APOD: Prometheus Rising Through Saturns F Ring (2010 Oct 19)

[neufer]

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

[emc]

Wow again! Thanks neufer and Chris! You’re a little like shepherding moons… I’m glad you’re here. I’m a little too old and a lot too intimidated to tackle astrophysics... or whatever orbital mechanics falls under

[DavidLeodis]

Can anyone identify the little dot in the lower right corner of the photo?

In information brought up through the 'above image' link in the explanation it states "visible in the lower right corner is what appears to be a small ring clump or moonlet in the F-ring core itself."

[biddie67]

just out of curiosity ----- in the formula above, P = Sqrt[(A*A+B*B)/3(A*A-B*B)] , I would have thought that the 3rd measurement "C" would have to be also used in the equation .......

[neufer]

just out of curiosity ----- in the formula above, P = Sqrt[(A*A+B*B)/3(A*A-B*B)] ,
I would have thought that the 3rd measurement "C" would have to be also used in the equation .......

Nope. It's basically a two dimensional problem in the orbital plane.

[neufer]

Click to play embedded YouTube video.