ISS passes

The station produces no light of its own. It is a mirror the size of a football pitch, and seeing it requires three things at once: it must be above your horizon, it must be in sunlight, and your sky must be dark. Miss any one and there is nothing to see, however precisely you know where it is.

That combination only happens for a couple of hours after sunset and before sunrise. In the middle of the night the station is usually in Earth's shadow — passing straight overhead, entirely invisible. In daylight it is lit but the sky is brighter. So a location with six overhead passes a day might have one worth going outside for.

Passes below 10° are not listed. Below that, trees, buildings and horizon haze make a sighting a matter of luck, and calling it a prediction would be overselling the geometry. A sky counts as dark when the Sun is more than 6° below the horizon — the end of civil twilight, and the conventional threshold for the brightest satellites.

What the calculation does not include is the weather. There is no cloud, humidity or transparency data connected to this platform, so a pass listed as visible is one that is geometrically visible and astronomically dark. Whether the sky above you is clear is a separate question that nothing here can answer.

From NASA's own trajectory file, not from a two-line element set. The station's position is interpolated between state vectors four minutes apart, converted into an Earth-fixed frame through precession, nutation and Earth rotation, and then into the elevation and bearing you would measure standing at the coordinates you gave. The frame conversion is checked against NASA's own equator-crossing longitudes, which it reproduces to within a couple of metres — that comparison is on the ISS page.

Predictions stop where the published ephemeris stops, about fifteen days after NASA generates it. Nothing is extrapolated past that point, because the station raises its orbit periodically and a trajectory computed through a manoeuvre would be confidently wrong.