Earth takes 365.25 days to complete its orbit around the Sun. Earth also travels at 67000 mph. Asteroid 2001 US16 (also known as 89136) takes 577 earth days to complete it's orbit around the Sun. to see the orbit of 2001 US16, go to  https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2001%20US16;old=0;orb=1;cov=0;log=0;cad=0#orb My question is, at what time in the orbit of Earth would be best to launch a rocket to 2001 US16 that can travel 36,000 miles per hour (~0.00038728 AU/h) to this asteroid?

Earth takes 365.25 days to complete its orbit around the Sun. Earth also travels at 67000 mph.

Asteroid 2001 US16 (also known as 89136) takes 577 earth days to complete it's orbit around the Sun.

To see the orbit of 2001 US16, go to its entry in the JPL Small-Body Database Browser.

At what time in the orbit of Earth would it be best to launch a rocket to 2001 US16 that can travel 36,000 miles per hour (~0.00038728 AU/h) to this asteroid?