X-Andrew-Authenticated-as: 7997;andrew.cmu.edu;Ted Anderson
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In article <15070@ut-emx.UUCP> sudhama@walt.cc.utexas.edu (Chandrasekhara Sudhama) writes:
>Hello, this is my first posting. Would someone please explain
>(either on this network or in private email) the stability of the
>equilibrium points in the Earth - Moon system?
From my L5 days, the straight line points, on the Earth-Moon line are 2/3 stablewhich means that the satellites placed at these straight-line libration points,
L1, L2, and L3 can move in a plane that is perpendicular to the line joining theEarth and the Moon, and the libration phenonenon at these 2/3 stable points actsso as to return the satellite to the libration point. But if the satellite moves towards the Earth or Moon, the satellite will continue approaching the Earth or Moon. Thus the L1, L2, and L3 points are 2/3 stable, i.e. they return to the libration point from 2 of the 3 possible dimensions it can traverse away from the libration point. On the othe
r hand, the L4 and L5 points are stable in all 3 dimensions. The satellite can move anywhere about the point (within some kidneyshaped bounds) and still experience forces that draw it back into the libration point.
The L5 point, namesake of the pioneering space settler society, is trailing the Earth in the Earth-Moon system cyclical progression (I believe) as the Earth andMoon rotate about their combined center of rotation. I think that was the case,and I believe the L5 Society decided on that location for settlement due to enhanced safety in case of emergency. The Earth would be moving away from the Settlement and pose less of a danger should the satellite orbit be perturbed.
The 2/3 stable points are useful despite the instability in the 3rd dimension. There was, and may still be, a satellite placed at the libration point between the Earth and the Sun, and set into an orbit about the line between the Earth and the Sun such that when viewed from the Earth (with appropriate equipment, not eyes, of course) the satellite would circumscribe the borders of the Sun. NASA had redirected this satellite into that orbit after it had completed some other mission. Perhaps it was called
Solar Max, I can't recall. Perhaps someone else out there would know. Maybe the L5er ==> NSS member who originally passed the news to me may be on the net and would know.
The mathematical formulations of the other postings on this subject are very interesing. It would be interesting to know what all those numbers mean. For instance the 24.999~, and the 27* ... etc. There must be a good reference?
To The Stars,
Greg Harrison
NSS member
------------------------------
Date: 19 Jul 89 15:51:09 GMT
From: asuvax!enuxha!kluksdah@handies.ucar.edu (Norman C. Kluksdahl)
Subject: Re: Apollo 8, 9, and 10
In article <17231@bellcore.bellcore.com>, ddavey@grits.ctt.bellcore.com (Doug Davey) writes:
> Does anybody remember whether the ascent or descent engine was used
> during Apollo 10's return from low orbit to rendezvous with the CSM?
> Either option seems difficult. On the one hand, I would not expect
> the descent engine to be restartable. On the other, firing the
> ascent engine and getting the ascent stage cleanly separated from the
> descent stage would be tricky since the descent stage was deigned to
> be firmly on the lunar surface during this operation.
>
The LM used nitrogen tetraoxide and hydrazine (was it UDMH or some other
chemical variant???) as oxidizer and propellant. These are hypergolic
propellants, which means that you don't need an igniter--the chemicals
hate each other so much that they ignite on contact (paraphrased from
"Chariots for Apollo"). So, if you can control the fuel and oxidizer
valves (simple, since the engines had to have thrust control, so valves
were there), you can re-start the engine repeatedly, until you run out
of fuel.
My memory indicates that the descent stage was cut free, and the ascent
stage was used for the rendezvouz. Again, the book "Chariots for Apollo"
gives some very human-oriented insight into this process. Some of the
engineers at Grumman who were responsible for the separation never did
watch or listen to a take-off from the moon. There were many pyrotechnic
charges for the separation, each of which powered a guilliotine to sever
electrical, water, air, etc, lines between the ascent and descent stages.
Failure of one of the guilliotines would have been catastrophic. If you
haven't read this book, find it. It is very good, IMHO.
