Short on fuel, but good at astrophysics? It is possible to tour the solar system on less than 30 Altairian dollars a day by using the Interplanetary Transport Network (ITN).
The ITN is based on gravity assist manoeuvres and low energy transfer orbits around and between Lagrange points. Using the ITN, it is theoretically possible to tour the solar system with an exceedingly economic use of fuel as long as you have an abundance of patience and don’t mind taking an often circuitous route to your destination.
If you imagine the whole solar system as a rubber sheet which is warped by gravity wells, then the planets are really just small depressions of different depths pressed into the sides the Sun’s overarching gravity well.
What’s important to this story is that the edges of those small depressions are nearly flat with respect to the otherwise steep slopes created by the Sun and the planets. It takes a lot less energy to move around on these flat edges, than it does trying to climb straight up the steep slopes.
The flat edge that is present around the Earth’s gravity well is land marked by Lagrange point 1 (or L1) lying directly between the Sun and the Earth – and Lagrange point 2 (L2) on the opposite side of the Earth directly away from the Sun.
It’s possible for a spacecraft to orbit a Lagrange point and be carried around the Sun with very little expenditure of energy. It’s because you are essentially riding the bow wave of the Earth as it orbits the Sun – so you are carried the Sun at the same orbital speed as the Earth (30 kilometres a second) without having to burn a lot of fuel in the process.
Also the Lagrange points represent junction points to enable low energy transfer between different planetary orbits. As though the solar system’s space-time curvature makes for a giant skateboard park, it’s possible to step off L1 and follow a trajectory down to Venus – or you can coast across the flat edge of Earth’s gravity well for about 3 million kilometres to L2 and then step off on a long winding path to the L1 of Mars. Here you might rest again before perhaps shuffling across to Mars’ L2 and then on to Jupiter.
Mathematical analysis of the gravitational interactions between three or four bodies (say, your spacecraft, the Earth and the Sun – and then add Mars too) – is complex and has some similarities with chaos theory. But such an analysis can identify interconnecting pathways right across the solar system, which ITN proponents refer to as ‘tubes’.
ITN principles have been adopted by a number of spacecraft missions to conserve fuel. Edward Belbruno proposed a low energy lunar transfer to get the Japanese probe Hiten into lunar orbit in 1991 despite it only having 10% of the fuel required for a traditional trans-lunar insertion trajectory. The manoeuvre was successful, although travel time to the Moon was five months instead of the traditional three days. NASA’s Genesis mission and the ESA’s SMART-1 are also considered to have used low energy ITN-like trajectories.
So impoverished hitchhikers, maybe you can still have that grand tour of planets by using the ITN – but make sure you pack a towel, it will be a very long trip.
(Recommended reading: Ross, S.D. (2006) The interplanetary transport network. American Scientist 94(3), 230–237.)
Groovy.
BTW, is it true Gore invented the series of interplanetary tubes too?
TL – why bring this up?
Gore never said he did that.
Here’s what he actually said, and what he actually did.
http://en.wikipedia.org/wiki/High_Performance_Computing_and_Communication_Act_of_1991
The “Gore Bill”, which was visionary back in 1991, created the National Information Infrastructure, which was pivotal in creating the backbone that serves the internet today.
Give credit where credit’s due.
ICE, the spacecraft that wouldn’t die.
http://en.wikipedia.org/wiki/International_Cometary_Explorer
For those interesting in the dynamical systems and mathematics behind this the following is an accessible paper
http://etd.caltech.edu/etd/available/etd-05182004-154045/unrestricted/rossthesis_5_11.pdf
LC
@ CEB:
Because that misconception combined with Ted Stevens of his own making is a joke that comes to my mind every time I see tubes that form networks.
[I can’t give credit there it is due without ruining the joke. In this comment, sure – of course Gore never said that, or there would be no joke.]
What is the source for the ITN “tube map”? I need to have this on the wall here at work!
Check out
“Cylindrical Manifolds and Tube Dynamics in the Restricted Three-Body Problem” by Shane David Ross, at the address
http://etd.caltech.edu/etd/available/etd-05182004-154045/unrestricted/rossthesis_5_11.pdf
The tubes are a generalization of the types of noncentral potential orbits one gets with oscillations around Lagrange points or strong perturbations with Molniya orbits. These are orbits which exist in accelerated reference frames, or due to perturbations in the n > 2 body problem. The WMAP probe at the L1 point performs an oscillation around that libration point due to the perturbation of the moon, as will the James Webb telescope. There is no central gravitational source at that point. One must perform what is called station keeping maneuvers on a spacecraft in order to make corrections.
Spacecraft which negotiate these orbits will require very precise control. These types of orbits are not intrinsically stable. Since these orbits are not around a central potential U = -k/r, k the usual constant GMm, these orbits are not governed by the same conservation laws. In particular with central point potentials a standard theorem is that the angular momentum direction for a two body problem is constant and perpendicular to the plane of the orbit. The other feature is that these orbits occur around effective potential functions which are often saddles. By that the potential is a well-like structure along one direction and a down sloping along another. So the orbit will over time drift away, and geodetic corrections are required. The WMAP is slated to close down, which means it will over time drift away and enter into an orbit that is not in the long run predictable.
LC
TL…
I laughed after reading it. It times in well with the the whole “network” thing.
There is a huge difference when using the Lagrange points as a stationary orbit, and using them as low energy methods of travel around the solar system. I don’t get why you would bring add a different subject to this blog when it doesn’t apply.
Look at the diagram in the main article above! Orbits around L1 points are examples of these “tubes.” This is a general mathematics for the dynamics of particles around a point, which itself may be moving, where that point does not define a central -1/r potential.
LC
@ Aodhan: Thanks!
Also, if you look at LBC’s reference, “The tubes are a generalization of the types of noncentral potential orbits one gets with oscillations around Lagrange points” becomes clear. (I think, I just had time to browse it.)
It doesn’t seem that the Lagrange points are just good way-stations but both nodes and parameters (extrema) of the problem.
@ LBC:
Nitpick: The usual convention puts L2 as the WMAP/JWT orbital neighborhood.
@ TL, yep my bad, L1 is the solar side L-point
LC
Chatted up the Cassini team recently about the possibility of using gravity pumping to alter the Cassini orbiter into an orbit around Enceladus at the end of the mission… but they said no. I’m not convinced it couldn’t be done…given enough time.
These tubes don’t exist everywhere, and the initial conditions have to be just right. These tubular orbit spaces are not that stable and they are a small measure of all possible orbits that can exist.
The first application of this might be to use the L2 point as a launch point. With the right resonance condition with the lunar orbital period a craft there could get a small delta v with each passiing of the moon. This could then be used to send it off to another planet.
LC
@ tek_604
The NASA subway map is reproduced from the Ross (2006) American Scientist article, as cited in the main story.
A similar version is also used in a New Scientist article here: http://www.newscientist.com/data/images/archive/2544/25441301.jpg
I am not aware that NASA has otherwise made it available online – but I understand NASA is the source.
Cheers Steve!
Setting up some sort of platform to launch things from Solar Lagrange point makes a lot of sense… again, provided we don’t mind taking the long scenic route in order to get to places.
perhaps something to think about as far as the next manned space station… even if we do something temporary at a Lunar Lagrange point.
We really do need some sort of outpost to conduct experiments where the Earth isn’t protecting us quite as much as opposed to the ISS. That doesn’t mean creating something the size or complexity of the ISS.
Also, if you’re looking for a true test for duration flight to Mars… an outpost at one the S or L Lagrange points makes a lot of sense.