Jim Conlin wrote:
A belt sander will do this job just as well and is much more widely useful
than a power plane.
In either case, finish the scarph surfaces with a sharp handplane. Check
with a straightedge.

The problem with using an edged tool on any surface that's been sanded
is that the inevitable grit that's left behind does a number on the
cutting edge. That's one major advantage of using a power planer rather
than a belt sander. The others are reduced sawdust and greater ease in
maintaining a flat surface. Belt sanders are great for rounding things
over. ;-)