-Z- (Z@Gundam.Com)
Sun, 04 Jun 2000 12:55:14 -0700


At 10:34 6/4/2000, you wrote:
> This begs an interesting question: Since you need the colony
>cylinders to match the vectors of the various Lagrange points, do you
>assemble the cylinders before hand, at say Luna II, and then accelerate the
>whole mass to final assembly at the Lagrange points?
>
> Or do you accelerate the raw materials to match velocities, and then
>assemble the cylinders at the (shifting) Lagrange points, and after final
>assembly make any fine adjustment to the vectors of the cylinders?

The original O'Neill "High Frontier" plan -- and, to my knowledge, every
space colonization plan ever proposed -- was to build the colonies in situ
from either raw materials or (relatively) small sub-components. The Moon
is the primary source of both, due to its much shallower gravity well. The
O'Neill plan specified a mass driver (essentially an electromagnetic rail
gun) on the Moon and mass catchers (big funnels, like the nets used to snag
butterflies, goldfish, and other delicate living creatures) in orbit. And,
of course, the whole idea of moving 3 Juno from the asteroid belt to
cislunar orbit was to provide a base of operations and an in situ material
source for colony construction. As construction wound down, 3 Juno was
parked at L3, renamed Luna II, and turned into first a Federation
administrative post and then an EFSF garrison.

There are two good reasons for in situ construction. First and foremost,
it's the least expensive. Most of the fuel and energy expended in current
space operations is in going up the first 300 miles. Once you're in low
Earth orbit, you're "halfway to anywhere" -- it's climbing out of Earth's
gravity well that's the killer. So, once you're up there, you stay up
there and use what's up there with you, which is the entire rest of the
Universe, now brought into reach.

The second reason is that you're supposedly going up there to stay. The
idea is to be an independent and self-sufficient colony, not a glorified
space station dependent on a very expensive pipeline from Mother Earth. So
you start out doing as much as you can on your own and bootstrap the colony
from a minimum supply of Earth-based resources.

> I think a pre-assembly at a near Earth orbit is more likely, since
>if you assemble at a point in lunar orbit (where L3, L4 and L5 will
>eventually pass through) the moon will also eventually come around and undo
>all your work... =)

If you assemble it in the Moon's orbit, it's orbiting just like the
Moon. Put it two miles "ahead" of the Moon and it will always stay two
miles ahead of the Moon. The Moon won't "catch up" with it any more than
you catch up with guy sitting in front of you on the bus -- you're all
traveling at the same rate in the same trajectory and will do so until
acted upon by some external force.

The more mass you assemble in any place, the more fuel and mass you'll have
to expend to move it later. It actually costs less to move mass from the
Moon to L5 (2,900 m/s delta-V) than it does from the Moon to LEO (6,300
m/s), and it will subsequently cost as much to move it from LEO to L5
(4,100 m/s) as it would to move it from LEO to lunar orbit, only now you'd
be trying to move the entire mass. So why not save the time and trouble
and move small, manageable pieces to L5 in the first place?

>>Yes, the Sun throws a few perturbations into the orbits, but its effect on
>>the Lagrange points of the Earth/Moon system is negligible.
>
> If I recall my reading materials correctly, Lagrange (the person)
>first demostrated his theoy with the Trojan asteroids of Jupiter as you
>mentioned. Specifically, Lagrange's theorem (does it have a name?) is for a
>three-body system, in which one of the bodies has negligible mass in
>comparison to the other two.

No, Lagrange's 1772 essay on the "three-body problem" predates the 1906
discovery of the Trojans by almost 135 years. See the Lagrange section of
my Gundam High Frontier page:

http://www.dyarstraights.com/msgundam/frontier.html#Lagrange

In fact, read the entire page, then let's talk about whatever I haven't
covered. It seems that I'm reiterating things I've already explained at
some length on the G:HF page and it's beginning to get tedious.

I'd rather break some new ground and possibly generate new material that I
can add to the page, as has happened with a number of other issues raised
here in the past.

> Back to the point. Why would the Sun's effect be negligble? After
>all, the Earth orbits the sun, so it's effect should be a lot more visible
>than what you are suggesting. Unless the gravitational effects of the Moon
>and the Earth in our situation is so pronouced that the Sun simply can't cut
>in. =) Sorts of leave Apollo out of the party, no?

The answer to that is explicated in excruciating detail in "Perturbation
Theory Based On Lie Transforms and its Application to the Stability of
Motion Near Sun-Perturbed Earth-Moon Triangular Libration Points" (A.A.
Kamel & J. Bleakwell, Stanford, 1970). Way too technical to discuss here.

> And an awfully good idea.. so long you remember to dispose of the
>trash properly. =) Will the area around a cylinder be cluttered with waste
>that cannot be easily reused or disposed? Or is there some sort of central
>disposal site, like the junkyard on the Moon in 0083?
>
> (Or do the colonies shoot their trash into the sun?)

Living on a planet where the air is free and you can run around naked
wherever the climate, weather, and cultural dictates permit, you have a
casual attitude to value of biomass or, for that matter, any mass. In
space, "waste" applies only to something that cannot be reused in any
fashion. Since any mass can always be used for propellant, if only by
throwing it away, there's really no such thing as waste. Everything is
and, to a certain extent, must be recycled, especially organics.

The Moon's a different situation. Like Earth, it's at the bottom of a
gravity well and thus some items are difficult to move.

>>Each agricultural blocks or farming satellite (farmsat) is about 645 km
>
> I assume you mean 645m, not km.

Oops! Yeah, my fingers got conditioned to typing "km" by all of the other
distances under discussion. These satellite farms are pretty hefty, for
all that. Each is a tad larger than the Bernal sphere, which is touted as
being capable of supporting 10,000 people, and here we have 72.

>>(2,110 feet) across, but is encompassed by a parabolic mirror about 1.3 km
>>(4,265 feet) across, so the ring would have a minimum circumference of 95
>>km (60 miles) and thus a diameter of about 30 km (18.6 miles).
>
> You are assuming that the parabolic mirrors are packed next to each
>other, with about a 20m gap in between them. That's an awfully close
>promixity.

Well, now, I did say "minimum circumference" and I meant it.

> The designers will probably want to spread them out a little more,
>maybe 100m gap between each mirror, so that any damage can be localized to a
>single module. The circumference will become.. like.. uhm.. a little over
>100km, give or take a few hundred meters. A diameter of some 32 km.. just a
>little wider.
>
> And that's if the number of satellites remain constant at 72.
>
>>Per the original O'Neill design, the ring would have a diameter of
exactly 32
>>km (20 miles) and serve as the forward attachment points for the mirrors,

The number was specified as 72 because the ideal diameter was equal to the
length of the colony and the size of the farmsat was optimized for
hydroponic agriculture and thus somewhat fixed. With a "fixed"
circumference (32 km) and a "fixed" farmsat size (1.3 km -- call it 1.5 km
to incorporate a "fixed" separation of 100 meters on either side), you get
a "fixed" number of farmsats, in this case 72.

> I recall about a month or two back someone mentioned a problem with
>the mirrors being attached at only one end? With these satellites, they
>would provide another anchor for the mirrors.

Different geometry, here. Each of the farmsats is a glass "hatbox" -- a
cylinder with the same width, height and depth. It's set into a parabolic
mirror that's essentially a disk with the cylinder at the focus. In
profile, it'd look something like this:

                  --+
                     \
             +--------+
             | |
SUN | |
             | |
             +--------+
                     /
                  --+

Seen face on, this would appear to be concentric circles.

>>they're going to be pulling considerable Coriolis forces if they are
actually
>>rotating in synch with the main cylinder, which they'd have to do if (but
>only
>>if) the mirrors were attached to them.
>
> Pardon me. Coriolis forces? I'm not familiar with the term..

AKA centrifugal and centripetal force, the radial acceleration that
produces pseudo-gravity for the colonies.

>>The minimum separation is equivalent to a colony-width (or, as we've
just seen,
>>nearly a colony-length) in each direction. That sums up to 90 km (55
miles) --
>>10% more than my ballpark figure.

I was mistaken here. The "ballpark" figure was actually my unconscious
recollection of the specified distance between the ballistic coupled colony
pairs, per O'Neill. It's derived from a complex mathematical equation that
takes into account both the estimated mass and the rotational speed --
again, way too technical for discussion here or even on my G:HF page, where
I've more or less presented derived figures as a given.

Suffice it to say that the two 32 km x 6.4 km cylinders with the 72
orbiting 1.3 km by 654 meter farmsats must be spaced 80 km (50 miles) apart.

Please note that this is the distance from axis to axis (or hub to hub, if
you will) of the two rotating cylinders.

> Would it change things if the cylinders are not aligned in the same
>direction? Let's say, if End A of one cylinder is aligned with End B of the
>other cylinder? I think you can squeeze the cylinders a bit closer together
>in this case.

No, the distance would be the same. What you'd have with this arrangement
is counter-rotation -- if colony A rotates clockwise, colony B rotates
counter-clockwise. Their relationship is ballistic, not gravitational, and
their mutual orbits are determined by their trajectory, speed, and rotation
relative to one another. In effect, they are in orbit around a point that
is in a halo orbit around the Lagrange point, which is in orbit around the
Earth.

>>Imagine that the colony is an ice skater doing a spin with her arms
>>extended. Taking off the mirrors and ring would have the same effect as
>>the ice skater pulling her arms in. She doesn't lose any mass, just
>>redistributes it, but the effect is dramatic.
>
> I get it. The mass distribution of a cylinder changes when you
>remove the mirrors and rings... but won't simply closing the mirrors have a
>similar effect? After all, the cylinder doesn't lose any mass, like the
>skater, but like her, the cylinder is changing the distribution of its mass
>too, when it does that.

If the mirrors are all drawn in at the same rate, the effect will be the
same and the colony will spin faster. This will increase the
pseudo-gravity at the hull and on the farmsats. If the farmsat ring can't
take the additional load, you'll end up losing considerable mass, as the
72 farmsats all go their separate ways. (^_^)

Conversely, opening the mirrors out to full perpendicular will make the
colony spin slower.

> (BTW, is it right to say the CG of a skater/ cylinder changes when
>this happens?)

The center of gravity for a rotating cylinder will always be the center of
mass, which ought to be somewhere along the axis, near the
midpoint. Blowing off one of the mirrors will indeed change the center of
mass, offsetting it from the axis along a vector midway between the two
remaining mirrors. Gundam 0083 would have you believe that this would send
the colony spiralling off its line of trajectory, but as noted previously
the real effect would be to cause oscillation of the axis of rotation.

The farmsat ring becomes an issue here, too, as the oscillations will cause
considerable torque on the docking bay block that serves as the hub for the
ring. If the ring does NOT disintegrate, the mass of the ring will serve
to stabilize the cylinder by opposing the shift in the CG/CM and dampening
the oscillations introduced by the loss of the mirror.

> I suspect that these farming satellites might be one of the things
>that the Zeon military will have stripped from the Operation British
>cylinders..

And they say that there's no such thing as a free lunch...!

-Z-

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