If one does a least squares fit for 2012 DA14's plane of motion on the geocentric celestial sphere one will find that the normal to the plane is near the direction of RA 5.749 hr and Decl 3.250°. In this plane the asteroid does a flyby of the Earth and is deflected by an angle of 28.0° as a result of passing through the Earth's gravitational field.
The width of the plot is 60 Earth radii which is approximately the average distance of the Moon from the Earth. One can see how much closer the asteroid comes to the Earth than the Moon. The orbit of the asteroid will change in a manner similar to that in which path of a spacecraft is altered by a gravity assist maneuver. The asteroid is 45 meters across which is about half the length of an American football field.
The JPL ephemeris uses 188 observations from about a year ago to compute the path the asteriod will follow. The computed positions were geocentric. An observer on the Earth's surface may notice some paralax as a result of the asteroid's proximity. This paralax could be used by a group of amateur astronomers to determine the distance and path that the asteroid takes as it flies by the Earth next month.