Survey of spacecraft trajectory design in strongly perturbed environments

A S KEPLER pointed out centuries ago, the motion of a spacecraft governed by a gravitating point mass is a wellbehaved conic section. In the low-energy regime, the conic section transcribes an ellipse and the motion is periodic and stable. Furthermore, the gravitational potential of a spherical mass with radially symmetric density is identical to that of a simple point mass located at the center of the sphere. Despite the fact that many perturbations are important when considering high-precision Earthorbiting applications, all perturbations combined are generally less than one part in a thousand compared with the dominant two-body term due to a spherical Earth. Therefore, the motion of a low-Earthorbiting ballistic spacecraft is very near periodic, and changes to the qualitative motion are slowly time-varying. For these reasons, the near-Earth environment indeed can be considered dynamically benign when compared with a great number of other locations of interest for space missions in our solar system. For the purposes of this paper, we will therefore consider strongly perturbed environments as those exotic locales beyond the near-Earth environment where perturbations to the Kepler two-body problem are no longer small. Notable examples of space missions in such highly perturbed dynamical environments include lunar missions; grand tours of the solar system and planetary satellite systems propelled by gravityassisted flybys; orbiters around major planetary satellites such as Jupiter’s Galilean moons and Saturn’s Titan and Enceladus; and missions to very small and irregular-shaped bodies such as comets, asteroids, and small planetary satellites. Drawing from common models such as patched conics of interplanetary missions and the restricted three-body problem (RTBP) of the libration point missions, this paper is organized in terms of the dominant perturbation forces on a spacecraft. The focus of this survey includes the wide-reaching perturbations that permeate globally the spacecraft environment over the course of a mission. Included are the third-body (TB) nonspherical gravity (NSG) and solar radiation pressure (SRP) perturbations. In their simplified forms, each of the main perturbations can be expressed as part of an autonomous and conservative dynamical system. Therefore, the ensuing analyses can benefit from a host of tools and insights including integrals of motion and system averaging that assist fast numerical methods and the recovery of equilibria and secular trends. Mission destinations of interest to the space science and space flight communities are discussed according to their respective dynamic environments. Special attention is given to orbit mechanics and its impact on mission and trajectory design techniques in the context of past and planned space missions to these dynamically rich environments. Mission classes and design techniques considered include lowand high-altitude orbiters, grand tour trajectories, patched conics, gravity-assistedflybys, Tisserand graphs, three-body models, periodic orbits, orbit averaging, and stable/unstable manifold design. A main result of this survey is a mission design reference (see Table 1 and the associated Fig. 1) that quantifies the absolute and relative importance of the main perturbations terms in the dynamic environments of many target bodies. It is acknowledged that atmospheric drag can induce extreme spacecraft heating and torques in the case of aerobraking, aerocapture, or entry decent and landing for missions to bodies with significant atmospheres such as Earth, Mars, Venus, or Titan. However, such extreme drag-related events are generally restricted to brief mission phases and can often be treated as nonpropellant propulsion (energy reducing) sources in the overall mission trajectory design. Therefore, atmospheric drag is not included in the scope of the paper. Finally, in the context of asteroids and comets, it is worth noting that small forces such as the Yarkovski and Yarkovsky–O’Keefe–Radzievskii– Paddacky (YORP) effects (arising mainly from imbalanced thermal radiation) and outgassing are important in the consideration of longterm small body orbital and spin rate evolution [1]. However, their indirect perturbations on the short-term dynamics of a nearby spacecraft are too small to warrant consideration in the current scope. For further information on the details and relative importance of dynamical perturbations on spacecraft in both the Earth and interplanetary environments, see [2–4].