Pass predictions are the determination of times when the satellite will have clear line-of-sight with a designated location the Earth's surface. This usually means the satellite is above the observer's horizon. Pass predictions may also be further filtered by additional constraints such as times in which the satellite is operating within certain frequency bands or modes (amateur radio satellites) or when the satellite is in the sunlight and the observer is in the darkness (twilight for visual tracking). A good source for on-line pass predictions is the Satellite Tracking Prediction Form. This does Amateur Radio and High Interest satellite pass predictions for over 700 cities. Terminology commony used for pass predictions includes: AOS - Acquisition of Signal (rise above the horizon) AZ - Azimuth (true compass direction 0o - 360o) CUL - Culmination point (maximum elevation or point closest to boresight) EL - Elevation (angle above the horizon) LOS - Loss of Signal (set below the horizon) Range Rate - relative velocity along the line of sight between the satellite and an observer (useful for Doppler computations) Slant Range - direct range from you to the satellite You can compute pass predictions by "brute force" by stepping along in time and checking the satellite's elevation until it rises above the horizon and then sets below the horizon. This can be time-consuming.  A faster and more elegant solution is to take bigger steps, computing the "elevation rate" as a vector function. A positive elevation rate means the satellite is rising; a negative elevation rate means the satellite is setting. A change from positive to negative elevation rate isolates a relative maximum elevation. If the relative maximum is above the observer's horizon, you've found a pass culmination point.  You then isolate the AOS and LOS times on either side of the CUL and you've determined the pass times.
 Pass predictions tell you when the satellite is above your horizon Satellites above the horizon are available for radio contact Visual observations require the satellite to be above the horizon, in the sunlight, and the observer to be in the dark Computer software automates pass prediction computations