Re: SOHO orbit

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

The Lagrange points of the earth-sun system (or any other two body system)
are those points at which an infinitesimally small object (or simply one
that has negligible effect on the first two) could be placed and projected
in such a manner as to maintain its relative position with respect to the
earth and the sun.  The calculation of these points (and, indeed, their
very existence) depends upon the approximation that the earth's and the
sun's orbits about each other are circular and also upon neglecting the
important influences of other planets.

The two forces from the earth and the sun do not "balance" at any of these
points. Rather, they combine to produce precisely the force needed to
maintain circular motion about the system center of mass with a period of
one year. It takes little imagination to see that there will be three
Lagrange points along the sun-earth line--one on the far side of the sun,
one between the earth and the sun, and one on the far side of the earth. 
The two others that lie approximately in the earth's orbital path and
approximately 60 degrees before and after the earth in its orbit take a
lot more thought.

The Lagrange point between the earth and the sun ("L1") turns out to be
about 1% of the way to the sun and is a great place to park satellites
monitoring the solar wind, especially if you want to correlate its
characteristics with observed effects in the magnetosphere and auroral
ionosphere.  SOHO is actually placed in a "halo orbit" around L1 that
keeps us from having to point telemetry antennas directly at the sun.  The
halo orbit is possible because L1 is stable for off earth-sun line motions
although it is unstable for along the line motions.

On Wed, 19 Feb 1997, Ken Fox wrote:

> 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.
>
> Here I have trouble: Is the net force at the Lagrange point zero? If so,
> how does it manage to orbit at all? Is it not an unstable equilibrium?
>
> I suspect that there is something rather rudimentary that I am overlooking
> and I also know that real world Physics is more complex that high school
> physics, but...I could use some help.

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