Chaotic Orbits


This morning I was reading about the interplanetary superhighway. It’s kinda interesting. Rather than thinking about the solar system as objects in elliptical orbits around the sun and using a Hohmann transfer orbit to get around, you think of the planet-sun systems (and planet-moon systems) and their Lagrange points. The first and second Lagrange points have orbits around them, and these orbits have sets of paths into and out of them. These orbits act as portals that transport objects from outside the orbit of the planet to orbits around the planet, and take objects orbiting around the planet to inside the orbit of the planet. There are other paths back as well. Following these paths allow you to get around the solar system using very little energy.

In Martin Lo’s words:

In the Copernican model, the Solar System is a series of planets moving in nearly circular orbits isolated from one another. […] Its conic-centric view is a legacy of the pre- computer age. Without the computer, it is hopeless to compute anything very far from a conic orbit.

The computer age gave nonlinear dynamics a new birth. The invariant manifolds of the IPS which were theoretical curiosities before, all of a sudden now can be computed and analyzed with the computer. The Three Body Problem which gave Newton headaches can now form the basis of a new model of the Solar System. The IPS models the Solar System as a series of Three Body Problems which are coupled.

Seeing such a complex array of chaotic behavior, one is tempted to despair. But just the opposite is true. This complex jumble can be analyzed and classified with the utmost precision using modern mathematical and computational methods. Furthermore, the existence of deterministic chaos is the source of “Low Energy Transport” within the Solar System. It is precisely deterministic chaos which permitted the design of a completely ballistic trajectory for the Genesis Mission […].


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Russell O’Connor: contact me