17001_1511@uwovax.uwo.ca (11/09/90)
Regarding synchronous rotation of natural satellites:
It is indeed common for satellites to be in synchronous rotation. Of
the nearly 60 satellites in the solar system that are known at present,
rotation states are reasonably well known for perhaps 40, and all but
3 or 4 are in synchronous rotation. Exceptions: Saturn's Hyperion and
Phoebe, Jupiter's Himalia (one of the very distant small satellites).
There might be one or two other small outer satellites of Jupiter whose
periods are now known from photometry and are not rotating synchron-
ously but I'm not quite up to date.
The reason is that orbiting bodies raise tides in each other. For
instance, the Moon raises a tide in Earth's oceans of a couple of metres
and a tide in the solid crust of a few centimetres. If the Moon once
rotated faster, the Earth must have raised a fairly large tide in the lunar
crust - certainly several tens of centimetres, I would guess (somebody
else can do the math!) This produces stresses and movements in the crust
which involve some energy dissipation. Therefore energy is slowly being
lost from the system, and that manifests itself as a gradual slowing of the
rotation period, until syncronous rotation is reached. At that point the
tidal deformation is still present but it is locked into one place with
respect to the crust and no more energy is lost. For this to work the
tidal effect must be large enough. We do indeed see that all satellites
close to even small planets like Mars and Pluto are tidally locked. Also
large satellites far from a planet, like Iapetus, are locked because the
tidal effect is greater across a large body (what counts is the difference
in strength of a planet's gravity from the near side to the far side of the
satellite, naturally greater across a larger diameter). The exceptions are
very small and very distant moons (Phoebe, Himalia) and the special case
of Hyperion which is in chaotic rotation because of its bizarre shape and
complex interactions with Titan as well as Saturn.
Phil Stooke
Department of Geography,
University of Western Ontario,
London, Ontario, Canada N6A 5C2logajan@ns.network.com (John Logajan) (11/10/90)
17001_1511@uwovax.uwo.ca Phil Stooke writes: >This produces stresses and movements in the crust >which involve some energy dissipation. Therefore energy is slowly being >lost from the system, and that manifests itself as a gradual slowing of the >rotation period, until syncronous rotation is reached. Okay -- so where does the angular momentum go? It has to be conserved. -- - John Logajan @ Network Systems; 7600 Boone Ave; Brooklyn Park, MN 55428 - logajan@ns.network.com, 612-424-4888, Fax 612-424-2853
marty@puppsr5.Princeton.EDU (Marty Ryba) (11/10/90)
In article <1990Nov9.190858.11889@ns.network.com>, logajan@ns.network.com (John Logajan) writes: |> 17001_1511@uwovax.uwo.ca Phil Stooke writes: |> >This produces stresses and movements in the crust |> >which involve some energy dissipation. Therefore energy is slowly being |> >lost from the system, and that manifests itself as a gradual slowing of the |> >rotation period, until syncronous rotation is reached. |> |> Okay -- so where does the angular momentum go? It has to be conserved. |> Into the orbit. Not very noticeable, since the relative period change is decreased by a factor of roughly (radius of moon/radius of orbit)^2 -- Marty Ryba | slave physics grad student Princeton University | They don't care if I exist, Pulsars Unlimited | let alone what my opinions are! marty@pulsar.princeton.edu | Asbestos gloves always on when reading mail
neufeld@physics.utoronto.ca (Christopher Neufeld) (11/10/90)
In article <1990Nov9.190858.11889@ns.network.com> logajan@ns.network.com (John Logajan) writes: >17001_1511@uwovax.uwo.ca Phil Stooke writes: >>This produces stresses and movements in the crust >>which involve some energy dissipation. Therefore energy is slowly being >>lost from the system, and that manifests itself as a gradual slowing of the >>rotation period, until syncronous rotation is reached. > >Okay -- so where does the angular momentum go? It has to be conserved. > It goes into orbital angular momentum, boosting the orbit of the moon (assuming that the moon was originally rotating around an axis parallel, not anti-parallel to the orbital axis). Our moon is moving away from us still, as it tries to lock the Earth to face it. Velocity in orbit decreases as the square root of the distance from the centre of rotation, so higher orbits have higher angular momenta, with an angular momentum proportional to the square root of the distance. >- John Logajan @ Network Systems; 7600 Boone Ave; Brooklyn Park, MN 55428 >- logajan@ns.network.com, 612-424-4888, Fax 612-424-2853 -- Christopher Neufeld....Just a graduate student | neufeld@helios.physics.utoronto.ca Ad astra! | S = k log W cneufeld@{pnet91,pro-micol}.cts.com | Boltzmann's epitaph "Don't edit reality for the sake of simplicity" |