jnc%MIT-CSR@MIT-Multics@sri-unix (06/07/82)
Reply-to: JNC@MIT-XX I am rereading an old favourite, "Fall of Mondust", and I find references to things stuck in Lagrangian points of the Earth-Moon system. Can anyone tell me who was the first person to come up with the idea of sticking orbiting things there? This book is copyright 1961, but the idea must predate that. -------
Jarrell.FSOEP@PCO-MULTICS@sri-unix (06/08/82)
i'm not sure who it is who thought of putting things there, put the idea is ancient. people have been talking about putting colonies up there for years. it's a favorite topic with sf writers. most of them at one point or another have had a colony called "l-5" or "l-4" (l-5 being lagrange point 5 , right between earth and moon, and l-4 being largrange 4, right behind the moon.) it's a great idea. i'm going to apply as soon as they build one. anyone else want to join? -Ron
cjh@CCA-UNIX@sri-unix (06/08/82)
Sorry...L4 and L5 are the trojan points (+/- 60 degrees in lunar orbit). The ones you describe are in the set L1-L3, which are balanced but not stable; this is why all the colonies are proposed for L5 or 4, leaving the groundhogs wondering what happened to the first three.
DIETZ@USC-ECL@sri-unix (06/08/82)
From: Paul Dietz <DIETZ at USC-ECL> I'm sure everyone else will jump on ron's error, but I might as well too. The L5 point is not between the earth and the moon. That's the L1 point (I think). L4 and L5 are in the moons orbit but 60 degrees ahead and behind (I forget which is which). I thought that it was decided that the L5 point is not where you want a space colony; rather, there is a two week orbit that can be reached from L2 (the point behind the moon) with a velocity change of as little as 30 feet per second, making lunar materials very easy to move. -------
POURNE@MIT-MC@sri-unix (06/09/82)
From: Jerry E. Pournelle <POURNE at MIT-MC> Sigh. L-4 and l-5 are the STABLE (well dynamically stable) points co-orbital with the secondary body; not the points in line. But if you were a member of thhe l-5 society you'd have seen that from the little map on the inside of the magazine Welcome aboard?
POURNE@MIT-MC@sri-unix (06/10/82)
From: Jerry E. Pournelle <POURNE at MIT-MC> Since the founding of the L-5 Society it has long been recognized that L4 and L5 are probably not the optimum points for locating a colony; certainly not for the first one. (I should say May Not Be optimum.) But surely we shouldn't have to change the name of the outfit every year or two, so we stick with L-5. L-5 trails; L-4 leads. In the TROJAN POINTS which is the Sun-Jupiter-Trojan asteroids system, the Greeks lead and Trojans trail: that is, the L-4 points were all named for Greek heroes of the Iliad, the L-5 points named for the Trojans. Alas, the convention wasn't established before two asteroids were named wrongly: there's a Greek spy in the Trojan camp adn vice versa. When we get out there we'll hjave enough energy to swap them back./..
ran@ho95b.UUCP (RANeinast) (01/29/85)
Here are the Lagrange points:
(4)
x
^
|
(1) (2) CoM (3)
x O x . O x
|
V
(5)
x
O-locations of large masses.
x-locations of Lagrange points.
CoM-Center of Mass of the two large masses (in this picture the right one
is more massive than the left one)
Arrows try to show direction of travel around the CoM.
Everything in the picture rotates about the CoM at the same rate.
The Lagrange points are those where the gravitational forces from the
masses and the centripetal force from the rotation of the point
cancel (for the nitpickers: where the grav forces equal the mass of an
object located at the point times the centripetal acceleration -- F=ma).
These are the only ones where this is true. 1, 2, & 3 are fairly easy
to see. 4 & 5 occur because the centripetal force is aimed at the
CoM so that the components of gravitational force perpendicular to
that line cancel (this is easiest to see if you consider the big
masses to be equal; the CoM is then exactly between them, one mass
pulls the point forward, the other back; the net effect is for the
point to just rotate around the center of mass at the same speed as
the big masses).
Regarding stability:
Stability is much more difficult to show (at least in a posting).
Essentially, the technique is,
for a particle located at one of the points,
to expand the potential (gravitational and centripetal)
in a small perturbation around that point.
This expended potential can look like either a hill or a valley.
If a valley, then the point is stable (that is, a particle at this point,
when perturbed, oscillates about that point, but stays near it, like
a ball at the bottom of a bowl).
If a hill, then the point is unstable (when perturbed, the particle
leaves the point, like a ball on top of an inverted bowl).
1, 2, & 3 are unstable points.
4 & 5 are stable.
--
". . . and shun the frumious Bandersnatch."
Robert Neinast (ihnp4!ho95b!ran)
AT&T-Bell Labstd@alice.UUCP (Tom Duff) (01/29/85)
L4 and L5 are only stable if the mass ratio of the two primary bodies is large enough. I'd have to do some figgurin' to reconstruct the limiting ratio, but as I remember, the Earth is just barely large enough to make the Earth-Moon L4 and L5 stable. A corollary is that the hotdog-shaped stable regions around the Earth-Moon Trojan points aren't very large or `deep'.
karn@petrus.UUCP (01/29/85)
Question: What is meant by a "barycentric" orbit? I've seen it mentioned in the NASA listings without explanation. The dictionary defines it as "orbiting around a center of mass" (which I thought all satellites did!) With the explanation of the L4 and L5 points as orbits around a common center of mass, are they really saying that these spacecraft inhabit these two Lagrange points? Phil
henry@utzoo.UUCP (Henry Spencer) (02/02/85)
> L4 and L5 are only stable if the mass ratio of the two primary bodies > is large enough. I'd have to do some figgurin' to reconstruct the > limiting ratio, but as I remember, the Earth is just barely large > enough to make the Earth-Moon L4 and L5 stable. A corollary is that > the hotdog-shaped stable regions around the Earth-Moon Trojan points > aren't very large or `deep'. As I recall it, the threshold is about a 30:1 ratio. The Earth/Moon system has about an 80:1 ratio, I believe, which would make things a bit more favorable than Tom suggested. But I'd have to look all this up to be absolutely sure. Note to people wanting a simple explanation of why the ratio has to be in excess of a threshold: as far as I know, there isn't one. You just have to work through the math. -- Henry Spencer @ U of Toronto Zoology {allegra,ihnp4,linus,decvax}!utzoo!henry
stevel@haddock.UUCP (02/04/85)
according to the New Dictionary and Handbook of Aerospace
Barycenter. Center of mass of a system of masses, as in "the barycenter
of the earth-moon system".
Barycentric elements. Orbital elements reffered to the center of mass
of the solar system.
To me this would say a barycentric orbit is one around the sun or around
the earth-moon system.
Steve Ludlum, decvax!yale-co!ima!stevel, {amd|ihnp4!cbosgd}!ima!stevel