Lim Jyue (lim_jyue@pacific.net.sg)
Mon, 05 Jun 2000 01:34:07 +0800

At 11:48 06/03/2000 -0700, -Z- wrote:
>The Moon, L3, L4 and L5 are all moving at the same speed, because they all
>transit the same orbit in the same period. L1 is in a lower orbit, with a
>correspondingly shorter circumference, but has the same period, so it's
>moving correspondingly slower; L2 is in a higher orbit, with a larger
>circumference, but again the same period, so it's moving that much faster.

And since the gravitational force exerted by the three objects --
i.e., the Earth, the Moon, and any object of sufficiently small mass at any
of the Lagrange points cancels each other out, as long as the object moves
along with the Lagrange points, it won't slide down any gravitational well.
Of course, this means the object must be accelerated to match the vector of
the Lagrange point -- easy for L3, L4 and L5, but more complicated for L1
and L2.

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?

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

>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.

This means, yes, all planets can have Lagrange points, so long they
have a moon or a sufficiently large satellite. Venus won't have a Lagrange
point, since it doesn't have a moon, unless you use the Sun as a primary
body and Venus as the secondary.

So, the Earth, if considered as a secondary body to the Sun, will
have yet another set of Lagrange points along Earth's orbit.. =) But we are
concerned more with intra-Earth system, meaning a Earth-Moon-small satellite
system.

(Is it possible to work out Lagrange points for four, five or even
more bodies?)

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?

>Well, the mirrors stick out quite a ways and effectively "widen" the colony
>by a factor of ten. (^_^) This near-invisible "width" is reinforced by
>the farming ring.

The mirrors are that big? ... oh, right. They *have* to be that big. =)

>The idea is that all industry and agriculture (and their accompanying
>pollution) takes place outside the main cylinder, which is exclusively
>residential.

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?)

>Each agricultural blocks or farming satellite (farmsat) is about 645 km

I assume you mean 645m, not km.

>(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.

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,

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.

>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..

>In any case, the cylinders would have to be at least 30 km apart -- the
>combined radii of the two rings -- to keep the farmsats from
>colliding.

For safety -- for the cylinders as well as any ships passing between
them -- I'll expect the distance apart to be twice that, or more. This
dovetails neatly with the 70 to 80 km figure you provided.

>(Unsupported mirror tips could be offset and even interleaved. although I

I won't either. =) Too many things can go wrong when a MS
"accidentally" crash into one of the tips. =)

>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.

Let me try to digest that.. You can't have the cylinders closer than
30km, because any closer and the mirrors or the farms are going to touch.
But because the cylinders are orbiting around a common CG, and that it's
actually spinning while orbiting, just 30km from cylinder to cylinder --
meaning, a 15km radius from the CG -- isn't exactly safe either.

But from what I understand from your post, the minimum distance from
the centre of gravity to the innermost farm is 30km, meaning the radius is
30km from the CG, and an inner diameter of 60km. Throw in the 30km of
cylinder width on both sides, and you get an outer diameter of 120km.. was
this what you meant?

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.

>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.

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

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

-------------
Lim Jyue
ICQ: 24737555

I am careful not to confuse excellence with perfection.
Excellence I can reach for; perfection is God's business.

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