How fast does a plane travel to chase but not catch the sunset?

Answer 1

Around a 1000 miles an hour at equater a little faster

Answer 2

Planes typically travel around 500-600 mph. To chase but not catch the sunset, the plane would need to fly at the same speed as the rotation of the Earth (roughly 1000 mph at the equator) in the opposite direction of the sunset to effectively stall its "setting."