Star Trail Calculator

Star trails record the rotation of the Earth rather than any motion of the stars themselves. The planet completes one turn relative to the fixed stars in a sidereal day of 23 hours 56 minutes 4 seconds, or 86,164 seconds, so the sky appears to rotate at 360 divided by 86,164 degrees per second, which is 15.041 degrees per hour or 15.041 arcseconds per second. A desired trail arc therefore fixes the shooting duration directly: 15 degrees of arc needs one hour, 90 degrees needs just under six hours, and a complete circle is impossible in a single night. Angular speed on the sensor also depends on where a star sits, scaling with the cosine of its declination, so stars near the celestial equator sweep the full 15 degrees per hour while stars close to Polaris trace tight inner circles. At a given latitude, everything with declination above 90 minus that latitude never sets and can trace an unbroken circumpolar arc. Individual frame length is limited by how far a star may drift before it stops reading as a point. The 500 rule divides 500 by the effective focal length, giving about 21 seconds on a 24 mm full-frame lens and about 14 seconds once a 1.5x crop factor is applied. The NPF rule adds aperture and pixel pitch terms and generally returns shorter, more conservative times on high resolution sensors. For trail work the point-source constraint matters less than gap control, since dead time between frames from card writes, mirror movement or in-camera long exposure noise reduction leaves visible dashes in the stacked result.

The astronomical constants behind star trail work predate photography by centuries. The distinction between the solar day and the shorter sidereal day was understood by Hipparchus and refined through Renaissance positional astronomy, and the 86,164 second figure follows from the same measurements that established precession. Photographic recording of that rotation began almost as soon as emulsions were fast enough: long guided and unguided exposures on glass plates in the late nineteenth century produced the first deliberate star trail images, and unintended trailing was for decades the standard evidence that an observatory clock drive had failed. The exposure guidelines are a much later, and much more informal, development. The 500 rule and its stricter sibling the 600 rule circulated as film-era rules of thumb without a single documented author, surviving because they were arithmetically trivial at the telescope or in the field. They proved too permissive once high resolution digital sensors made small amounts of trailing visible at 100 percent magnification, and a more explicit formula accounting for aperture, pixel pitch and declination was developed by Frederic Michaud of the Societe Astronomique du Havre and popularized as the NPF rule through the PhotoPills planning application in the mid-2010s. The shift from single multi-hour exposures to stacking many short frames followed digital sensor behavior, since dark current and amplifier glow accumulate badly over hours, and free tools such as StarStaX, written by Markus Enzweiler, made lighten-mode blending of hundreds of frames routine.