but the Earth wasn't rotating fast enough
to satisfy me.

Gerald oughta be satisfied with this...
Now I'm reminded of another truly
serendipitous observation: I was
observing Uranus (or was it Neptune?)
one evening when I noticed a 'star' that
showed some very obvious motion
relative to the planet. It didn't take long
for me to realize that the 'moving star'
was in reality neither moving, nor a star.
I had stumbled upon a geosynchronous
satellite!

Cool! I've never (knowingly) seen one of those...
Marty