QUESTION: 
 If there are no fixed features on Neptune, and weather constantly 
 changes, how do we know the period of rotation of Neptune?

ANSWER from Heidi Hammel on April 18, 1996:
When we talk about gas giant planets, we use two kinds of rotation
periods: (1) the internal rotation period or core rotation period,
and (2) atmospheric rotation periods.

The internal period, what you might think of as the "true" rotation
period, is tied to Neptune's magnetic field (which is tied to the core
of the planet), and was measured by the Voyager 2 spacecraft as it
flew by Neptune in 1989.  The radio antennae on Voyager detected short
bursts of of very intense radio emission starting about month before
the spacecraft got the planet, and lasting almost a month afterward. 
These bursts came every 16 hours 7 minutes.  That is what we call "the"
rotation period, since it presumably does not change, or at least
changes only very very slowly.

However, in addition to this internal period of 16 hours 07 minutes,
the winds on Neptune are confined to bands on the planet, much like the
winds of Jupiter blow in bands (these bands are the patterns of streaks
you see when you look at a picture of Jupiter or Saturn or Neptune).  We
can measure the wind speeds, or "atmospheric" rotation periods, by
tracking clouds in the atmosphere.

Although the clouds on Neptune do change all the time, the biggest ones
last long enough that we can track them moving.  And the clouds do NOT
usually have a rotation period of 16 hours 7 minutes.  Near Neptune's
equator, we see that the clouds are usually drifting more slowly.  Some
take as long as 18 hours to go all the way around the planet.   Near the
south pole of Neptune, we saw in Voyager images that the clouds move much
faster than the interior of the planet - sometimes taking only 12 hours
to drift all the way around the planet.  

It is not too hard to see why Neptune's clouds might have different speeds
than the deeper interior of the planet.  Just think of clouds you see here
on Earth.  If you stand outside on a cloudy day, and the clouds are
drifting eastward over your head, then you are seeing clouds moving faster
than the Earth rotation period of 24 hours.  If the clouds are standing
still, right above you, then they are drifting at the same rate as the
Earth's rotation.  And if they are drifting westward, then they are moving
more slowly than the Earth.  

This is just what happens on Neptune, with the biggest difference that
on Neptune at certain latitudes, the clouds are always drifting to the
east, at other latitudes they are always drifting west, and at a few
latitudes, the clouds move exactly with the interior of the planet.