James M. Longuski

Shape-Based Algorithm for Automated Design of Low-Thrust, Gravity-Assist Trajectories

Given the benefits of coupling low-thrust propulsion with gravity assists, techniques for easily identifying candidate trajectories would be extremely useful to mission designers. The computational implementation of an analytic, shape-based method for the design of low-thrust, gravity-assist trajectories is described. Two-body motion (central body and spacecraft) is assumed between the flybys, and the gravity-assists are modeled as discontinuities in velocity arising from an instantaneous turning of the spacecraft’s hyperbolic excess velocity vector with respect to the flyby body. The method is augmented by allowing coast arcs to be patched with thrust arcs on the transfers between bodies. The shape-based approach permits not only rapid, broad searches over the design space, but also provides initial estimates for use in trajectory optimization. Numerical examples computed with the shape-based method, using an exponential sinusoid shape, are presented for an Earth‐Mars‐Ceres rendezvous trajectory and an Earth‐Venus‐Earth‐Mars‐Jupiter flyby trajectory. Selected trajectories from the shape-based method are successfully used as initial estimates in an optimization program employing direct methods.

Graphical Method for Gravity-Assist Trajectory Design

A new analytical technique directly related to Tisserands criterion that permits the quick identification of all viable ballistic gravity-assist sequences to a given destination is introduced. The method is best presented by a simple graphical technique. The graphical technique readily demonstrates that gravity assists via Venus, Earth, and Jupiter are tremendously effective in sequences such as Venus-Earth-Earth-Jupiter and Venus-Earth-Mars-Earth. Estimates are made for the shortest flight times for a given launch energy to each planet. This graphical technique should provide mission designers with a potent tool for finding economical gravity-assist trajectories to many targets of high scientific interest in the solar system.

Spin-axis stabilization of symmetric spacecraft with two control torques

Abstract It is a well-known fact that a symmetric spacecraft with two control torques supplied by gas jet actuators is not controllable, if the two control torques are along axes that span the two-dimensional plane orthogonal to the axis of symmetry. However, feedback control laws can be derived for a restricted problem corresponding to attitude stabilization about the symmetry axis. In this configuration, the final state of the system is a uniform revolute motion about the symmetry axis. The purpose of this paper is to present a new methodology for constructing feedback control laws for this problem, based on a new formulation for the attitude kinematics.

Design and Optimization of Low-Thrust Trajectories with Gravity Assists

Missions such as Mariner 10, Voyager 1, Galileo, and Stardust all used gravity-assist flybys to achieve their mission goals efficiently. Methods to design such gravity-assist missions are fairly well developed and generally assume all major maneuvers are performed impulsively by chemical rockets. The recent success of the low-thrust Deep Space 1 mission demonstrates that low-thrust (high-efficiency) propulsion is ready to be used on future missions, potentially reducing the required propellant mass or the total time of flight. By combining both gravity-assist flybys and low-thrust propulsion, future missions could enjoy the benefits of both. To realize such missions, an effective design methodology is needed. A two-step approach to the design and optimization of low-thrust gravity-assist trajectories is described. The first step is a search through a broad range of potential trajectories. To speed up this search, a simplified shape-based trajectory model is used. The best trajectories are chosen using a heuristic cost function. The second step optimizes the most promising trajectories using an efficient parameter optimization. method. Examples of missions designed using this approach are presented, including voyages to Vesta, Tempel 1, Ceres, Jupiter, and Pluto.

Cycler orbit between Earth and Mars

A periodic orbit between Earth and Mars has been discovered that, after launch, permits a space vehicle to cycle back and forth between the planets with moderate maneuvers at irregular intervals. A Space Station placed in this cycler orbit could provide a safe haven from radiation and comfortable living quarters for astronauts en route to Earth or Mars. The orbit is largely maintained by gravity assist from Earth. Numerical results from multiconic optimization software are presented for a 15-year period from 1995 through 2010.

Automated design of gravity-assist trajectories to Mars and the outer planets

In this paper, a new approach to planetary mission design is described which automates the search for gravity-assist trajectories. This method finds all conic solutions given a range of launch dates, a range of launch energies and a set of target planets. The new design tool is applied to the problems of finding multiple encounter trajectories to the outer planets and Venus gravity-assist trajectories to Mars. The last four-planet grand tour opportunity (until the year 2153) is identified. It requires an Earth launch in 1996 and encounters Jupiter, Uranus, Neptune, and Pluto. Venus gravity-assist trajectories to Mars for the 30 year period 1995–2024 are examined. It is shown that in many cases these trajectories require less launch energy to reach Mars than direct ballistic trajectories.

Automated Design of the Europa Orbiter Tour

Before the Europa Orbiter can be placed in orbit about Europa, it will be placed into a 200-day Jovian orbit and targeted for Ganymede. After a series of gravity-assist flybys of the Galilean satellites, the orbital energy is reduced to lower the arrival hyperbolic excess velocity at Europa. These energy-saving techniques reduce the propellant cost for Europa orbit insertion to a minimum. Key constraints during the tour include total time of flight and radiation dosage. Tours may employ 10 or more encounters with the Jovian satellites; hence, there is an enormous number of possible sequences of these satellites. A graphical method based on Tisserands criterion is presented that greatly aids the design process. The Tisserand graph method facilitates the study of a wide range of arrival conditions, arrival dates, and satellite tours.

Circulating transportation orbits between earth and Mars

This paper describes the basic characteristics of circulating (cyclical) orbit design as applied to round-trip transportation of crew and materials between earth and Mars in support of a sustained manned Mars Surface Base. The two main types of nonstopover circulating trajectories are the socalled VISIT orbits and the Up/Down Escalator orbits. Access to the large transportation facilities placed in these orbits is by way of taxi vehicles using hyperbolic rendezvous techniques during the successive encounters with earth and Mars. Specific examples of real trajectory data are presented in explanation of flight times, encounter frequency, hyperbolic velocities, closest approach distances, and Delta V maneuver requirements in both interplanetary and planetocentric space.

Aerobraking tethers for the exploration of the solar system

Abstract In previous work the authors developed a model for the analysis of orbiting tethered spacecraft in an atmosphere. This model was used to demonstrate the feasibility of the aerobraking tether concept for a mission to Mars. The present work studies the possibility of using such vehicles in the exploration of the other atmosphere-bearing planets and satellites in the solar system. This includes Venus, Jupiter, Saturn, Uranus, Neptune and Titan. After establishing ground rules, a study is performed in which the propellant mass for a typical rocket propulsion system is compared to the tether mass required for the aerobraking system. In every case, the tether mass turns out to be less than the propellant mass. The results have significant implications for the design of a new class of exotic spacecraft for the exploration of the solar system.

A complex analytic solution for the attitude motion of a near-symmetric rigid body under body-fixed torques

Although analytic solutions for the attitude motion of a rigid body are available for several special cases, a comprehensive theory does not exist in the literature for the more complicated problems found in spacecraft dynamics. In the present paper, analytic solutions in complex form are derived for the attitude motion of a near-symmetric rigid body under the influence of constant body-fixed torques. The solution is very compact, which enables efficient and rapid machine computation. Numerical simulations reveal that the solution is very accurate when applied to typical spinning spacecraft problems.