Satellite Pass Predictor

Most people who go out to see the International Space Station have been handed a time and a direction by someone else. Behind that time sits a small chain of reasoning that is worth knowing, because every link in it can break. There is a description of the orbit that was true at one moment. There is a model that carries that description forward. And there are two separate questions about light: is the station in sunshine, and is your sky dark enough to show it?

Get any one of them wrong and you stand in a field looking at nothing.

Six numbers that are true for one moment

A satellite’s orbit is published as a set of mean orbital elements: inclination, the right ascension of the ascending node, eccentricity, argument of perigee, mean anomaly and mean motion, plus a drag term called B-star and an epoch, the instant they describe. For decades they travelled as two 69-column lines of text, the two-line element set, a format designed for punched cards. Each line ends in a checksum: add every digit on the line, count each minus sign as one, and keep the last digit. It catches a single mistyped digit every time, which matters when people still copy these lines by hand.

The word mean is the important one. Spacetrack Report No. 3, the 1980 United States document that first published the propagation models, warns that the elements are not a snapshot of where the satellite really was. They are averages from which particular periodic wobbles have been removed, and a prediction is only good if those wobbles are put back in exactly the way they were taken out. Feed the same numbers into a different model, even a more accurate one, and the report says the predictions get worse, not better. The elements and the model that reads them are one package.

That model is SGP4 for most satellites. The report credits it to Ken Cranford in 1970, built from Brouwer’s solution for the Earth’s gravity and a power-law density for the atmosphere. Objects whose orbit takes 225 minutes or longer use SDP4, Richard Hujsak’s 1979 extension that adds the pull of the Moon and the Sun and the resonances that matter for twelve-hour and one-day orbits. The station, at about 93 minutes a revolution, is firmly in SGP4 territory. A geostationary weather satellite is not.

There is a wrinkle in that history. Over the years the official code was corrected, and the public versions drifted apart. In 2006 Vallado, Crawford, Hujsak and Kelso gathered the fixes into one openly published version, with a set of test cases and their expected positions and velocities. That set is the reason an independent implementation can be checked at all. The predictor on this page reproduces every one of those test cases, near-Earth and deep space, to within a few millimetres, and stops with an error at the same step where the reference stops for the deliberately broken cases.

Why predictions go stale

An element set is a fit to tracking observations, and the fit holds best near its epoch. The report notes that the sets are refined periodically so that predictions stay reasonable, which is a polite way of saying that they do not stay reasonable by themselves. For a body in low orbit, SGP4 is generally good to about 1 km within a few days of the epoch. Further out, the error grows.

What does a kilometre mean at the eyepiece? NASA gives the station’s speed as about 28,000 kilometres an hour, so a kilometre along the track is about a seventh of a second. Ten or twenty kilometres, after a week or two, start to show as a pass arriving early or late by a few seconds, and a low pass skimming your minimum elevation can appear or disappear altogether. The station flies low enough to feel the thin upper atmosphere, and SGP4 describes that air with one fixed density law; a later model was designed to follow the Sun’s changing output instead, which says something about what the old one leaves out.

So the first habit of a careful observer is boring: get fresh elements on the day. CelesTrak, the long-running public source run by T.S. Kelso, refreshes its general perturbations data every 2 hours and asks software to download once per update, not every minute. The predictor follows that rule. It sends one request with the catalog number and nothing else, keeps the answer for two hours, and after any error reply it stops asking for the rest of the visit, because the usage policy says repeated failing requests get a network blocked.

The format itself is changing, which is a story in its own right. Five-digit catalog numbers ran out in July 2026, and CelesTrak publishes no two-line elements for objects numbered 100000 and above. CelesTrak now serves the same elements in the Orbit Mean-Elements Message keywords, as XML, CSV or JSON, with a full date for the epoch instead of a two-digit year. The tool asks for the JSON form and still accepts pasted two-line elements, checksums and all.

What makes a pass visible

The station shines only by reflected sunlight. NASA’s own guidance puts every sighting within a few hours before or after sunrise or sunset, and the reason is geometry. You need two things at once. The station must be outside the Earth’s shadow, and you must be inside it, deep enough that the sky behind the station is dark.

The second condition is easy to state with twilight. The US Naval Observatory defines civil twilight as ending when the centre of the Sun is 6 degrees below the horizon, nautical twilight at 12 degrees and astronomical twilight at 18. A bright object like the station shows up well before full darkness, so the predictor treats the sky as dark once the Sun is below -6 degrees, and lets you choose a stricter limit.

The first condition takes a model of the shadow. The tool uses the simplest honest one: a cylinder the width of the Earth stretching away from the Sun. A satellite inside that cylinder is in shadow. The real shadow tapers and has a fuzzy edge, the penumbra, so entry and exit times are approximate by a few seconds, and the tool says so rather than pretending otherwise.

Here is a worked example you can reproduce. Load the recorded International Space Station elements, epoch 21 October 2026, set the place to 51.48 north and 0.00 east, near Greenwich, with a minimum elevation of 10 degrees. One pass rises in the southwest at 04:30:14 UTC, peaks at 48.7 degrees in the south-southeast at 04:33:32, 557 kilometres away, and sets in the east at 04:36:50. It is only partly visible: the station leaves the Earth’s shadow at 04:33:05 and stays bright until it sets, while the Sun sits more than 19 degrees below the horizon.

The next pass, at 06:10, climbs to 86 degrees, almost overhead, and is useless, because by then the Sun is only 4.4 degrees down and the sky is too bright. Height alone tells you very little. A high pass in a bright sky is invisible, and a modest one in a dark sky with a sunlit station can be the best of the week.

The predictor does not estimate brightness. Doing that properly needs the station’s shape, attitude and the angle of reflection, and no source this tool relies on gives a method it can test. It tells you when the station is up, sunlit and set against a dark sky, and leaves the magnitude out.

Reading the sky plot

The sky plot is a map of the dome above you flattened onto a disc. The centre is the point straight overhead, the rim is the horizon, and the rings mark 30 and 60 degrees of elevation. Directions follow the horizontal coordinate system: azimuth measured from north through east, elevation measured up from the horizon. North is at the top and east to the right, the way a map is drawn, so remember to turn the picture to match the direction you face.

Each pass is a curved line from where it rises to where it sets, with arrows showing which way it moves. The part of the line where the station can actually be seen is drawn solid and thick, and the rest is dashed. The worked example looks like a fishhook that starts dashed in the southwest and turns solid just before its peak, which is exactly where you would first catch it.

Behind the plot sits some geometry worth naming. Your position is turned into Earth-centred coordinates on the WGS 84 ellipsoid, whose equatorial radius is 6,378,137 metres with a flattening of 1 in 298.257223563. The satellite’s position comes out of SGP4 in a frame tied to the stars, so it is rotated into the Earth-fixed frame by Greenwich mean sidereal time. The revisited report recommends exactly that step and notes that polar motion has historically been ignored for this kind of work; the tool ignores it too, along with the second or less between UT1 and UTC. Atmospheric refraction, which the Naval Observatory puts at about 34 arcminutes at the horizon, is left out as well, so elevations are geometric.

Every one of those choices was checked against an independent number, not just argued for. The Sun positions agree with NASA’s Horizons system to better than one arcminute on twenty dates spread over half a century, which is the accuracy the Naval Observatory states for its approximate formula. Sidereal time matches the Observatory’s own expression to a hundredth of a second. Rise and set times found by bisection match a brute-force search second by second on two hundred passes.

What the method cannot do

None of this replaces looking up. The prediction is only as current as the elements, and a cloud bank does not appear in any orbit model. The tool says how old its elements are at the start of the window and warns when they are more than three days or two weeks away from it.

It also cannot follow a satellite that has no public elements, and it will refuse elements whose checksum fails rather than guess what the missing digit was. The ground track and globe are drawn from the same propagation as the list, so they share its limits. Within those limits, a fresh element set, a dark sky and a sunlit hull are all you need to know when to step outside.