  The BlueWalker 3 (BW3) satellite was folded into a compact object when
launched on 2022 September 11. The spacecraft's apparent visual magnitude
initially ranged from about 4 to 8. Observations on November 11 revealed that
the brightness increased by 4 magnitudes which indicated that the spacecraft
had deployed into a large flat-panel shape. The satellite then faded by several
magnitudes in December before returning to its full luminosity; this was
followed by additional faint periods in 2023 February and March. We discuss the
probable cause of the dimming phenomena and identify a geometrical circumstance
where the satellite is abnormally bright. The luminosity of BW3 can be
represented with a brightness model which is based on the satellite shape and
orientation as well as a reflection function having Lambertian and
pseudo-specular components. Apparent magnitudes are most frequently between 2.0
and 3.0. When BW3 is near zenith the magnitude is about 1.4.
