1. How the Powerful Tides Shape Titan's Overall Geography
Titan has two related tidal forces,
both resulting from its elliptical orbit around Saturn:
* the force that wants to change the shape of Titan, trying to pull it
to more of an egg shape (tidal bulge) as it approaches Saturn and
letting it relax towards
rounder as it retreats form Saturn
* the libration force that pulls things eastward around periapsis and
westward around apoapsis.
These two tidal forces acting together would appear to explain much of
Titan's overall geography. Here's a chart showing the tidal forces on
Titan as I see them.
The blue arrows show
the maximum flow forces from libration: East then West all along the
equator, still pretty strong at mid latitudes, then decreasing rapidly
to zero at the north and south poles. (force = force at
equator times cosine of latitude.) As viewed from Titan,
Saturn is almost stationary in the sky, but it oscillates six degrees
eastward and westward during the 384 hours of a Titan day. Flow force
is maximum as
the libration shifts fastest through 0 degrees in its circuit from -3
to +3 degrees longitude: periapsis and apoapsis. Midway, the flow
forces come to a gradual halt and then reverse direction. Titan's
bulge is around 100 meters, and the libration forces wish to move this
entire bulge east and west with Saturn's apparent librations.
The green arrows show
the maximum flow forces due to the fact that Titan's tidal bulge wants
to become more
ellipsoidal, "egg shaped" as it approaches Saturn and more round as it
reality, the 45 degree arrows on the mercator projection represent flow
between the 0,0 and 0,180 degree points and the 90/270 degree longitude
circle in all directions. "Tidal bulge" flow forces are zero at these
"tidal poles" points and all along this "tidal equator" longitude,
which includes the north and south poles. Flow force is maximum as the
distance from Saturn changes most rapidly, part way between periapsis
and apoapsis, and so the force is around 90 degrees out of phase from
the libration flow force. The difference in tidal bulge between
apoapsis and periapsis is around 9 meters, and these forces wish to
change Titan's overall shape by this amount. While this might seem
minor compared to the east-west 100 meter force, it is acting to move
liquid (and air) back and forth over 90 degrees (º) instead of 6.
We might quantify the relative push from the two forces as
100m*6º=600 and 9m*90º=810. Obviously there is a lot more to
it than that, but it leads to the supposition that one force isn't
almost wholely predominant over the other.
The first thing we note is that only one force can push liquid (or
wind) north and south, and then only centered on two longitudes (0,180)
and it's null at the equator and the poles, while both forces can push
it east and
west, and these forces are strongest at the equator, hence turbulent
swampy seas and muddy flats wash east and west through the tropics
(creating undersea "dunes" it would seem), while calm lakes and dry
land predominate near the poles where both forces are null.
But these are approximations and the forces are not entirely
symmetrical. For example, Titan is moving a bit faster at periapsis
than at apoapsis, so the maximum "libration forces" are strongest at
periapsis as the Saturn and Anti-Saturn poles are at high tide and
weaker at apoapsis when they are at low tide.
At 90 and 270º longitude (the "tidal equator"), the tidal
bulge flow forces are null, and at the equator they are also null at
poles", 0º and 180º. Tides here may rise and fall, but the
liquid doesn't flow (from the egg-shaping forces). In between these
at the equator, the bulge flow forces are maximum. Thus, in four
areas, there is just the libration force shoving things east and west,
but in the four areas in between, there are both forces, about 90º
of phase, shoving things east and west.
Now we get back to the seas and the chart. If the two tidal forces
are not too dissimilar in strength, we might expect to find four
"collection basins" - seas - where there is only one flow force (0, 90,
180 and 270º). Because the liquid has less overall force pushing
it east and west there, it accumulates from the areas where it is being
pushed back and forth more strongly. With the weight of liquid, these
tend to become depressions. In the in between areas (45, 135, 225 and
315º), the liquid is being pushed harder most of the time (and at
a somewhat different time - out of phase). There we might expect to see
expect more river-like formations: channels that run between the basins.
I don't think it would be too far amiss to say that's
approximately what the map shows, given that Titan is a real world and
not just a perfect theoretical model, except everything - the seas and
channels - is displaced a little to the east of where it's expected, by
maybe 20 degrees. This would seem to result from the libration force
flowing eastward at periapsis being stronger than the westward force at
apoapsis. [Note: See Titan Rotation" in the footnotes of the title
Looking at the left 3/4 of the chart, the tropical area does in
fact look very much like the model: sea-channels-sea-channels-sea.
Other land shaping factors may alter the reality from the theoretical
model: The expected sea at 70 degrees appears to have run well north of
the equator, it doesn't seem to have any channels to the
("160 degrees") sea, and while the channelled nature of "the H" is not
entirely lacking, it is more in the nature of continuous seas through
to the sub-Saturn ("340 degrees") sea. Perhaps there was harder rock in
the way in the bright Xanadu area at 120 longitude, preventing erosion,
so the liquid had to find other courses. The two seas have the
appearance of trying their best, north of the equator, to work their
way past that 120 degrees longitude blockage, and there may even be
some narrow channels we aren't seeing.
The arctic lakes might extend southwards farthest near the 90/270
degrees longitude circle, but again they may be found to be displaced
eastwards by perhaps 20 degrees, to 70/250 degrees, unless other
factors prevail. (We may have to wait for a polar map(s) to get a good
visual on this.)
April 13th 2007. Previous chapter with earlier ideas deleted.
Material for next revision... If I can figure out the real reason the
seas are 20º east of where they should be!
And while I'm at it...
periapsis: Tidal bulge is max, so equatorial 0º and 180º are
approaching high tide. Flow owing to libration is maximum, towards the
east. Therefore, we have 'lots' (relatively speaking) of liquid at the
Saturn and anti Saturn poles, and 'less' at the 'tidal equator'
(90° & 270° latitude), and
along with the connecting channels all being pulled eastwards. Flow
through the channels to the west is counteracted by the libration
force, while the flow to the east is accelerated.
Outward bound: Libration tug is minimum - eastward tug ends and
westward tug begins. Tidal bulge is deceasing, causing flow from the
'tidal poles' towards the 'tidal equator' through the flow channels in
both directions, east and west.
apoapsis: Tidal bulge is minimum, so it is low tide at the 'poles'. The
air is dispersed towards the tidal equator in all directions. But
because the seas are confined to the north-south equator, instead of
dispersing all over the 'tidal equator', the liquid goes from the
0º and 180º seas toward the 90º and 270º seas, so
high tide in them. At the same time, the libration force is pulling the
liquid westwards, not as strongly as it is pulled eastwards at
periapsis, but for a longer period of time. Eastward flow through the
channels to the 90º and 27º areas is reduced while westward
flow is magnified.
Inward bound: Westward libration tug diminishes and eastward tug begins
again. The tidal bulge is again pulling liquid from the tidal equator
towards the tidal poles, equally eastward and westward.
It is my theory that the seas and channels are displaced about 20º
eastwards of the theoretical 0º, 90º, 180º and 270º
because the forces pushing eastward at periapsis are stronger than
those pushing westward at apoapsis - they have more 'punch' to wear
down the landscape. The liquid "sloshes" harder against its eastern
shores and more slowly and gently on the western ones. This can be seen
in the flow patterns visible in the seas in many Cassini images,
especially the antipodal sea ("Shangri La"): the 'shallows', 'lees',
'deltas' or whatever, lie to the east of larger obstructions.