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

come on....

[LMCBoy]

Dark Matter?! Absolutely negligible on interplanetary scales.

Confirmation at last

[Darth_brooks]

let's look at the facts: Big government bureaucracy. Foul smelling, funny looking employees. Interplanetary highway construction. It's all there in black and white.

NASA is run by the Vorgons.

Re:Confirmation at last

[Emugamer]

PROBABILITY .......... Infinity Minus One that NASA's metric ->english conversion will allow an accurate Interplanetary Highway to be built

Infinite Improbability Drive
Bush's Rise to Power

3-body problem?

[jedwards]

the sun is pulling, the Earth and moon and other objects are constantly pulling," said Martin Lo of NASA's Jet Propulsion Laboratory in Pasadena, California.

"Our theory has refined to the point where we can actually compute these trajectories

Really? I thought the 3-body problem was not solvable.

Re:3-body problem?

[gilroy]

Blockquoth the poster:

Really? I thought the 3-body problem [uoregon.edu] was not solvable.

It's not solvable analytically. But it's a breeze to model the diff eq's. Doing it accuractely for long can be tricky, though...

Re:3-body problem?

[LMCBoy]

You can't solve the three-body problem for a general case (meaning analytically, with the solution written as an equation). You can numerically model the behavior of a gravitational system with many bodies, given some initial conditions.

However, over time your numerical model will deviate more and more from the real evolution of the system. As long as the timescale of this error growth is much longer than a typical spacecraft's travel time, these numerical models are good enough to predict orbital trajectories accurately. Given that current models are estimated to be accurate for many thousands of years, it's no problem.

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.

it's local, folks

[gung-ho iguana]

The research is about finding low-cost paths through the solar system, not interstellar space. The dynamics of the solar system are very well understood, and all of the important gravitating bodies are known (there isn't any significant dark matter inside the solar system, by the way). You just have to do some heavy-duty computations to take advantage of all that.

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.

its called falling

[Edmund Blackadder]

any "effect" where you use grvity to move with zero fuel is called falling.

no need to give it fancy names.

Re:Warp Theory

[Alien54]

between the stars to minimize gravitational distortions affecting their flight path

Which makes sense for interstellar travel.

in interplanetary travel, these areas are probably constantly shifting, and so I wonder if the speed of shift is faster or slower than current space craft.

• Each planet and moon has five locations in space called Lagrange points, where one body's gravity balances another's. Spacecraft can orbit there while burning very little fuel. To find the Interplanetary Superhighway, Lo mapped all the possible flight paths among the Lagrange points, varying the distance the spacecraft would go and how fast or slow it would travel. Like threads twisted together to form a rope, the possible flight paths formed tubes in space. Lo plans to map out these tubes for the whole solar system.

They apparently delivered the software tool to NASA back in 2000.

The Layman's Translation

[MadFarmAnimalz]

Scientist1: Well, it appears that there's some parts of space where there's no gravitational pull. So, if we chuck the craft along one of these paths, it will umm...
Scientist2: It will probably need less energy.
Scientist1: Right. Since it doesn't have to do any work counteracting any gravity.
Reporter: Makes sense fellas. Now, you called a press conference. What's that all about?
Scientist1: Well, that was it.
Reporter: (short pause) I see. (another longer pause - an uncomfortable silence, actually) Now, seeing as you just worked this out, how did you fly craft before then?
Scientist2: Well, gas was so cheap and all...
(Scientist2 slaps Scientist1 and NASA lose what funding they have left)

IN RELATED NEWS: Liberal Arts graduate? Want to work for the JPL? We're hiring! Call NOW!

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.

Hard to get a driver's licence though

[Subcarrier]

I'd hate to take the written exams to pilot one my own space wagon, though.

You are at an intersection of 17 interstellar space lanes. You will now listen to the astrogation control channel for 30 seconds. Choose an entry vector to the roundabout, calculate a trajectory towards the Hyades Cluster, and engage warp drive. Remember to follow the astrogation control channel protocol. Refer to the attached astrogation table for nearby mass concentrations. You have two minutes to complete the procedure.

The driving test should be much better: you just grab the joystick, stamp on the warp pedal, and hope for the best.

Re:Chaos theory itself also rules this out...

[exploder]

Actually if either of you had bothered to do a Google search for "Lagrange Points", you'd know (at least) three things:

• Lagrange Points don't just refer two any two bodies, but to two bodies orbiting each other.
• They are not points where gravity "exactly balances out", but rather where the combined gravity of the two bodies exactly cancels the centripetal acceleration needed to rotate along with them.
• There are exactly five. (But two are unstable if the mass ratio is too low, below 25 or so)

Chaos theory mandates this

[WolfWithoutAClause]

The point is that the earlier you know that you are off the correct path, the earlier you can correct it, the less fuel you need to spend.

Contrary to what you say, the position of the planets is known to astonishing accuracy- it's only over millions of years that they move significantly chaotically, over a few months their position is entirely known.

A small body bouncing around between them is rather different however- that can be very chaotic.

Plotting a course through the solar system is quite routinely achieved. Remember Voyager?

Uh, wouldn't there be *TWO* such points? Think about it.

Do a web search on Lagrange points, you'll find it. There's 5. One between the earth and moon, one the other side of the moon, one opposite from the moon, one 60 degrees ahead of the moon and one 60 degrees behind.

Re:Chaos theory itself also rules this out...

[WolfWithoutAClause]

All the action takes place into a rotational reference frame, so you have to factor in some subtle forces like the Coriolis Force [uoregon.edu].

Actually not the coriolis force. In the frame rotating about the center of mass you only have to consider gravity and the 'centrifugal force'. If you draw a map of the overall forces you find that there are 5 points in the rotating frame where there are no overall forces acting; these are the lagrange points. It's all amazingly elegant actually.

The coriolis forces are important when you are moving around in this rotating frame however.

(mis)understanding the paper...

[slew]

Nowhere did Mr. Lo describe in his paper that the gravity cancels out on these paths (only that they were minimum energy and connected the Lagrange points).

The whole idea of a minimum energy paths through the solar system is that it's a dynamical systems of greater than 2 dimensions. The weird thing about dynamical systems of 3 dimensions is that trajectories in some of these systems exhibit a type of predictability called a "strange" attractor.

Strange attractors for trajectories are different than the attractors you normally see in 2 dimensions (like local minima or orbits that retrace themselves) in that small pertubations can cause greatly divergent behavior. Even though the behavior appears chaotic, in some systems, the behavior can still be described as nearby a "strange" attractor. This is effect is often called chaos, and the study of strange attractors is called chaos theory.

Apparently Mr. Lo has worked out a theory where the minimum energy trajectories under this complicated dynamical system (planetary gravitational attraction) exhibits attractors that looks like "tubes" that exhibit the chaos-like behavior of strange attractors.

At first glance, these tubes appear to have the dynamical structure similar to n-body orbits (this factoid about orbits was first discovered by Michel Henon in the 60's). "orbits" in n-body systems don't actually retrace themselves, but sort of looks like a coiled up extension cord. The envelope or attractor of the orbits look sort of like a mis-shaped torus (squished donut), where the orbits can pretty much be anywhere on the surface of the donut (the attractor), but the path it takes is somewhat unpredictable (chaos) and highly dependent on initial conditions. There are more complicated attractors (some involving little islands of stability inside the donut) depending on the energy level, but this is the basic idea. This discovery seems to extend this known factoid about orbits to the structure of minimum energy trajectories in n-body gravitational fields.

All this will be moot, however, when in the 2004 election, Al Gore wins the presidency by taking credit for inventing the Interplanetary Super-Highway while giving a campaign speech for an increased budget for Nasa leading all the l337 geek-crackers to rig the newly approved, non-tamperproof election computers... I boldly predict this will be henceforth called the "butterfly-ballot" effect... But I digress... ;^)

No not really.

[WolfWithoutAClause]

The point of the article isn't that they've calculated with more precision, more that they've worked out a way to plot courses through the solar system, more or less for free.

Basically what happens is that there are certain points near to the earth and every other body in the solar system called the Lagrange points. The researchers have worked out a way of calculating a route that passes through the regions around the Lagrange points to jump from planet to planet with almost no expenditure of fuel.

The only downside to this is that the route is probably going to be slow; several years to go from place to place. Still, the implications of being able to move cargo/fuel to say, Mars ahead of human habitation cannot be overestimated. The other downside is you have to be fairly high above the earth initially to be able to reach the 'superhighways', so don't expect the program to give directions from route 66 ;-)