Road Trip On The Interplanetary Superhighway

eegad writes: "CNN has an article about a new idea from NASA springing from chaos theory called the interplanetary superhighway. It will purportedly allow easier space travel by steering through regions where the net gravitational force exerted by nearby bodies is smallest. The actual NASA news release is here. Sounds like an interesting concept but it is unclear how the scientists will account for every source of gravity, including the elusive dark matter."

Comments

Computing versus solving

[sjbe]

You're right in that we (so far) cannot solve (in the sense of a mathematical proof) a 3 body problem using nice neat equations like we can for 2 body problems. However it is possible to calculate a trajectory and has been for some time. Takes a reasonably large amount of computing horsepower and a good idea of the initial conditions but a useful approximation can be calculated. Not an elegant or exact method but does work.

Another overhyped article

[BlowCat]

My understanding is that the JPL come with a way to calculate gravitational effects with more precision, thus saving fuel required to correct the orbit. Hardly anything exciting, but it became the "planet freeway" in the journalist's imagination. Another uninformed, overhyped article on CNN, not to mention the "Artist's concept of interplanetary superhighway", apparently not reviewed by any knowlegeable person.

The reference to "dark matter" makes no sence to anybody ever studied general relativity. External gravitational field doesn't vary significantly in the Solar system, therefore it's irrelevant. Even if we all accelerate in the gravitational field of some dark matter, we do it uniformly.

Re:3-body problem?

[EccentricAnomaly]

There's a faster converging series given by Steffensen (in german):
Steffensen, J.F.: 1957, 'On the Problem of Three Bodies in the Plane', Mat. Fys. Medd. Dansk. vid. Selskap. 31, No. 3.

Roger Brouke also gives a solution to the n-body problem using Steffensen's method (in english):
Brouke, R.,: 1971, 'Solution of the N-Body Problem With Recurrent Power Series', Celestial Mechanics, No. 4, pp. 110-115.

Painleve proved that there were no more integrals of the motion in the 3+ body problem when the mass of bodies were free to change (e.g., with collisions). This means, in this case, that the method used to solve the two-body problem won't work for 3 or more bodies. These series methods don't require integrals of the motion and work just fine for the 3+ body problem.

Numerical integration usually uses methods similar to these series solutions, but numerical integration only provides a single solution for a specific initial condition. These series solutions are general and provide the solution for any initial condition.