Orbital mechanics puzzle

[DataPacRat]

Originally Posted by Grouchy Chris

I can do it with 25 collimators. See my proposed array here.

This array has 17 collimators in orbit at 7.7 AU, so that one is always in range of Saturn, one always in range of Jupiter, and each is within range of its two neighbors. A single collimator is at Jupiter, and another 7 collimators orbit the Sun at 3 AU, so that one is always in range of Jupiter.

This array was designed for minimum number of collimators, at the expense of requiring a large number of connections to some targets, and also having a single point of failure at Jupiter. It also assumes minimal station-keeping for the collimators. This strikes me as doing things on the cheap and asking for trouble, but that's what the customer asked for.

Thank you /very/ much for taking the time and trouble to put that together - it clarifies a great deal.

(I'm starting to wonder if there's a reasonable question I can ask here where I /won't/ get a useful response. :) )


Depending on where Saturn and Jupiter are when the system starts getting put together, and that Jupiter moves at around 0.7 AU/year faster than Saturn, further savings could be made by only putting together enough of the outer ring of collimators to relay the beam, and tossing new ones out every few years as the two planets get further apart. (Or, perhaps, adding a new relay co-orbiting with Jupiter.)

[RogerBW]

If you've got the mass to build 25 small collimators, why not, as Anthony suggested, use the same mass to build one huge focusing system at the origin point of the beam? If a collimator's worth of mass gets you 3AU of range, 25 collimators' worth of mass ought to get you a whole lot more.

That's the question that I haven't seen a convincing answer to yet, and that lack of answer seems to pose a problem for the scenario as presented.

[DataPacRat]

Originally Posted by johndallman

It looks from the numbers you've given us that range is proportional to surface area. So the area of the plane of the solar system that a collimator covers is proportional to the square of surface area, and the volume is proportional to the cube of surface area.

So if mass is approximately proportional to surface area - which it looks like - and cost is proportional to mass, but effectiveness is proportional to square of surface area, then as few large collimators as practical is the cheapest option.

That does, indeed, seem to be the case. 3AU is, however, already about as large as practical, for reasons I describe below.

Originally Posted by RogerBW

If you've got the mass to build 25 small collimators, why not, as Anthony suggested, use the same mass to build one huge focusing system at the origin point of the beam? If a collimator's worth of mass gets you 3AU of range, 25 collimators' worth of mass ought to get you a whole lot more.

That's the question that I haven't seen a convincing answer to yet, and that lack of answer seems to pose a problem for the scenario as presented.

A standard cargo load in the setting is 40 tons; the standard fission-heated teakettle steamer freighter can haul such a load from Earth/Luna to the Jupiter Trojans in about 3 years (and, if not left in place for stationkeeping, take another 3 years deadheading back). However, using the glass-bead aerosol lens, a 40-ton collimator has a radius of just under 200 meters, giving it a range of 0.2 AU. Creating a mirror with a 3 AU range needs around 600 tons - requiring 15 freighter trips for just one 3 AU collimator. Some savings can be made by trying to manufacture closer to the site, using local materials; but none of the list of optically-non-linear mediums at https://en.wikipedia.org/wiki/Nonlin..._SHG_materials seem to match very closely to most asteroid compositions. So I'm figuring that at least 20% of the raw material will have to come from elsewhere, as well as a trip for the seed factory, bringing us down to 4 freighter trips per 3 AU collimator in Jupiter co-orbit. (The trips lake less time in smaller orbits, but more time for larger ones, so I'm just taking that as an average for this back-of-the-envelope description.)

Given that the steamers are also useful for hauling materials from mining asteroids to manufacturing asteroids, they're always in high demand. A dozen or more freighter-years per 3AU-collimator is kinda expensive. With a finite supply of freighters, and not being able to devote all of them to collimator production (because the spice - er, the metals must flow), that puts a bottleneck on how many can be used for such construction at any given time. And since the New Cold War might turn hot in any given year, a perfect system that's not going to be ready for another 20 years is going to be a risky time-sink compared to one that's at least partly functional in 5, and can be expanded upon as time passes.


(Of course, if I knew for sure what the answers would be, I wouldn't have started this thread, so feel free to point out flaws in the above. :) )

[johndallman]

So, build a 24AU collimator at Saturn. That weighs eight times as much as the 3AU collimator, but you don't have to haul it anywhere, and you can get 80% of the materials from Saturn's moons.

With 25 3AU collimators, you need 15x25 = 375 freighter trips to put them in place.

With the 24AU collimator, you would need 15x8 = 120 freighter trips to haul it somewhere, but since you only need to shift the 20% of its mass that isn't obtainable locally, that goes down to 24 trips, under a tenth the haulage of the big network, and equivalent to less than two of the 3AU collimators, unless I've misunderstood you.

[DataPacRat]

Originally Posted by johndallman

So, build a 24AU collimator at Saturn. That weighs eight times as much as the 3AU collimator, but you don't have to haul it anywhere, and you can get 80% of the materials from Saturn's moons.

With 25 3AU collimators, you need 15x25 = 375 freighter trips to put them in place.

With the 24AU collimator, you would need 15x8 = 120 freighter trips to haul it somewhere, but since you only need to shift the 20% of its mass that isn't obtainable locally, that goes down to 24 trips, under a tenth the haulage of the big network, and equivalent to less than two of the 3AU collimators, unless I've misunderstood you.

I don't think you've misunderstood a thing. Even assuming the Saturn trips take twice as long for the freighters, the numbers still seem favor that approach.

Now, assuming that this is, in fact, going to be the plan... my next steps are to start figuring out the various forms of misdirection that can be layered on top of it, taking into account that There Ain't No Stealth In Space. One layer can involve, as previously mentioned, using the freighters to drop off tanks of fuel, hiding the very existence of the collimator. Actually dropping off tanks of fuel in orbits that match a useful pattern of collimators, such as the pattern Grouchy Chris posted, could help hide both the location of the main collimator, and its actual range and abilities. Since cargo containers don't have to be kept at room temperature, then when the engine is turned off they're a lot harder to keep track of; so with some careful trickery as the freighters slingshot around Jupiter, and avoiding using the engine for as much of the trip afterward as possible, and possibly including dropping off inflatable decoys, then it could be made infeasible to tell that Saturn is an area of special interest to Our Heroes. That's a good start for off the top of my head, but there are undoubtedly a number of other relatively low-cost tricksy ideas that could be applied - anyone who wants to suggest some, feel free to post. :)

[Grouchy Chris]

Originally Posted by DataPacRat

Thank you /very/ much for taking the time and trouble to put that together - it clarifies a great deal.

You're welcome. I have to agree with others, though, who have suggested other designs. I think saying that you can do it with 25 3-AU collimators just sets an upper bound for the expense, against which you can measure the all-in-one-place design.

Originally Posted by johndallman

So, build a 24AU collimator at Saturn.

I think this is a sensible approach, but why 24 AU? The maximum Jupiter-Saturn separation is less than 16 AU.

[johndallman]

Originally Posted by Grouchy Chris

I think this is a sensible approach, but why 24 AU? The maximum Jupiter-Saturn separation is less than 16 AU.

It's the only collimator in the system. It lets you reach all the way across the inner system from Saturn's 10AU orbit to further out the other side, and lets you reach a large portion of Uranus' orbit and some of Neptune's. To some extent it was an arbitrary choice to show how One Big Collimator, within the parameters given, is cheaper than a lot of smaller ones. Thanks for doing the figures for the network, which were needed to show the relative costs.

[DataPacRat]

Originally Posted by DataPacRat

undoubtedly a number of other relatively low-cost tricksy ideas that could be applied

... which include fighting mirrors. Even if a spacecraft can't carry enough material for a mirror capable of handling the full power of the laser from Saturn, it can probably direct enough coherent energy onto a nearby rocket to really give that other rocket a bad day.

I wonder if Our Heroes having a policy of deliberate ambiguity about the weaponization potential of their 24-AU-range laser would be a net positive or negative...

[johndallman]

Originally Posted by DataPacRat

I wonder if Our Heroes having a policy of deliberate ambiguity about the weaponization potential of their 24-AU-range laser would be a net positive or negative...

It's going to be seen as a weapon the moment the Earth governments know about it. Think about how journalists will view "The rebel exiles have built a giant laser on Saturn that can fire as far as Earth!"

[DataPacRat]

Originally Posted by johndallman

It's going to be seen as a weapon the moment the Earth governments know about it. Think about how journalists will view "The rebel exiles have built a giant laser on Saturn that can fire as far as Earth!"

... oddly enough, you've just reminded me of the basic theme of my own setting: that the Earthly governments have become paranoid about small groups having access to big weapons.

Our Heroes having an asteroid colony way out in the boonies has already resulted in journalists accusing them of only doing so so that they could brew up bioweapons far away from any possible supervision; and some intelligence moles in the asteroid doing so themselves and framing Our Heroes for it. Similarly, their freighters are capable of nudging rocks to land on Earthly cities (though noone's managed to frame them for actually doing that), the fact that their spacecraft are /nuclear/ (and thus Our Heroes have the capacity for building nuclear bombs, regardless of the fact that dropping rocks would provide more blam), that Our Heroes have started building computers from scratch specifically to avoid the built-in surveillance chips required on Earth, etc, etc. (Similar accusations are leveled against anyone else in orbit who hasn't surrendered to Earthly authority - Our Heroes' asteroid is far from the largest such group.)

The fact that Our Heroes have not, in fact, used any WMDs they are described as possessing seems to escape mention. Ditto that various items they are accused of having are, simply, required in order to simply go about the business of living out in the asteroid belt. Unless something changes - and I'm not quite sure what that might be - Our Heroes are unlikely to win any PR battles on Earth about their nefarious plots... so, looking at things that way, would adding one more nefarious plot to the list make all that much difference?

The Grand Tour of the Solar System which Our Heroes will be undertaking (and during the Saturn stop of which the seed factory for the laser will be installed) is already, in part, to be a demonstration of their technological prowess. ("Hey, look what we can build!") Various Earthly intelligence agencies have shown no compunctions about trying to assassinate Our Heroes (one's already down to being a brain in a jar). There are significant trading blockades between Earth and Our Heroes' asteroid. And Our Heroes are at least loosely aligned with the major orbitals which are in a New Cold War with Earth...


... say, does anyone have any good references on the Cuban Missile Crisis, and alternate-history versions thereof?