Full Version: Asteroid Grand Tour

This article from JPL describes recent efforts to derive a main belt multi-asteroid mission trajectory...any of you orbitsmiths out there have some early thoughts/observations?

I don't know if this is original with me, but I have always liked this concept. (note, this may not fulfill all the mission objectives, or be the fastest)

Launch your probe to pass 60 degress ahead of Jupiter at the time it crosses Jupiter's orbit. You time launch to pass 1 or 2 asteroids in the main belt on your way to encountering a leading Jupiter Trojan. Keep moving out past Jupiter, maybe you get lucky and go by Hidalgo or Chiron (maybe not . . .). Your orbit about the sun is timed to fall back towards the sun so that you cross Jupiter's orbit when the trailing Trojan's are going by and you get to encounter one of them. After that, you fall back through the asteroid belt, and you get to encounter 1 or 2 more asteroids.

If your period about the sun is an integer # of years, the probe comes close to earth again, maybe gets a little gravitational nudge to go back out to the asteroid belt again, maybe out of the ecliptic a little bit this go round. (this time, Jupiter Trojans probably elsewhere, so you don't get to see them again, but you do get to go out through the asteroid belt and back again, might pick up to 4 more 'roids)

So if the timing isn't too tricky, you get to see up to 8 mainbelts and a couple of Trojans. If you really want to see Chiron, well, you might be jamming up some of the other encounters. Otherwise, if you aren't too picky about which main belts you see (afterall, you get to see up to 8 if luck holds) timing of your launch is pretty much every 13 months or so, might be easier to fly with a little flexibility, rather than trying for a 1 in how many millions shot at 4 specific ones.

Launch your probe to pass 60 degress ahead of Jupiter at the time it crosses Jupiter's orbit. You time launch to pass 1 or 2 asteroids in the main belt on your way to encountering a leading Jupiter Trojan. Keep moving out past Jupiter, maybe you get lucky and go by Hidalgo or Chiron (maybe not . . .). Your orbit about the sun is timed to fall back towards the sun so that you cross Jupiter's orbit when the trailing Trojan's are going by and you get to encounter one of them. After that, you fall back through the asteroid belt, and you get to encounter 1 or 2 more asteroids.

If your period about the sun is an integer # of years, the probe comes close to earth again, maybe gets a little gravitational nudge to go back out to the asteroid belt again, maybe out of the ecliptic a little bit this go round. (this time, Jupiter Trojans probably elsewhere, so you don't get to see them again, but you do get to go out through the asteroid belt and back again, might pick up to 4 more 'roids)

So if the timing isn't too tricky, you get to see up to 8 mainbelts and a couple of Trojans. If you really want to see Chiron, well, you might be jamming up some of the other encounters. Otherwise, if you aren't too picky about which main belts you see (afterall, you get to see up to 8 if luck holds) timing of your launch is pretty much every 13 months or so, might be easier to fly with a little flexibility, rather than trying for a 1 in how many millions shot at 4 specific ones.

I thought that article was interesting but wish they'd published some details of the winning trajectory...

--Emily

--Emily

Yeah, Emily. It was notably short of specific targets and/or down-selects, wasn't it? I interpreted this as strictly early concept development activity...nobody's gonna get assertive unless & until a feasible mission strategy emerges.

Classic example of a press release about a science/tech item that leaves out the most important piece of info. I see them all the time, and they're not all by ESA press flunkies... not by a long shot!

The trajectory details for the 2006 GTOC 1 are here:

http://www.esa.int/gsp/ACT/mad/pp/GTOC1/gtoc1results.htm

Presumably the results for GTOC 2 have yet to be uploaded.

http://www.esa.int/gsp/ACT/mad/pp/GTOC1/gtoc1results.htm

Presumably the results for GTOC 2 have yet to be uploaded.

LOVE it...

EVEEEJSJA

EVVEEVVEVEJSJA

EEVEEJSA

Makes Galileo and Cassini seem like a quick trip to the shops round the corner.

Doug

EVEEEJSJA

EVVEEVVEVEJSJA

EEVEEJSA

Makes Galileo and Cassini seem like a quick trip to the shops round the corner.

Doug

30-year mission duration for those long hauls using only 60 kg of propellant...amazing!

Any idea what "v-infinity" means in the JPL results? To me, it means the "hyperbolic excess," but the show it with positive values even for elliptic orbits.

--Greg

--Greg

Last year's was a very different challenge. From the Problem Description (PDF):

--Emily

QUOTE

The main objective of the optimisation is to maximise the change in the semi-major axis of the asteroid 2001 TW229 subsequent to the impact of an electric propelled spacecraft.

1-The target

Consider the asteroid 2001 TW229 and its osculating orbital elements in the J2000.0 heliocentric ecliptic reference frame:

a (semi-major axis, AU): 2.5897261

e (eccentricity): 0.2734625

i (inclination, deg.): 6.40734

ω (argument of pericenter, deg.): 264.78691

Ω (Right Ascension of the Ascending Node, deg.): 128.34711

M (mean anomaly at epoch 53600 MJD, deg.): 320.47955

2-The spacecraft

Consider a nuclear electric propelled spacecraft with a wet mass of 1500 kg (dry mass can be considered to be zero) and equipped with a thruster with the following capabilities: specific impulse Isp=2500 sec., maximum thrust level T=0.04 N.

3-The mission

The spacecraft has to be transferred from Earth to the asteroid 2001 TW229 with a launch in [3653-10958] MJD2000 (Modified Julian Date 2000), corresponding to years 2010 to 2030. The maximum time of flight is 30 years. At arrival the quantity {equation: J = mf |U-rel dot v-ast|} has to be maximised, where mf is the final mass of the spacecraft, U-rel is the velocity of the spacecraft relative to the asteroid at arrival and v-ast

is the heliocentric velocity of the asteroid. The launcher available for the mission is able to provide a 2.5 km/sec escape velocity to the spacecraft with no constraint on the escape asymptote direction. Consider also a constraint on the minimum allowed heliocentric distance of 0.2 AU.

4-The dynamical models

Consider only the Sun gravity as an external force acting on the spacecraft. Planets may be used to perform swing-bys, in this case the effect should be modelled as an instantaneous direction change on the spacecraft velocity relative to the planet, subject to a constraint on the angle magnitude (a minimum pericenter radius has to be considered, see table below for details). The planet ephemerides used should have an accuracy equivalent to that of JPL DE405 ephemerides (http://ssd.jpl.nasa.gov/horizons.html). Use the numerical values given below and assume the astronomical unit equal to AU=1.4959787066e+008 km, and the Earth standard gravitational acceleration to g0=9.80665 m/s2.

I'm more interested in this year's results...I'd love to see a multi-asteroid tour. Dawn will get two, but that's in part because it's aiming for two very specific ones, and is going into orbit at both. Another mission that was less constrained could surely survey more in shorter time.1-The target

Consider the asteroid 2001 TW229 and its osculating orbital elements in the J2000.0 heliocentric ecliptic reference frame:

a (semi-major axis, AU): 2.5897261

e (eccentricity): 0.2734625

i (inclination, deg.): 6.40734

ω (argument of pericenter, deg.): 264.78691

Ω (Right Ascension of the Ascending Node, deg.): 128.34711

M (mean anomaly at epoch 53600 MJD, deg.): 320.47955

2-The spacecraft

Consider a nuclear electric propelled spacecraft with a wet mass of 1500 kg (dry mass can be considered to be zero) and equipped with a thruster with the following capabilities: specific impulse Isp=2500 sec., maximum thrust level T=0.04 N.

3-The mission

The spacecraft has to be transferred from Earth to the asteroid 2001 TW229 with a launch in [3653-10958] MJD2000 (Modified Julian Date 2000), corresponding to years 2010 to 2030. The maximum time of flight is 30 years. At arrival the quantity {equation: J = mf |U-rel dot v-ast|} has to be maximised, where mf is the final mass of the spacecraft, U-rel is the velocity of the spacecraft relative to the asteroid at arrival and v-ast

is the heliocentric velocity of the asteroid. The launcher available for the mission is able to provide a 2.5 km/sec escape velocity to the spacecraft with no constraint on the escape asymptote direction. Consider also a constraint on the minimum allowed heliocentric distance of 0.2 AU.

4-The dynamical models

Consider only the Sun gravity as an external force acting on the spacecraft. Planets may be used to perform swing-bys, in this case the effect should be modelled as an instantaneous direction change on the spacecraft velocity relative to the planet, subject to a constraint on the angle magnitude (a minimum pericenter radius has to be considered, see table below for details). The planet ephemerides used should have an accuracy equivalent to that of JPL DE405 ephemerides (http://ssd.jpl.nasa.gov/horizons.html). Use the numerical values given below and assume the astronomical unit equal to AU=1.4959787066e+008 km, and the Earth standard gravitational acceleration to g0=9.80665 m/s2.

CODE

Mercury Venus Earth Mars Jupiter Saturn Sun

Gravitational Constant, km^3/sec^2

22321 324860 398601.19 42828.3 126700000 37900000 1.32712428 e+011

Minimum pericenter radius allowed during fly-by, km 2740 6351 6678 3689 600000 70000 N/A

Gravitational Constant, km^3/sec^2

22321 324860 398601.19 42828.3 126700000 37900000 1.32712428 e+011

Minimum pericenter radius allowed during fly-by, km 2740 6351 6678 3689 600000 70000 N/A

--Emily

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. It would be trivial to set a course intersecting any two asteroids named as primary goals. Other encounters would happen automatically, with the craft passing the radial position of some asteroid or other every few **hours**. Of course, in most cases, the distance would be quite great, but every few months should bring a somewhat close encounter even if only by chance. With a few more manuevers and a little planning, it should be easy to set up a large number of encounters, albeit fast ones. This would result in a lot of encounters that would map only half of an asteroid (with the craft flying by too fast to see the other half rotate into daylight), but the numbers should roll up rather impressively. I would think a dozen encounters would be a conservative estimate.

Your flyby velocity would be ENORMOUS though - you might sail past something like Matilde or Eros at 4 or 5km/sec on a conventional flyby - and then maybe 20km/sec if you were going the other way....eek. I'm fairly sure that you could do something like CONTOUR for asteroids with some intelligent trajectory design, 3, 4 asteroids with 3 or 4 times the data collected at each one. If you picked them right, you would get a good 'grab bag' of different types of bodies. Going the other way I imagine the spacecraft would be going "ARHGHHHHHHHHHhhhhhhhhhhhhhhhhhhhhhhhhh" all the time Perhaps you could bounce in and out ot the asteroid belt using Mars as a grav-assist teach time. Dawn but without the orbiting - you could get really nice long lazy flybys of many asteroids I would have thought. If you're going to Jupiter you would have to have crazy Juno/Rosetta like solar arrays, and if you're getting THOSE< might as well just use 2-3kw and chuck an ion engine or 5 on the back.

Doug

Doug

Well, DI's encounter with Tempel-1 was 10 km/s so that's "only" twice as slow. I don't believe high flyby speeds would be a major drawback here. Most of these bodies are very small so you get spatially resolved datasets only in the immediate vicinity of the target (say a couple of hours) and you're not likely to stick around for much of (rotational) global coverage even with speeds in the 5 km/s range. What I'm saying is the benefit of a slow encounter isn't that great. Of course, you'd really want to put cameras capable of getting more than one image per minute **cough*Cassini*cough** to maximize science return, but even DI had that. The potential for visiting many more targets seems to outweigh this drawback to me.

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?...

The four asteroid tour (each a different type) is a very interesting problem. It is a hard version of the traveling salesman problem where you try to minimize the travel distance of visiting a bunch of cities (a NP-complete problem). To make it interesting, all the cities are moving around—they are asteroids--and you don’t know which four to pick initially. While a great deal is known about NP-complete problems, the asteroid tour is a new twist. To get a winning tour requires bring together a team with great math and computer algorithm skills as well as models for where several thousand asteroids of the four types are going to be for the next several years. Since a frontal approach to the problem would take up years of computer time (if not the age of the universe) the trick is to come up with brilliant assumptions and shortcuts that make it a problem that is doable on reasonable computer (or cluster) in a few weeks. My hats off to the team from Polytechnic of Turin, Italy.

Floyd

Floyd

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!

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

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

--Greg

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... )

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.

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

--Greg

--Greg

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?)

(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?)

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.

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?

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.

Click to view attachment

Click to view attachment

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.

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

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...

"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

"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

"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

"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?

Certainly it would be desirable to plan the trajectory rather than pick a trajectory and hope for the best. How much good the planning would do is an empirical matter. Probably a little bit of propulsion would go a long way so that a little delta-v before a targeted encounter could set it up to be quite close. It may be that some launch opportunities would be considerably better than others. Of course, some targets are more interesting than others. All told, it's probably better to get 20 to 60 close flybys of interesting targets than to get 1000 distant flybys of random ones. All told, it's a complex paradigm with time as one parameter and assessments of scientific interest as another. And the interest of a set of targets would not the sum of the interest of each of them.

It'd be fun, but hard, to model this out; it's hard to assess how that would go without getting deep into the details.

It'd be fun, but hard, to model this out; it's hard to assess how that would go without getting deep into the details.

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