Orbit plot analysis is a vibration analysis method that measures problems in engines by analyzing shaft vibration. It involves using XY transducers to observe rotor shaft vibration and a keyphasor transducer to detect a notch, producing time base plots that combine into an orbit plot. Different orbit shapes indicate different problems - ellipses indicate unbalance, acute ellipses indicate misalignment, two dots indicate oil whirl, and various irregular shapes indicate issues like rubs or oil whip. Spectrum analysis of orbit plots provides further information about the direction and nature of vibration precession.