Ballistic transfers, confused

[Bishop149]

In light of all the fuss around Elon Musk's speech about going to Mars I was looking into Mars transfer orbits.

Now I'm pretty familier with Hohmann transfers as I'd imagine most people who play KSP would be, but from the flight times this obviously isn't Musk's plan, so I found stuff on "ballistic trasnfers" and am confused. As far as I can see the idea is to eliminate the costly insertion burn to enter orbit. The principle from the few rather dumbed down articles I've found it seems to be to almost match orbit with the target but going slightly slower and upon catching up with the spacecraft the target body gravitationally captures it. Which sounds pretty simply but then how the hell do you do the first bit?

To get out to Mars orbit would require a transfer orbit would put apoapsis somewhere out in Mars' orbital path and Periapsis somewhere along Earth's. To "match orbit" with Mars you'd have to lift periapsis to up near Mars' orbital path which would presumably take a crap ton of fuel. Less than a capture burn? I don't get it. 

Was trying to find some diagrams to explain the ideas but the only time this has been done is Earth -> Moon so those are the only ones I can find. As far as I can see its a lot of clever mucking about with lagrange points to get into the correct orbit which obviously isn't applicable to Mars with its tiny moons and much high DeltaV required. 

Can someone explain? Articles explaining this kind of thing are always one of two extremes, "Too dumbed down to be useful" and "University level mathematics required for understanding".

[Neil1993]

Could you maybe provide links to your articles? It might make it easier for others to explain it to you.

[Bishop149]

Sure:

http://www.gg.caltech.edu/~mwl/publications/papers/lowEnergy.pdf

http://www.universetoday.com/117615/making-the-trip-to-mars-cheaper-and-easier-the-case-for-ballistic-capture/

http://www.scientificamerican.com/article/a-new-way-to-reach-mars-safely-anytime-and-on-the-cheap/

I've been reading some more, the key is to enter the planets SOI with less than escape velocity . . . . which is impossible if only one body is involved, you need a second bodies influence to slow down your spacecraft to achieve this. I don't know how this would work with Mars, it has no moons with any kind of decent mass so I suppose you'd need some kind of planetary conjunction. . . . which strikes me as pretty specific circumstances

[Steel]

Ref: Belbruno & Topputo, http://arxiv.org/abs/1410.8856

So as far as I can see, the manoeuvre exploits the dynamics of the Mars-Earth-Sun system. It's a weak stability boundary (WSB) transfer (which are a horrible set of things to have to try and come to terms with fully, having spent much of the past half-day trawling papers on them) which involves a set of stable points around Lagrange points as far as I can tell.

Basically, the transfer is performed in such a way such that the burn to insert into the desired orbit (point x_c in the diagram above) will have lower dV requirements (in some cases) that the burn that you would have to perform to shed excess hyperbolic velocity if you were doing a Hohmann transfer. These transfers have the advantage that they are not too sensitive to the relative position of the two planets - so you can transfer to Mars outside the ideal window for Hohmann transfers - and that in certain cases they can save dV.

If you're trying to rationalise these orbits in terms of what you know from KSP, then don't. These transfers cannot be done in a 2-body regime because these orbits exploit features that don't exist in those regimes, so you'll just give yourself a headache for nothing

Edited September 29, 2016 by Steel

[YNM]

Using L1 to enter orbit around a planet ? Now THAT's interesting. Yeah, certainly the dV requirements is going to be a bit lower than straight entry burn, but how long will it be, I'm not sure.