The interplanetary transport network. Gravitational tugs of the different planets and their moons create a vast network of passageways by which a spacecraft can travel over large distances while expending very little energy. (Image Courtesy of NASA/JPL, Artist: Cici Koenig)
The mathematical study of how artificial and natural objects move in the solar system is called celestial mechanics. Closely related to celestial mechanics is the subject of dynamical systems, which interprets the motion of an object using geometry. There are three key ideas from celestial mechanics and dynamical systems that are used to reveal the interplanetary transport network.
Credit: Jen Christiansen (for American Scientist)
The first idea is the existence of
Lagrange points, points in space where the net forces on an object placed at that point are zero. Spacecraft can even go into orbit around a Lagrange point, even though the point has no mass.
Credit: Jen Christiansen (for American Scientist)
The second idea is that here are
tubes of trajectories which approach and depart Lagrange point orbits; they're called stable and unstable manifolds.
Credit: Jen Christiansen (for American Scientist)
The third idea is that the many planets and moons create a network of these tubes twirling through space which are well suited for space travel. Where two different
tubes intersect, one has a heteroclinic trajectory. If a spacecraft is placed on such a trajectory, it will move a large distance under the influence of gravity and without the use of any fuel.
So it is possible for a spacecraft to travel huge distances in space just by hopping from the neighborhood of one Lagrange point to another.