Chris Peterson wrote:
When posting the earlier I debated whether this wobble could properly be called "libration". A little research into the meaning of the term convinced me it could- that libration refers to wobble in a body with a synchronous rotation, regardless of the forces responsible for that wobble.
I've done a little research myself on:
- I) gravity gradient stabilization and
II) the corresponding pitch oscillation wobble/libration
using the book _Orbital mechanics for engineering students_
(page 541) by Howard D. Curtis
As I understand it (and we all know I have goofed before
):
- 1) near spherical satellites like the moon have rather long pitch oscillation wobble/libration periods
[not to be confused with the simple standard kinematic lunar libration]
2) but oblong satellites like Prometheus have pitch oscillation wobble/libration periods
comparable to the orbital period (as appears to be the case in the youtube video)
In fact, the dimensions of Prometheus suggest that its
pitch oscillation
wobble/libration period
is in NEAR resonance with the orbital period
If that is the case then the periodic interaction with the F-ring may, in fact, be
the primary driving force for maintaining the
pitch oscillation wobble/libration.
Also, as the the F-ring continues to snow
on one end of Prometheus
the moon will continue to elongate until its shortening
pitch oscillation wobble/libration period
IS IN RESONANCE with the orbital period
-------------------------------------------------------
- The pitch oscillation wobble/libration of
a gravity gradient stabilized ellipsoid of dimensions A, B, C
is P times the orbital period where:
- P = Sqrt[(A*A+B*B)/3(A*A-B*B)]
for Prometheus: A=119km, B=87km & C=61km
so the equation above gives: P ~ 1.05 !!!
Hence, the pitch oscillation wobble/libration of Prometheus
is almost in resonance with the orbital period of F-ring forcing