Polyurethane piano finishes were developed in the mid 1960s in
Germany, and later produced in Japan by all piano manufacturer's there.
Polyester was introduced in the mid 1980s and both finishes are very
hard, almost like glass.

In order to polish this type of finish you must first remove the
scratches.  The best solution to this problem is to use (Meguiar's)
Mirror Glaze Car Polish (scratch remover); rub on, wait, then rub off
with a clean tee-shirt material until the scratches are removed.  Then
use Mirror Glaze No. 7 (Show Car Glaze); rub on, wait until it dries,
then polish with a clean tee-shirt material until you reach the desired
gloss.

Polyurethane or polyester finishes are very similar to automobile
finishes so are very durable; however, they need this kind of care
every so often to keep their shine.  In between these applications
there are many products available to keep the finish looking good.
Try never to use things like Pledge or Behold; these products cause
buildup of residue (oil).  I hope these pointers help.

Sincerely
Kim Bunker
http://www.playerpianos.com/