Re: Tag-team orbits and tidal locking


Erik Max Francis wrote:

>During a swap, from the point of view of the co-orbital
>that is ahead and above in its orbit, the other approaches
>from behind and below it, then they change positions,
>and so the other now received behind and above.

They don't, of course, swap positions instantaneously
as if by a teleporter. From the point of view of an
observer in a "medium" orbit between the two satellites,
they appear to swing around each other, each following
a 180 degree arc before settling into the new orbits.

+----> direction of orbits
|
|
v
toward Saturn
----------------------------------------------------------
First half of exchange event:

.----<---<--- satellite A, in higher slower orbit
/
|
v o ^ o = virtual observer, in "medium" orbit
|
/
>-->-----" <-- satellite B, in lower faster orbit


----------------------------------------------------------
Second half of exchange event:

<--<-----. <-- satellite B, now in higher faster orbit
\
|
v o ^
|
\
"----->---> satellite A now in lower faster orbit

----------------------------------------------------------


>Since they're all synchronous with
>respect to Saturn, neither body rotates during this
>exchange, and so any given point on any given body
>will always see the same view of the other body,

I think you're having a visualization problem, here.

Look at the above diagram of the exchange. If both
satellites are tide-locked with Saturn, then the sides
of the satellites facing each other will definitely
change! It would be like our view of the Moon if the
Moon were tide-locked with the Sun. If the Moon were
tide-locked with the Sun, the side we see on a new
Moon would be the opposite side we see on a full Moon.

OTOH, what if the satellites were somehow tide-locked
to each other? This means that during this exchange,
there would be one particular side facing "o", the
virtual observer.

So, for example, let's say the rotational speed of
the satellites around "o" at closest approach is 1/49
revolutions per day, and the period between closest
approach is 1500 days. Then maybe the satellites are
"tide-locked" to 1500 days, with a rotational period
of 50 days. Whenever the satellites make their
exchange, they appear roughly tide-locked to each
other--always showing the same closest face to each
other on closest approach. It's not completely
synchronized, because 1/49 is slightly different from
1/50. But of course, a "true" sychronization is
impossible anyway since the satellites aren't really
following perfect 180degree circular arcs with respect
to each other.

Basically, you could draw two smiley faces on the two
moons. Most of the time, these smiley faces just
revolve around at a seemingly arbitrary rate. However,
whenever the two moons do their exchange dance, the
two faces happen to face each other throughout the
closest approach.

Isaac Kuo

.

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