There has been a lot of discussion on this subject while I've been gone, That is good. It seems you all get the picture. Now I want to play another scenario for everyone to think about.
If an airplane takes off from Chicago, Illinois and it's destination is Albuquerque, New Mexico. Instead of heading directly towards Albuquerque, which is 1,126 miles away, the plane flies directly south towards Cherokee, Alabama for one hour at a speed of 500mph. After one hour of flight time, where Cherokee used to be would now be Albuquerque. Because the lateral distance between the two cities is 1000 miles and the Earth rotates W-E around 1000 mph the plane saved one hour of flight time. That is a big savings.
Your principle is good but the velocities are not - they change by latitude. (1000 mph is the approximate speed
at the equator)
(Latitudes & Longitudes)(approx. velocity at that latitude)(41.8369 N, 87.6847 W) (772 mph) Chicago
(34.7583 N, 87.9685 W) (852 mph) Cherokee
(35.1107 N, 106.6100 W) (848 mph) Albuquerque
It is complicated since Cherokee and Albuquerque are both moving...
So, if the plane flew from Chicago to Cherokee, AL approx 500 mi at 500 mph, Cherokee would have moved 80 mi (852-772) east by the time it got there. So flying to Albuquerque would still require the whole 1086 mi or so - from Cherokee.
I think you mean:
Flying from Chicago
due south,
initially aiming at Cherokee, AL but not flying toward it throughout the trip. In 1 hour, Cherokee would be 80 mi east. The E-W
velocity difference between Chicago and Albuquerque is only 76 mph (848-772). So unfortunately, Albuquerque would only be about 76 miles closer...
What might also be confusing is people using the N. Pole and equator in examples to simplify things. N. Pole (90.0000 N)(0 mph) and equator (0.0000 N/S, 1000 mph). The velocity difference is 1000 mph (1000-0).