I don't really see why they should, because shadows are cast by objects that are rotating with the Earth in your vicinity. They only move at a speed determined by the motion of the Sun in the sky and your latitude on the Earth with a speed of about 1 degree per 15 minutes or so.
All answers are provided by Dr. Sten Odenwald (Raytheon STX)
for the
NASA IMAGE/POETRY
Education and Public Outreach program.