When an amateur astronomer observes an object such as a comet or asteroid passing near the Earth the only data that he usually can get are a number positions in the night sky and their times. The positions can be found by triangulating the object's observed position from the known positions of nearby stars. If one plots the data on a celestial sphere one will find that the object tends to follow a great circle on the celestial sphere. To illustrate this I plotted the binocular observations of the positions of Comet Hyakutake that I made in 1996 on a sphere.
These observations were made shortly after sunset and shortly before sunrise as weather permitted from Mar 21 to Apr 23 of 1996. Something similar could be done with 2012 DA14. But now one can document the observations by astrophotography with a digital camera.