Invariant manifolds, discrete mechanics, and trajectory design for a mission to Titan

With an environment comparable to that of primordial Earth, a surface strewn with liquid hydrocarbon lakes, and an atmosphere denser than that of any other moon in the solar system, Saturn's largest moon Titan is a treasure trove of potential scientific discovery and is the target of a proposed NASA mission scheduled for launch in roughly one decade. A chief consideration associated with the design of any such mission is the constraint imposed by fuel limitations that accompany the spacecraft's journey between celestial bodies. In this study, we explore the use of patched three-body models in conjunction with a discrete mechanical optimization algorithm for the design of a fuel-efficient Saturnian moon tour focusing on Titan. In contrast to the use of traditional models for trajectory design such as the patched conic approximation, we exploit subtleties of the three-body problem, a classic problem from celestial mechanics that asks for the motion of three masses in space under mutual gravitational interaction, in order to slash fuel costs. In the process, we demonstrate the aptitude of the DMOC (Discrete Mechanics and Optimal Control) optimization algorithm in handling celestial mechanical trajectory optimization problems

A survey of impulsive trajectories Final report

Literature survey of astrodynamics problems on intercept, transfer, and rendezvous trajectorie

Navigation Solution for a Multiple Satellite and Multiple Ground Architecture

This research presents the phased development of an algorithm to plan impulsive orbital maneuvers based on the relative motion between multiple satellites and multiple ground locations. The algorithm leverages the state transition matrix derived from the equations of motion and the equations of variation for the non-spherical Earth and air drag effects. The algorithm determines the impulsive maneuver to achieve the user-defined terminal conditions. The first phase solves for the first burn of an orbital transfer between user-defined altitudes. The optimum trajectory is determined and compared to the first burn in a Hohmann Transfer. The results are expanded to include varying the inclination and eccentricity of the initial orbit. The second phase solves for the minimum time trajectory resulting from a fixed fuel maneuver to transfer a satellite between user-defined altitudes. The results include the transfer time and transfer angle for the minimum time trajectory. The third phase places a satellite within a sphere, of user-defined radius, centered on a non-maneuvering satellite within a constrained time. The results are presented for prograde orbits. An empirical method to determine the optimum Delta V is provided. The fourth phase places a satellite within the overlapping spheres, of user-defined radii, centered on multiple non-maneuvering satellites, within a constrained time. Empirical methods are presented to determine the separation distance and optimum Delta V. The final phase culminates by delivering a satellite within the overlapping spheres, centered on multiple non-maneuvering satellites and ground locations, constrained by range and elevation angle, within a constrained time. An empirical model to calculate the optimum Delta V is shown. All results illustrate mission design trade-offs including ballistic coefficient, orbit inclinations, eccentricity and orbit sizes

Geosynchronous Earth Orbit/Low Earth Orbit Space Object Inspection and Debris Disposal: A Preliminary Analysis Using a Carrier Satellite With Deployable Small Satellites

Detailed observations of geosynchronous satellites from earth are very limited. To better inspect these high altitude satellites, the use of small, refuelable satellites is proposed. The small satellites are stationed on a carrier platform in an orbit near the population of geosynchronous satellites. A carrier platform equipped with deployable, refuelable SmallSats is a viable option to inspect geosynchronous satellites. The propellant requirement to transfer to a targeted geosynchronous satellite, perform a proximity inspection mission, and transfer back to the carrier platform in a nearby orbit is determined. Convex optimization and traditional optimization techniques are explored, determining minimum propellant trajectories. Propellant is measured by the total required change in velocity, delta-v. The trajectories were modeled in a relative reference frame using the Clohessy-Wiltshire equations. Mass estimations for the carrier platform and the SmallSat were determined by using the rocket equation. The mass estimates were compared to the mass of a single, non-refuelable satellite performing the same geosynchronous satellite inspection missions. From the minimum delta-v trajectories and the mass analysis, it is determined that using refuelable SmallSats and a carrier platform in a nearby orbit can be more effcient than using a single non-refuelable satellite to perform multiple geosynchronous satellite inspections

Minimum-fuel aeroassisted coplanar orbit transfer using lift-modulation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76271/1/AIAA-19945-331.pd