The orbits of comets, asteroids, planets are all calculated in the same way: multiple observations are made astronomically from which the position of the object at the point in time of each observation can be worked out. The more observations the better since this will give you more points along its orbital path. read more
Asteroids (and comets) are subject to radiation pressure, the Yarkovsky effect, and the YORP effect. These are very hard to estimate. One of the key purposes of the upcoming Osiris-REx mission is to get a better handle on the Yarkovsky effect. read more