Re: Tethys' Lagrangian Points and Telesto/Calypso

JRS: In article <Xns97FDD6F698D2Arickyralexandriacc@xxxxxxxxxxxxxx>,
dated Tue, 11 Jul 2006 13:10:56 remote, seen in news:sci.astro, Ricky
Romaya <something@xxxxxxxxxxxxx> posted :

On Wikipedia, it is said that several moons have companion moons in their
Lagrangian points, such as Tethys
http://en.wikipedia.org/wiki/Natural_satellite). After looking the data on
Tethys, such moons are Telesto and Calypso, residing in L4 and L5 of
Tethys. What I expect is the three moons will have the same semi-major
axis, orbital period and inclination around Saturn and Saturn's Equatorial
plane, respectively. While the semi-major axis and orbital period is
confirmed, the inclinations are different, with

Tethys : 1.12
Telesto: 1.19
Calypso: 1.56

Well, you don't give the unit of inclination. Ideally, that would imply
radians, but you probably mean degrees. Telesto and Calypso are only
very slightly inclined with respect to Tethys.

I'm under the impression that the Lagrangian points are all on the plane in
which the satellite orbits the main body. If that is true, considering
Saturn is the main body, and Tethys is the satellite, then why Telesto and
Calypso have different inclinations?


FROM L4/L5, Saturn & Tethys are equi-distant; but Tethys is about 1/100
of the diameter of Saturn, and so will have a very much smaller field
there, maybe about 3-4 ppm.

A body which happens to pass near a Lagrange point in an orbit of the
same shape and size as that of Tethys will be quite happy to return to
that point after every half-orbit. Given the stability of bodies at the
Lagrange points themselves, ISTM that as long as the period is correct
other orbits should share the stability over a reasonable range of
inclinations and eccentricities.


Remember that in the original case, that of the Sol-Jupiter L4 & L5
points, there are numerous Trojans/Greeks at each Point; they must have
different orbits, since otherwise there would be just one heap of "rock"
at each of L4 L5. And they cannot be going round the Sun in a neat
fixed formation; Newton & Kepler forbid that.

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