Displaced solar sail orbits : dynamics and applications

We consider displaced periodic orbits at linear order in the circular restricted Earth-Moon system, where the third massless body is a solar sail. These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. Prior results have been developed by using an optimal choice of the sail pitch angle, which maximises the out-of-plane displacement. In this paper we will use solar sail propulsion to provide station-keeping at periodic orbits around the libration points using small variations in the sail's orientation. By introducing a first-order approximation, periodic orbits are derived analytically at linear order. These approximate analytical solutions are utilized in a numerical search to determine displaced periodic orbits in the full nonlinear model. Applications include continuous line-of-sight communications with the lunar poles

On the stability of displaced two-body lunar orbits

In a prior study, a methodology was developed for computing approximate large displaced orbits in the Earth-Moon circular restricted three-body problem (CRTBP)by the Moon-Sail two-body problem. It was found that far from the L1 and L2 points, the approximate two-body analysis for large accelerations matches well with the dynamics of displaced orbits in relation to the three-body problem. In the present study, the linear stability characteristics of the families of approximate periodic orbits are investigated

Analysis and control of displaced periodic orbits in the Earth-Moon system

We consider displaced periodic orbits at linear order in the circular restricted Earth-Moon system, where the third massless body is a solar sail. These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. In this paper we will use solar sail propulsion to provide station-keeping at periodic orbits above the L2 point. We start by generating a reference trajectory about the libration points. By introducing a first-order approximation, periodic orbits are derived analytically at linear order. These approximate analytical solutions are utilized in a numerical search to determine displaced periodic orbits in the full nonlinear model. Because of the instability of the collinear libration points, orbit control is needed for a spacecraft to remian in the vicinity of these points. The reference trajectory is then tracked using a linear Quadratic Regulator (LQR). Finally, simulations are given to validate the control strategy. The importance of finding such displaced orbits is to obtain continuous communications between the equatorial regions of the Earth and the polar regions of the Moon

Solar sail orbits at the Earth-Moon libration points

Solar sail technology offers new capabilities for the analysis and design of space missions. This new concept promises to be useful in overcoming the challenges of moving throughout the solar system. In this paper, novel families of highly non-Keplerian orbits for solar sail spacecraft at linear order are investigated in the Earth-Moon circular restricted three body problem, where the third body is a solar sail. In particular, periodic orbits near the collinear libration points in the Earth-Moon system will be explored along with their applications. The dynamics are completely different from the Earth-Sun system in that the Sun line direction constantly changes in the rotating frame but rotates once per synodic lunar month. Using an approximate, first order analytical solution to the nonlinear nonautonomous ordinary differential equations, periodic orbits can be constructed that are displaced above the plane of the restricted three-body system. This new family of orbits have the property of ensuring visibility of both the lunar far-side and the equatorial regions of the Earth, and can enable new ways of performing lunar telecommunications

Solar sail trajectories at the Earth-Moon Lagrange points

Paper presented during Session 3, Orbital Dynamics, Symposium C1, Astrodynamics, Paper Number 13. This paper investigates displaced periodic orbits at linear order in the circular restricted Earth-Moon system, where the third massless body is a solar sail. These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. The solar sail Earth-Moon system differs greatly from the Earth-Sun system as the Sun line direction varies continuously in the rotating frame and the equations of motion of the sail are given by a set of nonlinear non-autonomous ordinary differential equations. By introducing a first-order approximation, periodic orbits are derived analytically at linear order. These approximate analytical solutions are utilized in a numerical search to determine displaced periodic orbits in the full nonlinear model. The importance of finding such displaced orbits is to obtain continuous communications between the equatorial regions of the Earth and the polar regions of the Moon. As will be shown, displaced periodic orbits exist at all Lagrange points at linear order

Displaced periodic orbits with low-thrust propulsion

Solar sailing and solar electric technology provide alternative forms of spacecraft propulsion. These propulsion systems can enable exciting new space-science mission concepts such as solar system exploration and deep space observation. The aim of this work is to investigate new families of highly non-Keplerian orbits, within the frame of the Earth-Moon circular restricted three-body problem (CRTBP), where the third massless body utilizes a hybrid of solar sail and a solar electric thruster. The augmented thrust acceleration is applied to ensure a constant displacement periodic orbit above L2, leading to simpler tracking from the lunar surface for communication applications. Using an approximate, first order analytical solution to the nonlinear non-autonomous ordinary differential equations, periodic orbits can be derived that are displaced above/below the plane of the CRTBP

Asymptotic analysis of displaced lunar orbits

The design of spacecraft trajectories is a crucial task in space mission design. Solar sail technology appears as a promising form of advanced spacecraft propulsion which can enable exciting new space science mission concepts such as solar system exploration and deep space observation. Although solar sailing has been considered as a practical means of spacecraft propulsion only relatively recently, the fundamental ideas are by no means new (see McInnes1 for a detailed description). A solar sail is propelled by reflecting solar photons and therefore can transform the momentum of the photons into a propulsive force. Solar sails can also be utilised for highly non-Keplerian orbits, such as orbits displaced high above the ecliptic plane (see Waters and McInnes2). Solar sails are especially suited for such non-Keplerian orbits, since they can apply a propulsive force continuously. In such trajectories, a sail can be used as a communication satellite for high latitudes. For example, the orbital plane of the sail can be displaced above the orbital plane of the Earth, so that the sail can stay fixed above the Earth at some distance, if the orbital periods are equal (see Forward3). Orbits around the collinear points of the Earth-Moon system are also of great interest because their unique positions are advantageous for several important applications in space mission design (see e.g. Szebehely4, Roy,5 Vonbun,6 Thurman et al.,7 Gomez et al.8, 9). Several authors have tried to determine more accurate approximations (quasi-Halo orbits) of such equilibrium orbits10. These orbits were first studied by Farquhar11, Farquhar and Kamel10, Breakwell and Brown12, Richardson13, Howell14, 15.If an orbit maintains visibility from Earth, a spacecraft on it (near the L2 point) can be used to provide communications between the equatorial regions of the Earth and the lunar poles. The establishment of a bridge for radio communications is crucial for forthcoming space missions, which plan to use the lunar poles.McInnes16 investigated a new family of displaced solar sail orbits near the Earth-Moon libration points.Displaced orbits have more recently been developed by Ozimek et al.17 using collocation methods. In Baoyin and McInnes18, 19, 20 and McInnes16, 21, the authors describe new orbits which are associated with artificial Lagrange points in the Earth-Sun system. These artificial equilibria have potential applications for future space physics and Earth observation missions. In McInnes and Simmons22, the authors investigate large new families of solar sail orbits, such as Sun-centered halo-type trajectories, with the sail executing a circular orbit of a chosen period above the ecliptic plane. We have recently investigated displaced periodic orbits at linear order in the Earth-Moon restricted three-body system, where the third massless body is a solar sail (see Simo and McInnes23). These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. It was found that for a given displacement distance above/below the Earth-Moon plane it is easier by a factor of order 3.19 to do so at L4=L5 compared to L1=L2 - ie. for a fixed sail acceleration the displacement distance at L4=L5 is greater than that at L1=L2. In addition, displaced L4=L5 orbits are passively stable, making them more forgiving to sail pointing errors than highly unstable orbits at L1=L2.The drawback of the new family of orbits is the increased telecommunications path-length, particularly the Moon-L4 distance compared to the Moon-L2 distance

Potential Effects of a Realistic Solar Sail and Comparison to an Ideal Sail

Solar sail technology offers new capabilities for space missions due to the opportunities for non-Keplerian orbits. In this paper, novel families of highly non-Keplerian orbits for spacecraft utilising solar sail at linear order are investigated in the Earth-Moon circular restricted three-body problem. Firstly, it is assumed implicitly that the solar sail is a perfect reflector. Based upon the first-order approximation, an analytical formulation of the periodic orbits at linear order is presented. The approximate analytical solutions offer useful insights into the nature of the motion in the vicinity of the libration points, and are used to give periodic solutions numerically in the full nonlinear system. These orbits were accomplished by using an optimal choice of the sail pitch angle, which maximize the out-of-plane distance. Thereafter, the resulting effects of the non-ideal flat sail model have been computed and compared with an ideal solar sail. A square sail configuration, which is likely to be chosen for various near-term sail missions is used to illustrate the concept. The main effect of the non-perfect sail is to reduce the out-of-plane displacement distance which may be achieved for a given characteristic acceleration. It is also observed that there is a significant deviation in force magnitude between the realistic solar sail and the ideal solar sail model

Designing displaced lunar orbits using low-thrust propulsion

The design of spacecraft trajectories is a crucial task in space mission design. Solar sail technology appears as a promising form of advanced spacecraft propulsion which can enable exciting new space science mission concepts such as solar system exploration and deep space observation. Although solar sailing has been considered as a practical means of spacecraft propulsion only relatively recently, the fundamental ideas are by no means new (see McInnes1 for a detailed description). A solar sail is propelled by re ecting solar photons and therefore can transform the momentum of the photons into a propulsive force. This article focuses on designing displaced lunar orbits using low-thrust propulsion

Present and potential land use mapping in Mexico

The Mexican Water Plan (MWP) conducted studies of present and potential land use in Mexico using LANDSAT-1 satellite imagery. Present land use studies were carried out all over the country (197 million hectares); nine soil uses were mapped according to the first classification level recommended by the U.S. Geological Survey. Also 6.3 million hectares of land with advanced erosion were detected. Work was executed at a rate of 8 million hectares per month; reliability was 90% and the cost of only 0.1 cents/hectare. The potential land use study was performed in 45 million hectares at a rate of 4 million hectares per month and at a cost of 0.33 cents/hectare. Soil units according to FAO classification were delineated scale 1:1 million; interpretative maps were also prepared dealing with potential agricultural productivity carrying capacity for cattle, water, erosion risk, and slope ranges