Trade-Off Between Fuel and Time Optimization

Shane D. Ross
Control and Dynamical Systems, California Institute of Technology
MC 107-81, Pasadena, CA 91125, USA. E-mail:


Several studies have shown that low fuel consumption (measured as low Delta-V's) can be achieved at the expense of a long time of flight by taking advantage of N-body effects and repeated gravity assists. However, the flight time required for some low Delta-V missions can be prohibitively long. The purpose of the present study is to determine the trade-off between Delta-V and flight time for an example problem. Using the planar, circular, restricted three-body problem as the model, we study trajectories from an Earth orbit to the Earth's moon.

Using the method of Schroer and Ott [1997], together with methods for achieving ballistic capture (Koon, Lo, Marsden, and Ross [2000,2001]), we find a transfer with a flight time of 65 days which uses a total Delta-V of 860.1 m/s. Thus we take one-tenth of the time as the Bollt and Meiss [1995] trajectory using only about 100 m/s more fuel.

This method of determining the Delta-V vs. time of flight trade-off has been applied to only one three-body system thus far. As a continuation of this work, we will adapt the method to missions in N-body systems (N > 3) systems, such as a mission to orbit multiple moons of Jupiter (Gomez et al. [2001], Koon et al. [2002]), e.g., the recently proposed Jupiter Icy Moons Orbiter. The development of sophisticated control technology for this mission would not only make it possible to consider a realistic mission for orbiting three of Jupiter's planet-size moons -- Callisto, Ganymede and Europa -- one after the other, it would also reduce fuel costs compared to the previously proposed Europa Orbiter mission (Sweetser et al. [1997]; Ludwinski et al. [1998]). Furthermore, the rest of the outer solar system could be opened up to detailed exploration in later missions using this approach (Burris and Arberg [2002]). This trade-off method has been applied to only one three-body system thus far. In the future, we wish to adapt the method to missions combining several restricted three-body systems.

extended abstract (pdf)