# PhD Dissertation Idea: NEO Trade Network Analysis

Frequently I wish I could afford to have a personal orbital dynamics minion that I could have run analyses for me whenever I have a complex orbital dynamics question and would like to test my intuition. Unfortunately, Altius isn’t successful enough yet for me to afford that luxury, and while we have friends and advisors with the relative skills, I don’t have enough money to have them run every analysis I’m interested in. So I figured maybe I could toss this out as a potentially useful topic for someone’s PhD dissertation instead.

Short version: I’d like to do an analysis to see how hard it is (in delta-V, travel time, and launch window frequency) to get from one NEO to another, versus going from a NEO to a planet and back.

I’ve got a lot of friends (bless their hearts) who like to turn up their nose at poor benighted planetary chauvinists, and who go on and on about “once you’re out of a gravity well, why would you want to go back into one?” My intuition suggests they may be wrong, but I’d like to see numbers to either back up my opinion, or shoot it down. My intuition suggests that without atmospheres or the Oberth effect, you’re going to pay big delta-V penalties at each end of the trip, unless the synodic periods are really really long.

My thoughts on how to run the analysis:

1. Before you start, pick some subset of the NEO population above a certain size (say 100m diameter, or maybe 1km depending on available computing resources). Gather ephemeri for all of them.
2. Pick a random NEO in that group.
3. Depending on computing resources pick some specific number of other asteroids to analyze (say 50 or 100 or 1000), and randomly select them from the population.
4. Calculate pork-chop plots for travel from the initial asteroid to the other asteroid, and then back again.
5. Automatically extract from the pork-chop plots say the minimum delta-V for both legs of the trip, and the associated trip times, stay times, and estimated revisit frequency.
6. Run steps 4 and 5 using the Earth, Mars, and Venus as destinations, both with and without aerocapture/aerobraking at the planet end.
7. Repeat steps 3-6 a bunch of times (say 100 or 1000 times depending on how much parallel computing capability you have, and how thorough you want to be).
8. Analyze the data.

My hunch says that especially if you have aerocapture, you’re going to find that most of the time it’s easier for a given NEO to regularly “trade” with planets than it is with other NEOs, because you can both take advantage of the Oberth effect on departures from the planets, and you can take advantage of aerocapture on the way in. But I’d love to see someone run the numbers–I could be completely wrong.

An analysis like this would be really useful for figuring out what trade networks might look like in the future between NEOs and other solar system entities. If it turns out it’s much harder to get from one NEO to another on a regular basis, as my intuition suggests, it would suggest planets may remain the trade hubs with NEOs being more mining bases. If my hunch is wrong, maybe I owe my NEO-chauvinist friends an apology. ๐

Bonus points if you can run the analysis using both high-thrust impulsive maneuvers as well as low-thrust, high-Isp maneuvers (like Solar Electric Propulsion systems can provide), to see if SEPs noticeably change the equation–I really have no intuition on how realistic SEPs change or don’t change the equation for NEO transportation.

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#### Jonathan Goff

President/CEO at Altius Space Machines
Jonathan Goff is a space technologist, inventor, and serial space entrepreneur who created the Selenian Boondocks blog. Jon was a co-founder of Masten Space Systems, and is the founder and CEO of Altius Space Machines, a space robotics startup in Broomfield, CO. His family includes his wife, Tiffany, and five boys: Jarom (deceased), Jonathan, James, Peter, and Andrew. Jon has a BS in Manufacturing Engineering (1999) and an MS in Mechanical Engineering (2007) from Brigham Young University, and served an LDS proselytizing mission in Olongapo, Philippines from 2000-2002.

## About Jonathan Goff

Jonathan Goff is a space technologist, inventor, and serial space entrepreneur who created the Selenian Boondocks blog. Jon was a co-founder of Masten Space Systems, and is the founder and CEO of Altius Space Machines, a space robotics startup in Broomfield, CO. His family includes his wife, Tiffany, and five boys: Jarom (deceased), Jonathan, James, Peter, and Andrew. Jon has a BS in Manufacturing Engineering (1999) and an MS in Mechanical Engineering (2007) from Brigham Young University, and served an LDS proselytizing mission in Olongapo, Philippines from 2000-2002.
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### 11 Responses to PhD Dissertation Idea: NEO Trade Network Analysis

1. Marshall Eubanks says:

Don’t forget, for the Earth, Mars and Venus, while _leaving_ the gravity well takes delta-V, returning does not, or does not take nearly as much (as you can use aerobraking). This can be true even your ship can’t survive a full re-entry.

I have done these sorts of runs for asteroid prospecting. Basically, you need to think in terms of a, e and i – semi-major axis, eccentricity and inclination. To change any of these by a lot takes delta V. (I am going to ignore gravity assists for now.) So, if you have a set of asteroids with nearly the same a, e and i, you can find trade routes (or prospecting chains) that travel around between them for very little delta-V.

Now, for the NEA, that means that ones with a ~ 1 AU, e ~ 0 and i ~ 0 are “close” to the Earth, and (no surprise) these are the ones that NASA’s ARM are interested in. Many NEA, though, have values like a ~ 1, e ~ 0.2 (Eros), a ~ 1 e ~ 0.8 (Icarus) or even a ~ 2 e ~ 0.4 (Amor). These will take (roughly) 10 – 20 km / sec to get to (to rendezvous with, not a fast flyby) and 10 – 20 / km sec to get back from (unless you do a gravity assist or aerobraking). So, if you are going to one such body, you might as well go to several with similar orbital parameters.

2. briang says:

if there are multiple development sites in the asteroid belt, i think the travel will be similar to pacific island trade circles more than strictly back and forth.

3. Doug Jones says:

Using a planet slingshot might make unlikely NEO pairs able to do a low-dV transfer- once in a lifetime.

4. Doug,
I totally agree that if you’re just trying to get form random asteroid to random asteroid once (and don’t care which asteroid the next one is), there are probably all sorts of clever one-off tricks that can make a huge difference. Which is great for prospecting. I was mostly just setoff by Randall’s “planetary chauvanism” dig. The reality to me is that NEOs don’t really seem like that great of places to colonize. Mine? Sure. But they’re going to be lonely outposts trading primarily with those gravity wells. I think that if large colonies spring up not on planetary bodies (or in their atmospheres), that they’ll most likely be in orbit around the planetary bodies, and not out in the NEOs (with certain rare exceptions).

I could of course be wrong.

~Jon

5. Paul451 says:

[Second attempt. I’ve just discovered that accidentally hitting the escape key blanks the comment field. D’oh!]

For bulk cargo, you’d use a short surface-mounted tether-arm, rotating tangentially to the asteroid’s surface. Put the hub on the asteroid’s equator and you’ll sweep out the entire sky. Pick your tether speed/radius, your release time, and… bam! Free transfer trajectory. With propellantless plane change to boot.

For softer, wetter payloads, you’d use a much much longer (lower g-load) free-flying momentum-exchange tether co-orbiting near the asteroid. This can also operate in any plane. To prevent the momentum which is exchanged coming from the tether itself, you throw waste-mass from the asteroid in the opposite direction to balance the system.

To save even the small amount of fuel needed for transferring from the asteroid surface to the hub of the MET, you can use the surface-mounted tether-arm at much lower g-loads.

If you can solve the capture/hook-up problem, then you can also use the same type of system at the other end of the trip. The only fuel required will be for minor course corrections (and tether intercept timing).

(Ironically, I wrote “if you can solve” meaning second-person-generic, like every other “you” in this comment, but in this case it might literally be you, Jon, who solves the capture problem.)

Aside: Asteroids and small moons also have very low stationary orbit heights compared with planets. For example, Phobos’ is just 3km, even Ceres is only 700km. (Contrasting with 37,000km for GEO and 60,000km for the moon.) That means that you can have full-blown space elevators at asteroids at a technology level not much higher than we have now.

(Aside#2: The surface tether-arm would also be wildly useful on the moon. But the lunar gravity makes it much harder to keep the arm from hitting the ground. The system becomes much more complex.)

In sum: The problem that you suspect, is really only apparent for current-generation robotic missions and very early human missions. If there is ever an actual human space civilisation, it is readily solvable. And the solution shows that just how bad a choice planets are. ๐

6. ken anthony says:

No possible liability with randomly changing the orbits of those rocks eh?

7. gbaikie says:

Well, Dawn is going from Vesta to Ceres.
I would guess the traveling from one Jupiter Trojan asteroid to another Trojan asteroid would require small amount of delta-v.
[[“Estimates of the total number of Jupiter Trojans are based on deep surveys of limited areas of the sky. The L4 swarm is believed to hold between 160รขโฌโ240,000 asteroids with diameters larger than 2 km and about 600,000 with diameters larger than 1 km.”- wiki]]

But you said NEO. And NEOs are rocks that cross or come close to Earth orbit:
“In terms of orbital elements, NEOs are asteroids and comets with perihelion distance q less than 1.3 AU. Near-Earth Comets (NECs) are further restricted to include only short-period comets (i.e orbital period P less than 200 years). The vast majority of NEOs are asteroids, referred to as Near-Earth Asteroids (NEAs). NEAs are divided into groups (Aten, Apollo, Amor) according to their perihelion distance (q), aphelion distance (Q) and their semi-major axes (a). ”
http://neo.jpl.nasa.gov/neo/groups.html
So if limited NEOs to say Atens [or Atiras {or IEO}], it seems those would best NEOs to select, using Mercury, Venus, and/or Earth gravity wells to alter inclination and trajectories would part of the reasoning of why they would be best.
Though generally speaking selecting same group whether would be either Aten, Apollo, or Amor would good idea. One could say if not worried about how time it takes
travel between them then asteroid which were Amors could also good subgroup.
Also at http://neo.jpl.nasa.gov/neo/groups.html it says Apollos are 62% of the NEOs found with next most populated ground being Amors 32% of all NEOs found.

8. Chris (from MN) says:

You’ll be pleased to know that Paul Krugman (as an assistant professor) wrote a paper on “The Theory of Interstellar Trade:” https://www.princeton.edu/~pkrugman/interstellar.pdf

“How should interest rates on goods in transit be computed when the goods travel at close to the speed of light? This is a problem because the time taken in transit will appear less to an observer traveling with the goods than to a stationary observer.”

“while the subject of this paper is silly, the analysis actually does make sense. This paper, then, is a serious analysis of a ridiculous subject, which is of course the opposite of what is usual in economics.”

9. Hop David says:

I have always been a hard core J. S. Lewis fan. Asteroids all the way! But my (amateur) efforts at orbital mechanics have led me closer to the dark side of planetary chauvinism.

If we could have launching platforms from high lunar orbits or EML1/2, the Oberth advantage would be huge. And if our infrastructure was at a level where NEOs are trading with each other, such platforms aren’t a stretch.

I don’t like your step #4. A problem with pork chop plots is they rely on Lambert iterations. If departure and destination are 180 degrees apart and orbits are only slightly inclined to one another, these iterations will lead to a polar orbit! A 90 degree plane change at each end is a needlessly costly path that can be largely mitigated by broken plane transfer orbits. I try to explain this in Deboning the Porkchop Plot.

For NEO to NEO routes this problem can be even more pronounced since many of these rocks have healthy inclinations.

Unfortunately I don’t know of a way to find optimum broken plane transfer orbits.

10. Jonathan Goff says:

Hop,
I agree on your comment about broken plane transfers. I was handwaving that into step 4, under the assumption that you’d include some sort of modified porkchop plot that included the better dV of the standard transfer vs a broken-plane transfer.

~Jon

11. morganism says:

In my musings, i keep looking at the transfer times, and believe you can carry a few spare engines, some spare SRBs, an app and some optics, you could have your transport containers partly loaded with powdered materials to 3D print another Miner/Prospectror frame on the 2-3 year trip out. By the time you were ready to leave, with a loaded freighter, you could send a load home and send a miner on to the next rock. If you were to find enough alum\Mg on the isru rock, you could also form up more SRBs for quicker transfers.