Without a glitch (Quantum Leap) they would effectively bump into each other at one exact millimeter on the path, as not two objects can occupy the same space.
The only way for a Quantum Leap to occur in this example is for the small increment of time that sunrise and sunset differ because of the path of the earth's rotation around the sun. If she was able to travel nearly the distance of the path in that small variation of time a glitch would occur in the relative time.