This page works offline except for this one button. When you press it, your browser downloads the satellite's latest orbital elements (a two-line element set, TLE) from CelesTrak (celestrak.org). Nothing about you is sent. Please do not press it more than once every couple of hours; the elements change only a few times a day.
A satellite has no light of its own. You see it when it is in sunlight while your own sky is dark, usually in the hour or two after sunset or before sunrise. Later in the night it is usually inside Earth's shadow and vanishes, sometimes in the middle of a pass.
The orbit is computed from the TLE with the standard SGP4 model, using the satellite.js library (MIT licence) bundled with the page. Positions are good to about a kilometre near the TLE's date and drift by a few kilometres a day after it, more for low satellites when solar activity is high, so download fresh elements if they are more than a few days old.
The shadow uses a conical model: Earth's umbra is a cone narrowing away from the Sun, surrounded by the wider penumbra, worked out from the true sizes and distance of the Sun and Earth (Earth as a sphere of 6,378 km, without the extra dimming of the atmosphere). The Sun's position comes from the astronomy-engine library. The map shows the outline of the umbra and penumbra at the satellite's current height.
A pass is listed as visible when, at the same moment, the satellite is in sunlight (outside the umbra), the Sun is more than 6° below your horizon, and the satellite is above the horizon; the pass must climb higher than 10° while visible. Directions are compass points from true north. Brightness is not predicted, and clouds, trees and buildings are not considered.