On Sat, Mar 05, 2016 at 05:07:51PM -0500, Freelance Traveller wrote:
> You are on a world that rotates in 18 standard hours.
>
> Your world has a single satellite that orbits in 20 standard hours,
> non-retrograde.
[...]
> What would I see, in terms of satellite-rise, satellite-set,
> movement across the sky, et cetera?

With the satellite having such a short orbital period, it must be
relatively close to the planet (average 2-3 diameters).  The time
above horizon will be reduced by this, the visual speed slightly
increased, and the area of the surface over which the satellite is
visible at any given time will be reduced.

It will also be in eclipse frequently.  If its orbital plane is
similar to that of the planet, it will be fully eclipsed every 20-ish
hours for about an hour.  If the orbital planes are quite different,
it may only be eclipsed during certain portions of the planet's year.

If the satellite's orbit were equatorial and circular, then it would
appear to slowly cross the sky over about an 80 hour period (4 local
days), in the same direction as the local sun but much slower.  It
would stay below the horizon for about another 6 local days.  It would
not be visible from polar areas at all.

If the satellite's orbit were not perfectly equatorial then it would
also wander north and south during its path across the sky, completing
a cycle every 20 hours.  Some places further from the equator may only
see it above the horizon for parts of its orbital period.

If the orbit were elliptical, then the apparent size and speed would
also vary.  Having such similar periods, even a fairly small
eccentricity would mean some apparent retrograde motion each 20 hours
where it appears to travel opposite the direction of the stars and
sun(s).  It may also appear visibly larger at these times.

The greater the eccentricity, the more rapid this retrograde motion
would appear.  For a very eccentric orbit and from the right areas on
the surface at the right times, it may shoot across the sky in the
"wrong" direction in less than an hour, disappearing below the
horizon.  Then it would rise from the same horizon a couple of hours
later (quite a bit smaller) and traverse the sky in the "right"
direction again for the next dozen or so hours, shrinking for the
first half and growing again for the second.  Then it would set below
the horizon again, and make a similar but not identical performance
when it rises: this time slowing and reversing direction without quite
making it to the horizon after its rapid sweep.

So there are many possibilities, depending on what other parameters
its orbit may have in relation to the planet's rotation.

- Tim