Asteroid Grand Tour Options

[nprev]

Yeah...seems as if the prime filter would be choosing specific asteroids of given types, then running optimization NLPs on that set & comparing it to others. Not a trivial problem at all...I just survived two quarters of numerical systems optimization, can really appreciate the work that went into this effort!

[Greg Hullender]

With only four asteroids, I don't the choice of the order in which to visit them adds much to the difficulty of the problem. Even the travelling-salesman problem is easy to solve with 4 (or even 10) cities, just by exhaustive search.

Which is not to say it's an easy problem overall, of course. :-)

--Greg

[nprev]

I think things like minimizing propellant consumption & transit times might add more complexity that you'd think at first glance, Greg, combined with the fact that they're apparently not looking at four pre-selected "hard targets" but instead trying to choose from (presumably) thousands of four compositional categories. Not the way I'd necessarily do it as I said in my previous post, but that's probably how most of the teams will approach the problem in order to try to find a truly optimal solution (they probably have some major processing capability and the latest in solvers, after all... )

[Floyd]

Greg, you are correct in that the traveling salesman problem is trivial for 4 cities--can be solved exactly with ease. However, in the asteroid tour, you don't know which asteroids you will visit, only that you will visit one of each of four kinds. Thus you have to find the most efficient way to get to four line up asteroids of the four different kinds out of the thousands all dancing around. The cities are moving and you won't know their names until you have your solution.

[Greg Hullender]

As I said, it's not an easy problem, but that's not because it's anything like the Travelling-Salesman problem.

--Greg

[tasp]

Has anyone gone back and looked at the Voyager paths through the asteroid belt? Did they plausibly get close to anything?

(keeping in mind the tremendous number of asteroids discovered since the 70s, is it most likely anything they got close to was unknown at the time?)

[nprev]

A couple of years ago I read that Dawn might flyby six or more asteroids during its mission because of all its extra delta-V.

Hmm. Wonder if this activity is actually intended to design an extended mission for Dawn.

[tedstryk]

I think they were more thinking about tweaking its trajectory to take advantage of serendipitous flyby when it is in the asteroid belt but not studying Vesta or Ceres.

[JRehling]

It may be that some variation of JR's idea was explored by some of the teams in this year's trajectory optimization competition, but their focus seems to be on deriving planetary "pump-up" gravitational assists. If I'm visualizing this correctly, such assists cannot occur for a spacecraft in a retrograde orbit?...

I think my idea fails the listed criteria, because zooming out to 5.2 AU is bound to take more time up front than a mission that follows a more Dawnlike trajectory. And it's probably more costly, too. But it would visit a lot more asteroids. I'd like to see teams concoct the most productive tours in a retrograde orbit. Honestly, if you had a craft with a long lifespan and you did nothing but wait for serendipitous flybys, it seems like dozens would be possible -- maybe one every eight months for 20 years or so. My idea is just plain "bigger" than the stated contest asks for.

It would be exciting to see, though, what a shrewd plan could accomplish, looking ahead like Deep Blue to find the cleverest mission. Could 30 flybys be possible? 50?

[JKreider]

Retrograde Asteroid Fly-by Trajectories, RAFT

I've spent quite a bit of time on this problem and my conclusion is that the time it requires is more of an issue than the delta-V. Attached are Phase I and II orbit diagrams for a RAFT mission. A candid summary of my work is online at:
Jaqar Astrodynamics Forum

Comments are welcome.

[SFJCody]

Very interesting work. I wonder if it would be worthwhile for such a spacecraft to carry small impactors. They wouldn't need to have that much mass what with the huge velocity differences involved.

[Holder of the Tw...]

Such impactors would be excellent for spectral studies, but you wouldn't be sticking around for very long to study the crater.