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 , 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 
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. , Koon et al. ), e.g., the recently proposed
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
mission (Sweetser et al. ; Ludwinski et al. ).
Furthermore, the rest of the outer solar system could be opened up to
detailed exploration in later missions using this approach
and Arberg ).
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.