From: "JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439" <JLU@hep.anl.gov>
Date: Wed, 19 Feb 1997 18:06:05 -0600 (CST)
Hi Ken-
You write:
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I am confused by a question brought to me by one of my students who has
been reading about the SOHO spacevehicle. It has been inserted in an orbit
about the Sun at a Lagrange point ( defined as a point where Sun's Gravity
and Earth's Gravity fields balance). The press release I just read from the
net say it should be stable there fro 20 years due to wonderful work of
insertion.
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"Stable for 20 years" does not mean "stable". The issue is,
how fast does it move away from the equilibrium point if the velocity
at that point is "nearly" zero.
The scale of the acceleration is something like the local
acceleration of the sun (earth's orbit = 1 yr) times (a displacement
divided by the earth-sun distance)^2. The relevant displacement is
probably of the order of a few m/s (or less, depending upon how well
the initial position is controlled) times a time of the order of 1 yr.
This estimate gives an acceleration of about 10^(-4) times the local
acceleration of the sun during a 1 year period. Thus, with a few
retro-rockets for position keeping, it should be easy to keep the
vehicle within a few tens of km from its initial point for a time
of the order of tens of years.
Regards,
Jack