Author Topic: Asteroid Transit Map  (Read 17343 times)

Offline mikelepage

Asteroid Transit Map
« on: 11/14/2015 07:13 am »
Cards on the table: I'm enthusiastic about the Mars and Moon exploration missions in planning, but given that I don't think building a colony in or around an asteroid is necessarily any harder than building a habitat on the Moon or Mars, I don't see any intrinsic reason why planetary surfaces should be priorities for colonisation ahead of the asteroids that are energetically easier to get to.

If the water ice on an asteroid is as good as the water ice on the Moon/Mars, or if the metal deposits (or any other resource "x") on an asteroid are as good as those on a planetary surface, why would you spend the energy to transport your colonists down into a gravity well? (and back out again when they want to come home).  You've just sailed across an ocean, so why forego the ocean-accessible harbour in favour of going straight to building your house on top of a mountain?  People will settle the mountains eventually, but picking the (energetically) low hanging fruit seems like an easier first step.

So with that in mind, let's assume that colonies will start popping up around every resource base in order of cost/accessibility, be it planetary or asteroid-based, even if each asteroid can only support a smaller total number of people than the planetary surfaces will eventually.

Now let's add the complication that unlike on a 2D map like our planetary surface, these locations (and the relative dV between them) are constantly changing.  The relative value of the goods that might be transported from place to place (or the price people are willing to pay), will change with time in transit and the energy required to make the trip (but in a predictable fashion).

Why the transit map analogy? Once a city becomes densely populated enough, it becomes more efficient to transport people/goods through mass transit than it is through direct point-to-point.  Although faster to go directly, it can be cheaper to (for example), catch the bus to the train, train to boat, etc.  Like these public transport vehicles, the asteroids may not be going precisely where one wants to go (anything of worthwhile size is probably too big to move), but the infrastructure that develops around resource bases (habitation/agriculture/radiation protection), may make it possible to "asteroid-hop" the same way you might "train hop" in a city with a big subway system.

Planning is the key however, and the cities that plan well for public transport, have those measures in place long before they're really needed, or else the city suffers for it.  So here's the question: If there was some guiding philosophy for which asteroids were chosen for colonisation, over and above what resources they could provide, what would it look like?

Would the orbital inclination (of Mars/Vesta/Ceres/other big resource bases) mean that you more highly prioritise asteroids with similar orbital inclinations, such that in future you could maximise rendezvous/trade opportunities?

Would you pick asteroids with particular orbital periods, that return to Sun-Earth L1,4,5 or Sun-Mars L1,4,5 on regular intervals?

Any pair of asteroid colonies with low approach velocities might meet each other once and then not again decades or longer, while there might be other pairs with high approach velocities that meet each other twice a year.  Is there a particular family of asteroids with orbital characteristics which are more amenable to regular meetings?  Is there a sweet spot?

What I'm really trying to get at is the idea that even in the early stages of asteroid mining and exporting back to Cis-Lunar space in a point-to-point fashion, a bit of long-term planning could lead to a better way of selecting asteroid mining candidates based on an expectation of widespread exploration.
« Last Edit: 12/06/2015 08:47 am by mikelepage »

Offline Proponent

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Re: Asteroid Transit Map
« Reply #1 on: 11/14/2015 08:51 am »
Changing orbital planes is a big deal, so you'd definitely prefer objects of similar inclination and, to the extent that inclination is non-zero, similar right ascension of ascending node.

As for the trade-off between low delta-V and frequent transit opportunities, I would guess it would depend on how many bodies are involved.  If there are lots and lots of bodies, then you could presumably get any given commodity from many of them.  Hence, frequent launch windows to any particular body don't much matter, and it's all about minimizing delta-V.  On the other hand, if there are only one or two sources for something you need, then you'll prioritize regularity of launch windows over low delta-V.

Figure 2 on page 5 of the first attachment might be informative.  If nothing else, it makes clear the unfortunate inverse relationship between accessibility (low eccentricity and similar semi-major axis) and frequency of launch windows (synodic period).  This applies to accessibility from Earth, but could easily be generalized to other bodies, provided they're in circular orbits, using Tisserand's Parameter.

Offline Burninate

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Re: Asteroid Transit Map
« Reply #2 on: 11/14/2015 12:03 pm »
At least six parameters need to be briefly identical between two bodies for an orbital rendezvous to occur in a pair of simplified two-body systems.  There are several ways to transform this group of six parameters from one set of defined terms to some other set of defined terms,  and mix them together, but six degrees of freedom need to be preserved in even the simplest case.

We're not really built for visualizing six dimensions.

As such, without extensive programmatic simulation it's going to be difficult to talk about this sort of thing productively.

The actual relevant terms deal with higher level complexity in a real solar system, over and above these two sets of six parameters.  You need tens of terms to represent the major sources of orbital perturbation, though we've tried to work out some simplifications that are good enough for just identifying the object:
https://en.wikipedia.org/wiki/Proper_orbital_elements
https://en.wikipedia.org/wiki/Osculating_orbit
https://en.wikipedia.org/wiki/Tisserand%27s_Criterion
« Last Edit: 11/14/2015 12:23 pm by Burninate »

Offline SpacedX

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Re: Asteroid Transit Map
« Reply #3 on: 11/14/2015 12:11 pm »
I hope that when actual transportation of goods between asteroids is contemplated some paradigms will have changed:
- A society of humans living around an asteroid will have lots of energy.
- The energy used to transfer goods would be recaptured (to some extent) at the destination.
- Transportation automation obviates some of the need for a network.
- Space itself makes it that you can just aim your payload and forget about it.

My $0.02 and I agree with you in that we should go to the asteroids.


Offline AlanSE

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Re: Asteroid Transit Map
« Reply #4 on: 11/15/2015 03:29 am »
I have been considering a side-project to build some web apps around the JPL asteroid database which will compute asteroid-to-asteroid parameters, which would be great fun for asteroid hopping scenarios.

There are really two problems I'm interested in. Start from one asteroid, and then consider at some particular time:
1. What are the closest nearby asteroids?
2. What are the quickest to get to, and most energetically favorable to get to?

The first question is stupidly straight-forward, but I would like to bring some greater degree of granularity to the table. Inevitably, you will find a nearby asteroid at a reasonable distance away (by that, I mean reasonable to travel the distance in a matter of weeks). But what type of population will we be talking about? How fast does that population change over time? What are the sizes and spectral types? How do the orbital parameters vary?

This is a problem space where many rocket scientists will lead you down fruitless paths. Hohlmann transfers between asteroids in the asteroid belt will take over a year. That's industrially wasteful. Propellant is money, but time is money too. If you're a real asteroid hopper, you want to leverage the full population of asteroids.

This brings us to optimization of point (2), but it is a higher-dimensional problem. I will posit that a single parameter can bring it back to simplicity. One single parameter can represent the trade-off between time and propellant. This can be as simple as a ratio of dollar costs between the two. On my space ship, I declare that one lost month is worth 0.5 km/s delta_v. There. We've specified the problem. I will only deal with single-trip optimization. Combinatorial trips have little added mathematical difficulty, and the interesting stuff will be rung out with my problem as it stands.

So for a given time-to-speed trade-off, we have a new population of asteroids defined by a Figure Of Merit. These are the interesting ones. How close are they? What kind of trip does it lead to? That's where the cool stuff is. Consider the extreme cases, if delta_v is effectively free (the space-age civilization referenced in another comment), then problem #2 simplifies to problem #1 as a limit case. You can move infinitely fast, so the movement of the asteroids themselves ceases to matter. This is unrealistic for any practical situation, but it's instructive.

There is another possibility. Instead of assuming that a space ship makes landings on every comment (because it's mining or something), what if it is just a flyby craft. Now this gets really exciting. You can consider a future timeline of the probe-to-asteroid separation distances and make some solid visuals to identify which ones are obvious to aim for next. Given sufficient patience, you can even use a gravity assist from one asteroid to get to another one. This enables multiple flybys at absurdly low delta_v costs. What's more, this is actually totally practical for a near-term spacecraft. We have done plenty of asteroid flybys, but think about it, have we ever optimized to capture data about the diversity of asteroids? This is an enormous scientific gap in our knowledge, and it would have tremendous public image implications. Just think if we could get imagery and scientific measurements of literally 100s of asteroids.

A probe like this would scarcely even have any hard end-of-life. An ion drive could allow continual course corrections with good efficacy. Good asteroid hunting grounds aren't all that far from home. Traditional issues of deep-space missions won't be that bad. It's not all that ambitious of a concept. I think it's a killer concept.
« Last Edit: 11/15/2015 03:33 am by AlanSE »

Offline mikelepage

Re: Asteroid Transit Map
« Reply #5 on: 11/15/2015 04:53 am »
Wow! thank you all for the really thoughtful replies!

Proponent: thank you for the pdf.  Really interesting reading! And also my forgetting to include ascending node was a big omission on my part so thanks.

Burminate: obviously extensive modelling would have to be done, and would almost certainly turn up some surprises once you actually run the real data.  Still, I think there is some productive in-principle discussion to be had about the idea.

SpacedX: Yes any colony will have access to 24/7 sunlight, and hopefully other forms of producing energy too but it seems to me each colony will probably grow to use the energy it has, so they'll never have excess energy beyond redundant needs.  As far as "recapture" goes, it would be cool but hard to see how it works.  In the very far future I could imagine some kind of rail gun linear accelerator that would itself be moved by SEP in association with a colony, but could either throw or catch cargo payloads for quick delivery times.

AlanSE I really like your time=dV equivalence principle.  It's something that most mission planners do I think, but not so simply, and getting the general public to wrap their heads around orbital mechanics is difficult enough without complicating things further.

The gravity whip idea would also be cool, but I'm fairly sure most asteroids wouldn't be massive enough for it to be worth it.  When discussing the New Horizon's trajectory beyond Pluto earlier this year, I asked someone in the team about whether they would alter NH's flyby window past Pluto so as to gravity whip in the direction of the most promising candidate beyond.  I was told that they wouldn't, mainly because 1) the science goals of the mission dictated a certain flyby trajectory, but also 2) the maximum deviation that a gravity whip past Pluto could provide was about a quarter of the capability of the on-board propellant, so it wasn't worth such a loss in science goals for such an incremental gain.  If a body as massive as Pluto could only provide such a tiny gravity whip, it's hard to imagine making whips around any but the most massive asteroids worthwhile.  Granted, NH was moving very fast relative to Pluto, but Pluto is also a giant compared to pretty much every asteroid. 

What I think would be an interesting project is, if it was determined that a given subset of asteroids could combine to form a proper transit map with regular rendezvous, I could envisage a program to proactively visit those asteroids with transponder probes that would go to the asteroids and do some more detailed analysis of size, composition, etc.  Phase 2 could be to seed selected asteroids with probes designed with the singular purpose of going to the asteroid, drilling a hole in the surface, and inflating a BA330 type module under the regolith.

Now, every seeded asteroid would not only be a known resource base, it would have a basic solar storm shelter facility, and be part of a planned transit system, whether or not a colony ended up developing there.  I personally think any colony at an asteroid would more likely be an orbiting station designed to produce spin G (rather than trying to build the whole colony inside the asteroid in microgravity, or trying to spin rubble-pile asteroids), but a critical piece of infrastructure would be to have a buried storm shelter that crew could retreat to, when they get the 8-24 hour warning of an incoming solar storm.

Offline AlanSE

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Re: Asteroid Transit Map
« Reply #6 on: 11/15/2015 12:20 pm »
Here's an example of a separation-distance graph. Only, this is for the distance between our sun and nearby stars:



It's quite trivial to imagine such a graph for asteroids - any given asteroid, looking at distances to nearby asteroids. Actually, I think this graph of stellar distances here is boring. Stars in our stellar neighborhood are mostly randomly distributed. Asteroids are lumped into all kinds of groups based on orbital parameters. Graphs like these might reflect some structure in the asteroid belt.

Now, every seeded asteroid would not only be a known resource base, it would have a basic solar storm shelter facility, and be part of a planned transit system, whether or not a colony ended up developing there.  I personally think any colony at an asteroid would more likely be an orbiting station designed to produce spin G (rather than trying to build the whole colony inside the asteroid in microgravity, or trying to spin rubble-pile asteroids), but a critical piece of infrastructure would be to have a buried storm shelter that crew could retreat to, when they get the 8-24 hour warning of an incoming solar storm.

Even if you built a spinning space station, it doesn't necessarily have to be orbiting. For a 1 km asteroid, for example, you might just connect it to the asteroid with a truss. Orbits will have poor stability around such a body anyway since its gravity is so weak. Also, if it's a rubble pile, that implies that it will have voids inside it, and one of these voids is possibly large enough to fit your entire rotating space station into, so you can get gravity and radiation protection at the same time. No excavation required.

In fact, this option might be only 1 or 2 realistic locations to get Earth gravity with low radiation. The other one I have in mind is the magnetically shielded equatorial orbit.

Offline mikelepage

Re: Asteroid Transit Map
« Reply #7 on: 11/16/2015 03:52 am »
Here's an example of a separation-distance graph. Only, this is for the distance between our sun and nearby stars:



It's quite trivial to imagine such a graph for asteroids - any given asteroid, looking at distances to nearby asteroids. Actually, I think this graph of stellar distances here is boring. Stars in our stellar neighborhood are mostly randomly distributed. Asteroids are lumped into all kinds of groups based on orbital parameters. Graphs like these might reflect some structure in the asteroid belt.

Now, every seeded asteroid would not only be a known resource base, it would have a basic solar storm shelter facility, and be part of a planned transit system, whether or not a colony ended up developing there.  I personally think any colony at an asteroid would more likely be an orbiting station designed to produce spin G (rather than trying to build the whole colony inside the asteroid in microgravity, or trying to spin rubble-pile asteroids), but a critical piece of infrastructure would be to have a buried storm shelter that crew could retreat to, when they get the 8-24 hour warning of an incoming solar storm.

Even if you built a spinning space station, it doesn't necessarily have to be orbiting. For a 1 km asteroid, for example, you might just connect it to the asteroid with a truss. Orbits will have poor stability around such a body anyway since its gravity is so weak. Also, if it's a rubble pile, that implies that it will have voids inside it, and one of these voids is possibly large enough to fit your entire rotating space station into, so you can get gravity and radiation protection at the same time. No excavation required.

In fact, this option might be only 1 or 2 realistic locations to get Earth gravity with low radiation. The other one I have in mind is the magnetically shielded equatorial orbit.

Oh, hey Al :) I wondered if it was you (we met at ISDC 2011).  Australia is a bit too far for me to make it to more conferences unfortunately.

A graph I've been imagining for a long time would essentially be a  this graph (for asteroids) combined with elements from figure 2 of the link in Proponent's post: i.e. x axis = time, y axis = separation distance, z axis = dV.  In the dV axis you have envelopes for each approaching asteroid, colour coded by forms of propulsion that could achieve a transfer (hotter colours for chemical thrusters, cooler colours for SEP and the like).

As far as ELEO goes, I'm in full agreement with regards to all practical aspects, I'm just wondering how geopolitics of launch sites will play into that?  You should probably set up a new topic in the forums here to discuss it if you haven't already: I'm curious about the mass penalty for launching from Cape Canaveral/Brownsville etc.

Offline Hanelyp

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Re: Asteroid Transit Map
« Reply #8 on: 11/16/2015 04:43 pm »
Distance is of little interest in space travel except how it impacts time and delta-V to make the trip.  Of more use would be a graph of if I leave at a given time on a minimum delta-V trajectory for the target, what are the flight time and delta-V.  Or if you can display a 3D graph properly, what is the trip time vs. delta-V vs. departure time.  Or various cross sections of trip time for a given delta-V or delta-V for a given max trip time.

Offline AlanSE

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Re: Asteroid Transit Map
« Reply #9 on: 11/17/2015 01:21 am »
Oh, hey Al :) I wondered if it was you (we met at ISDC 2011).  Australia is a bit too far for me to make it to more conferences unfortunately.

A graph I've been imagining for a long time would essentially be a  this graph (for asteroids) combined with elements from figure 2 of the link in Proponent's post: i.e. x axis = time, y axis = separation distance, z axis = dV.  In the dV axis you have envelopes for each approaching asteroid, colour coded by forms of propulsion that could achieve a transfer (hotter colours for chemical thrusters, cooler colours for SEP and the like).

As far as ELEO goes, I'm in full agreement with regards to all practical aspects, I'm just wondering how geopolitics of launch sites will play into that?  You should probably set up a new topic in the forums here to discuss it if you haven't already: I'm curious about the mass penalty for launching from Cape Canaveral/Brownsville etc.

Extremely unexpected misunderstanding - I am not Al, the NASA contractor who wrote the paper on equatorial orbits. I was connecting that idea to the idea of colonies in asteroid pores based on a purely technical similarity. They are both low-radiation micro-gravity environments under consideration for long-term habitation. I have had no communication with him, and only know of him as the author of such papers.

Distance is of little interest in space travel except how it impacts time and delta-V to make the trip.  Of more use would be a graph of if I leave at a given time on a minimum delta-V trajectory for the target, what are the flight time and delta-V.  Or if you can display a 3D graph properly, what is the trip time vs. delta-V vs. departure time.  Or various cross sections of trip time for a given delta-V or delta-V for a given max trip time.

(bold emphasis my own)

In a previous comment, I said "rocket scientists will lead you down fruitless paths". The bold text above is exactly what I was predicting. Minimum delta-V calculations are just not useful for asteroid hopping. If I want to visit 1,000 asteroids, then minimum energy hops will make that trip take something like 2,000 years.

After that bold part, you were going in the right direction. But putting a cap on time taken isn't great. It might do okay, but not great. The optimization problem is extremely sensitive to departure time and extremely non-linear. Consider, as a case-in-point, an asteroid passing relatively close by at an acceptably low delta-v. You will want to leave your home asteroid and make a burn to intercept the target asteroid an exact time in the future (first burn), then once the target goes by, you do a burn to match its velocity (second burn). Sure, you could put this in terms of Hohmann transfer optimization. Useful hops might even survive your maximum time criteria. Maximum time is a linear programming tool, it's like a fence on the solution space that works well when the solution lies on the fence. What I'm saying is that almost all solutions which are worth a darn are not on the fence of the solution space. They just pop up at random times. My point is just that it's not conceptually complicated, and we can get by with fairly light rocket science revisions if you start out with a nice little map of the neighborhood.

Offline KelvinZero

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Re: Asteroid Transit Map
« Reply #10 on: 11/17/2015 06:26 am »
I wanted to ask a similar question to the OP. The initial problem is just how to phrase the answer in a meaningful way.

I was wondering how close asteroids were to each other with respect to travel time and effort. I mean, would an inhabited asteroid belt be a place where most asteroids were only a few hours from several other destinations, or a few days or what?

It isn't really possible to lock down a reasonable travel time, delta-v or asteroid mass so the best answer I can think of would have three dimensions and basically ask "for an average asteroid, how many other candidates could be visited, if we limit travel time to T, delta-V to V, minimum considered candidate size to S (which could be mass or average radius or whatever)

I guess the easiest way to fill in a table like this would be to generate a random asteroid belt of similar density to our own and just brute force it for each asteroid and average the result. Limit minimum asteroid size to keep computation time reasonable. Do we have the statistics to generate such an asteroid belt?

Hopefully outlier asteroids would not distort this result too much. Otherwise we have to add a less well defined criteria to ignore these.

Offline Hanelyp

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Re: Asteroid Transit Map
« Reply #11 on: 11/17/2015 04:43 pm »
Density is not a sufficient criteria for a simulated asteroid belt.  Velocity distribution is also important.  It is possible for a pair of asteroids to pass near each other with a large relative velocity, or otherwise requiring a large delta-V to make the transit.

Offline JasonAW3

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Re: Asteroid Transit Map
« Reply #12 on: 11/17/2015 07:14 pm »
when you titled this thread as an "Asteroid Transit Map", I suddenly envisioned a sort of subway system between asteroids in the Asteroid Belt!
My God!  It's full of universes!

Offline mikelepage

Re: Asteroid Transit Map
« Reply #13 on: 11/18/2015 06:42 am »
Oh, hey Al :) I wondered if it was you (we met at ISDC 2011).  Australia is a bit too far for me to make it to more conferences unfortunately.

Extremely unexpected misunderstanding - I am not Al, the NASA contractor who wrote the paper on equatorial orbits. I was connecting that idea to the idea of colonies in asteroid pores based on a purely technical similarity. They are both low-radiation micro-gravity environments under consideration for long-term habitation. I have had no communication with him, and only know of him as the author of such papers.

Aha, understood, and that does make sense.  I guess it really depends how big the voids in such asteroids can be.

when you titled this thread as an "Asteroid Transit Map", I suddenly envisioned a sort of subway system between asteroids in the Asteroid Belt!

Exactly.  This is a useful visualisation I've seen before but came across once more today:


Sure, it's not as if there can be "train tracks" or dedicated "trade routes" as such because of the changeability of the transit paths, but the sheer number of asteroids out there is huge (I've read projections of upwards of 5 million asteroids over 100m in diameter) and although the distances are vast, I find it hard to believe that asteroid based colonies should be any harder that surface based colonies.  We have fairly good evidence to suggest there are substantial amounts of relatively pure water ice in the belt (which is even more accessible from the surface of the asteroids once you get outside the snow line at 2.7 AU), and so once you solve the "sustainable space habitat" problem (which you have to solve to live on Mars anyway), there's no particular reason to limit yourself to planetary surfaces. 

So yeah, I find the arguments between Moon-firsters and Mars-firsters to be fairly small minded.  A couple of years ago (when I started writing a scifi novel) it occurred to me that people in the future would probably have a label for this region of space which humanity had been able to expand out to with current propulsion (rocket/SEP) and energy technology (PV): It's this loosely defined area of the inner ecliptic where solar panels are still useful for energy, which contains resource bases like the Earth and Moon, Mars, (Venus?), and the asteroids of low inclination.  The "Incliptic" was what I decided to use.

What I think would be a really fun/useful (for you computer science majors reading this ;) ) is to actually design what I imagined in my novel might called SDoDView (Spectral Differentiation of DeltaV View): i.e. the actual program and 3D projection that navigators on spacecraft would use to plot their own courses.  You know how much propulsion your craft is capable of, and you have a database of asteroids which will be making close approaches over time, so if you're looking at 3D projection, you would probably design the program to use colour to differentiate between and highlight different courses that the navigator could plot.  What does that piece of software actually look like?   I've heard of Kerbal Space Program, but the only demos I've looked at seemed focussed on helping people to understand building rockets and doing orbital rendezvous, moreso than something that would crunch the numbers and show you a whole "tree" of potential paths.

Offline JasonAW3

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Re: Asteroid Transit Map
« Reply #14 on: 11/18/2015 01:43 pm »
"The 5:19 to Ceres, Vesta, Eros and all parts in between, now loading on track 9!  All Aboard!"

Sorry!  Just had to be said.
My God!  It's full of universes!

Offline Hop_David

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Re: Asteroid Transit Map
« Reply #15 on: 11/18/2015 03:10 pm »
If nothing else, it makes clear the unfortunate inverse relationship between accessibility (low eccentricity and similar semi-major axis) and frequency of launch windows (synodic period).

Yes, the closer asteroid semi-major axis is to 1 A.U., the longer the synodic period.

And it gets worse. As you say, a launch window opens each synodic period. A launch window to a bitangential transfer orbit. However the low delta Vs often cited assume a bitangential orbit that reaches the asteroid at aphelion. See Shoemaker and Helin's paper.

For bitangential orbits, departure Vinf and arrival Vinf sum to nearly the same quantity regardless of where the transfer orbit touches the asteroid orbit. Asterioid aphelion rendezvous usually means a smaller arrival Vinf but a larger departure Vinf. But a larger departure Vinf is mitigated by the Oberth benefit since the ship is departing from a deep gravity well. So an aphelion rendezvous means a lower delta V budget.

The sort of transfer orbits Shoemaker and Helin imagine occur much less frequently than each synod.
« Last Edit: 11/18/2015 03:18 pm by Hop_David »

Offline mikelepage

Re: Asteroid Transit Map
« Reply #16 on: 11/30/2015 05:37 am »
If nothing else, it makes clear the unfortunate inverse relationship between accessibility (low eccentricity and similar semi-major axis) and frequency of launch windows (synodic period).

Yes, the closer asteroid semi-major axis is to 1 A.U., the longer the synodic period.

And it gets worse. As you say, a launch window opens each synodic period. A launch window to a bitangential transfer orbit. However the low delta Vs often cited assume a bitangential orbit that reaches the asteroid at aphelion. See Shoemaker and Helin's paper.

For bitangential orbits, departure Vinf and arrival Vinf sum to nearly the same quantity regardless of where the transfer orbit touches the asteroid orbit. Asterioid aphelion rendezvous usually means a smaller arrival Vinf but a larger departure Vinf. But a larger departure Vinf is mitigated by the Oberth benefit since the ship is departing from a deep gravity well. So an aphelion rendezvous means a lower delta V budget.

The sort of transfer orbits Shoemaker and Helin imagine occur much less frequently than each synod.

Excellent post David.  Sorry it took me so long to respond but there's a lot in there and I wanted to give myself time to absorb it :)

Would it be correct to say that if we limit ourselves to using bitangential transfer orbits, it's likely we're looking at average transfer times of months (or years)? in which case a human-rated space craft would need the required facilities to support life for that long, which in turn will increase the mass of the transfer craft substantially, and also increase the risk of being exposed to potentially fatal solar radiation storms, etc etc.  I can't see how it wouldn't only be cargo that is moved this way...

If instead, we assume a network of asteroids as resource centres with radiation protection and agricultural facilities (i.e. colonies which are largely self-sufficient for basic necessities), then for human space flight it becomes economic to build low mass transfer vehicles which have the capability of high g-force departure and and arrival burns (probably with SEP in-between).  Humans are incredibly valuable assets in space, so in pure $$ terms the optimisation becomes less to minimise for dV and more to minimise the amount of time people are kept cooped up in small tin cans.  What I'm more curious about is what those trajectories look like? and what the most important characteristics of the orbits of those asteroids are?  Imagine the transfer craft are Orion-sized or slightly bigger,  designed for an average transfer time of a week or two, with emergency capacities of 100 days or so.

Obviously, you still want to minimise dV, but the question I'm asking is not how to optimise trajectories for two given asteroids or a specific Earth/asteroid combination, but how you pick the groups of asteroids that make regular, short-duration asteroid hopping possible?  (In my original post I explained why I think this kind of plan is worth having early on)

Offline Hop_David

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Re: Asteroid Transit Map
« Reply #17 on: 11/30/2015 08:41 pm »
If nothing else, it makes clear the unfortunate inverse relationship between accessibility (low eccentricity and similar semi-major axis) and frequency of launch windows (synodic period).

Yes, the closer asteroid semi-major axis is to 1 A.U., the longer the synodic period.

And it gets worse. As you say, a launch window opens each synodic period. A launch window to a bitangential transfer orbit. However the low delta Vs often cited assume a bitangential orbit that reaches the asteroid at aphelion. See Shoemaker and Helin's paper.

For bitangential orbits, departure Vinf and arrival Vinf sum to nearly the same quantity regardless of where the transfer orbit touches the asteroid orbit. Asterioid aphelion rendezvous usually means a smaller arrival Vinf but a larger departure Vinf. But a larger departure Vinf is mitigated by the Oberth benefit since the ship is departing from a deep gravity well. So an aphelion rendezvous means a lower delta V budget.

The sort of transfer orbits Shoemaker and Helin imagine occur much less frequently than each synod.

Excellent post David.  Sorry it took me so long to respond but there's a lot in there and I wanted to give myself time to absorb it :)

Would it be correct to say that if we limit ourselves to using bitangential transfer orbits, it's likely we're looking at average transfer times of months (or years)?

For accessible near earth asteroids, we're talking about bitangential trip times of 6 months, plus or minus.

in which case a human-rated space craft would need the required facilities to support life for that long, which in turn will increase the mass of the transfer craft substantially, and also increase the risk of being exposed to potentially fatal solar radiation storms, etc etc.  I can't see how it wouldn't only be cargo that is moved this way...

If instead, we assume a network of asteroids as resource centres with radiation protection and agricultural facilities (i.e. colonies which are largely self-sufficient for basic necessities), then for human space flight it becomes economic to build low mass transfer vehicles which have the capability of high g-force departure and and arrival burns (probably with SEP in-between).  Humans are incredibly valuable assets in space, so in pure $$ terms the optimisation becomes less to minimise for dV and more to minimise the amount of time people are kept cooped up in small tin cans.  What I'm more curious about is what those trajectories look like? and what the most important characteristics of the orbits of those asteroids are?  Imagine the transfer craft are Orion-sized or slightly bigger,  designed for an average transfer time of a week or two, with emergency capacities of 100 days or so.

Obviously, you still want to minimise dV, but the question I'm asking is not how to optimise trajectories for two given asteroids or a specific Earth/asteroid combination, but how you pick the groups of asteroids that make regular, short-duration asteroid hopping possible?  (In my original post I explained why I think this kind of plan is worth having early on)

Some good points there.

Let's say we have 26 communities named A thru Z (let's call earth E). A will have launch windows to B, C, D, etc. Every body will have launch opportunities to 25 other bodies. Obviously there is much more opportuntiy of trade, isolation would be less severe.

And as you say, airless worlds might have the option to launch without using reaction mass. Rail guns, slings, in some cases Clarke Style elevators (Ceres and Vesta are well stuied for Clarke style beanstalks).

My PDF I pointed to only works for coplanar circular to elliptical orbits. But transfers between asteroids would usually be between two non-coplanar ellipses. Software for making porkchop plots could work for finding low delta V routes between rocks. These rely on Lambert Space Triangles. This works well for most bitangential transfers except if the two tangent points are nearly 180 degrees apart. But in the case of two ellipses, the 180 degree separation between tangent points will be rare.
« Last Edit: 11/30/2015 08:46 pm by Hop_David »

Offline mikelepage

Re: Asteroid Transit Map
« Reply #18 on: 12/04/2015 08:45 am »
Let's say we have 26 communities named A thru Z (let's call earth E). A will have launch windows to B, C, D, etc. Every body will have launch opportunities to 25 other bodies. Obviously there is much more opportuntiy of trade, isolation would be less severe.

And as you say, airless worlds might have the option to launch without using reaction mass. Rail guns, slings, in some cases Clarke Style elevators (Ceres and Vesta are well stuied for Clarke style beanstalks).

My PDF I pointed to only works for coplanar circular to elliptical orbits. But transfers between asteroids would usually be between two non-coplanar ellipses. Software for making porkchop plots could work for finding low delta V routes between rocks. These rely on Lambert Space Triangles. This works well for most bitangential transfers except if the two tangent points are nearly 180 degrees apart. But in the case of two ellipses, the 180 degree separation between tangent points will be rare.

You sir, do love your information-dense posts :) But I'm learning plenty, so thank you!

Regarding "transfers between asteroids would usually be between two non-coplanar ellipses"... Need they be?
The first asteroids we visit will not be present on this plot:



But perhaps an appropriate philosophy of expansion would prioritise the large energy requirements of plane changes, and start specifically with NEOs that are basically coplanar to "anchor" locations, such as Mars and/or other prominent families of asteroids?  the idea being that once one has moved planes, it will generally be cheaper to stay within that plane.

Some potential "anchors":
Mars is at 1.85 inclination, longitude (of ascending node) 49.6
Massalia is at 0.7 inclination, longitude 206.5
Vesta is at 7.1 inclination, longitude 103.9
Ceres is at 10.6 inclination, longitude 80.3

Perhaps those first 26 bodies colonised will all (by choice) have very similar orbital characteristics to one (or a small number) of these anchors...? 


Offline AlanSE

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Re: Asteroid Transit Map
« Reply #19 on: 12/05/2015 03:05 am »
But something that is close to Ceres on that plot may not be "close" either physically or energetically in terms of the delta_v needed to make the transfer. Consider two objects that both have a 10 degree inclination. You still have to specify the angle at which that angle applies. Worse case scenario, the planar difference is actually 20 degrees from one object to the other, even though they lie smack dab in the same spot in the plot.

That presents a huge energy barrier to making the transfer, and this is so far hand waving all of the absurd minimum-energy transfer window synchronization stuff that Hop loves to write about. Mathematically, this has a large number of independent variables. If that asteroid plot had 6 axes, then could easily act as a visual representation of the difficulty of making the transfer burns. Maybe fewer. Dimensional reduction is a very intellectually demanding exercise. "Clusters" of colonies in well-known asteroid orbital groups might be less appealing than they appear. Or it might depend on the cluster, since the entire orbital plane is correlated between members.

Regarding NEAs, don't they typically have higher inclination values? Something about being near the inner system planets lends better suitability to more chaotic high-inclination orbits, which the asteroid belt is defined largely by resonances with Jupiter. This is mostly an anecdotal statement, so please feel free to correct me.

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