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Asteroid Grand Tour
nprev
post Apr 8 2007, 06:07 PM
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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!


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Greg Hullender
post Apr 8 2007, 07:11 PM
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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. :-)

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nprev
post Apr 9 2007, 12:53 AM
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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... smile.gif )


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Floyd
post Apr 9 2007, 01:44 AM
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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. biggrin.gif


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Greg Hullender
post Apr 9 2007, 03:15 AM
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As I said, it's not an easy problem, but that's not because it's anything like the Travelling-Salesman problem.

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tasp
post Apr 9 2007, 01:59 PM
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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?)
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nprev
post Apr 9 2007, 02:44 PM
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QUOTE (monitorlizard @ Apr 9 2007, 06:25 AM) *
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.


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tedstryk
post Apr 17 2007, 03:35 PM
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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.


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JRehling
post Apr 17 2007, 04:40 PM
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QUOTE (nprev @ Apr 8 2007, 08:07 AM) *
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?... huh.gif


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?
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JKreider
post Sep 29 2009, 07:20 PM
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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.

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SFJCody
post Sep 29 2009, 07:44 PM
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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.
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Holder of the Tw...
post Sep 29 2009, 09:10 PM
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Such impactors would be excellent for spectral studies, but you wouldn't be sticking around for very long to study the crater.
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HSchirmer
post Jan 7 2017, 02:52 PM
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QUOTE (JRehling @ Apr 7 2007, 11:39 PM) *
I'll echo my concept of a retrograde solar orbit for a truly grand tour of the asteroids. A craft would use a Jupiter gravity assist to enter a retrograde orbit with perihelion 2.6 AU and aphelion 5.2 AU. When it first returned to the asteroid belt, it would fire its engines to enter a roughly circular orbit barreling in reverse right down the middle of the asteroid belt.




Hmm, circular orbit at 2.5 AU down the 3:1 gap, should have roughly 2,200 asteroids within .1 au.
Figure 30 months orbit at that distance, but retrograde should pass everything in 15 months.
That's an average of 2.4 close approaches per day.
Wonder if it's possible to program such complex targeting sequences...


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Phil Stooke
post Jan 7 2017, 06:33 PM
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"roughly 2,200 asteroids within .1 au."
"That's an average of 2.4 close approaches per day."

It's a nice idea... but 0.1 AU is 15 million km, so most of these are not exactly close approaches in the sense we think of them with typical flybys. You could do great survey work and really expand the phase angle photometry, but you would probably have to work hard to get more than a handful of close approaches.

Phil


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HSchirmer
post Jan 7 2017, 07:32 PM
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QUOTE (Phil Stooke @ Jan 7 2017, 07:33 PM) *
"roughly 2,200 asteroids within .1 au."
"That's an average of 2.4 close approaches per day."

It's a nice idea... but 0.1 AU is 15 million km, so most of these are not exactly close approaches in the sense we think of them with typical flybys. You could do great survey work and really expand the phase angle photometry, but you would probably have to work hard to get more than a handful of close approaches.

Phil


Yep, I typed and retyped "close" versus "closest"...
but "close enough for spectra and phase curves" is what you'd get.

(edit)
Hmm, quick fact check- visibility at .5AU.
New Horizons got usable data from two ~100-150 km KBOs at .5 & 1.8AU distance, in really low light.
Illumination comparison would be asteroids at ~3 au versus KBOs ~40AU, is square of distance
so 40AU^2 = 1600 while 3AU^2 ~10, so asteroids get about 160 times the illumination that KBOs do.
KBOs visibility x 150km^2 = 1 illumination unit x .5AU distance
Asteroid visibilty x 12km^2 = 160 illumination units x .5AU distance

So, New Horizon's camera in the asteroid belt could get light curves from 12km objects at .5AU?
Then, eh 5.3km objects within .1AU?
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