integrated magnetorquers and reflectivity control devices. Resulting spacecraft have a typical thickness of less than 50 μm, are 80 mm in diameter, and have a mass of less than 100 mg resulting in sail loads of less than 20 g/m 2 . TF -SLRs are currently designed for direct dispensing in swarms from free flying 0.5U Interplanetary CubeSats or dispensers attached to launch vehicles. Larger 160 mm, 320 mm and 640 mm diameter TF -SLRs utilizing a CubeSat compatible TWIST deployment mechanism that maintains the high A/m ratio are also under development. We are developing a mission to demonstrate the utility of these devices as a test bed for experimenting with a variety of mission designs and control laws. Batches of up to one hundred TF- SLRs will be released on earth escape trajectories, with each batch executing a heterogeneous or homogenous mixture of control laws and experiments. Up to four releases at different points in orbit are currently envisaged with experiments currently being studied in MATLAB and GMA T including managing the rate of separation of individual spacecraft, station keeping and single deployment/substantially divergent trajectory development. It is also hoped to be able to demonstrate uploading new experiment designs while in orbit and to make this capability available to researchers around the world. A suitable earth escape mission is currently being sought and it is hoped the test bed could be on orbit in 2017/18

Time-optimal formation establishment around a slowly rotating asteroid

A study is conducted to find a solution to the problem of time-optimal formation establishment around a slowly rotating asteroid, whose gravity is approximated as a second-degree and second-order gravitational field (SDSOGF). Similar to the methodology used for identifying the classical J2-invariant relative orbits, two necessary conditions are analytically derived to guarantee bounded relative motion in an SDSOGF. In particular, it is shown that when the nonspherical harmonic coefficients of the asteroid gravity are first-order small, the resulting necessary conditions are consistent with the recent literature results. Based on the analytically obtained constraints, the problem of time-optimal formation establishment is then emphasized via an indirect approach, in which the initial unknown costate vector is calculated with a scaling technique to alleviate its sensitivity to the initial guess problem

Natural and sail-displaced doubly-symmetric Lagrange point orbits for polar coverage

This paper proposes the use of doubly-symmetric, eight-shaped orbits in the circular restricted three-body problem for continuous coverage of the high-latitude regions of the Earth. These orbits, for a range of amplitudes, spend a large fraction of their period above either pole of the Earth. It is shown that they complement Sun-synchronous polar and highly eccentric Molniya orbits, and present a possible alternative to low thrust pole-sitter orbits. Both natural and solar-sail displaced orbits are considered. Continuation methods are described and used to generate families of these orbits. Starting from ballistic orbits, other families are created either by increasing the sail lightness number, varying the period or changing the sail attitude. Some representative orbits are then chosen to demonstrate the visibility of high-latitude regions throughout the year. A stability analysis is also performed, revealing that the orbits are unstable: it is found that for particular orbits, a solar sail can reduce their instability. A preliminary design of a linear quadratic regulator is presented as a solution to stabilize the system by using the solar sail only. Finally, invariant manifolds are exploited to identify orbits that present the opportunity of a ballistic transfer directly from low Earth orbit

Easily retrievable objects among the NEO population

Asteroids and comets are of strategic importance for science in an effort to understand the formation, evolution and composition of the Solar System. Near-Earth Objects (NEOs) are of particular interest because of their accessibility from Earth, but also because of their speculated wealth of material resources. The exploitation of these resources has long been discussed as a means to lower the cost of future space endeavours. In this paper, we consider the currently known NEO population and define a family of so-called Easily Retrievable Objects (EROs), objects that can be transported from accessible heliocentric orbits into the Earth’s neighbourhood at affordable costs. The asteroid retrieval transfers are sought from the continuum of low energy transfers enabled by the dynamics of invariant manifolds; specifically, the retrieval transfers target planar, vertical Lyapunov and halo orbit families associated with the collinear equilibrium points of the Sun-Earth Circular Restricted Three Body problem. The judicious use of these dynamical features provides the best opportunity to find extremely low energy Earth transfers for asteroid material. A catalogue of asteroid retrieval candidates is then presented. Despite the highly incomplete census of very small asteroids, the ERO catalogue can already be populated with 12 different objects retrievable with less than 500 m/s of Δv. Moreover, the approach proposed represents a robust search and ranking methodology for future retrieval candidates that can be automatically applied to the growing survey of NEOs

Long-term perturbations due to a disturbing body in elliptic inclined orbit

In the current study, a double-averaged analytical model including the action of the perturbing body's inclination is developed to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials truncated up to the second-order term, and then is averaged over the periods of the spacecraft and the perturbing body. The efficiency of the double-averaged algorithm is verified with the full elliptic restricted three-body model. Comparisons with the previous study for a lunar satellite perturbed by Earth are presented to measure the effect of the perturbing body's inclination, and illustrate that the lunar obliquity with the value 6.68\degree is important for the mean motion of a lunar satellite. The application to the Mars-Sun system is shown to prove the validity of the double-averaged model. It can be seen that the algorithm is effective to predict the long-term behavior of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged model presented in this paper is also applicable to other celestial systems.Comment: 28 pages, 6 figure

Extension of Earth-Moon libration point orbits with solar sail propulsion

This paper presents families of libration point orbits in the Earth-Moon system that originate from complementing the classical circular restricted three-body problem with a solar sail. Through the use of a differential correction scheme in combination with a continuation on the solar sail induced acceleration, families of Lyapunov, halo, vertical Lyapunov, Earth-centred, and distant retrograde orbits are created. As the solar sail circular restricted three-body problem is non-autonomous, a constraint defined within the differential correction scheme ensures that all orbits are periodic with the Sun’s motion around the Earth-Moon system. The continuation method then starts from a classical libration point orbit with a suitable period and increases the solar sail acceleration magnitude to obtain families of orbits that are parametrised by this acceleration. Furthermore, different solar sail steering laws are considered (both in-plane and out-of-plane, and either fixed in the synodic frame or fixed with respect to the direction of sunlight), adding to the wealth of families of solar sail enabled libration point orbits presented. Finally, the linear stability properties of the generated orbits are investigated to assess the need for active orbital control. It is shown that the solar sail induced acceleration can have a positive effect on the stability of some orbit families, especially those at the L2 point, but that it most often (further) destabilises the orbit. Active control will therefore be needed to ensure long-term survivability of these orbits

Deep neural networks of Optimal Low-Thrust Orbit Raising

Geostationary Earth orbit (GEO) satellites are of great significance in the space market. Low-thrust propulsion has been highly developed in the last decades because it is fuel saving. Therefore, the design of GEO satellites is rapidly changing from classic high-thrust propulsion more and more toward low-thrust propulsion. However, the transfer time will be quite long using low-thrust propulsion and it will be very expensive if the ground supports the whole orbit raising. Therefore, autonomous orbit raising is necessary. Deep neural networks are trained to learn the optimal control. Results show that DNNs can be applied in this long-duration optimal control problem and have excellent performance

Periodic orbits related to the equilibrium points in the potential of Irregular-shaped minor celestial bodies

Abstract We presented an overview of detailed continuation results of periodic orbit families which emanate from the equilibrium points (EPs) of irregular-shaped minor celestial bodies (hereafter called minor bodies). The generation and annihilation of periodic orbits (POs) related to the EPs are discussed in detail. The branch points of families of POs are also investigated. We presented 3D bifurcation diagrams for periodic orbits families emanating from the EPs of minor bodies which have five EPs totally. Structures of the 3D bifurcation diagrams depend on the distribution of EPs with different topological classifications. We calculated orbit families emanating from the EPs of asteroids 433 Eros and 216 Kleopatra, including the Lyapunov orbit family, the Vertical orbit family, the orbit families bifurcating from the Vertical orbit family, as well as the nonplanar orbit family