Fixed Tripod Exposure Length Back | Up | Next

The maximum exposure you can shoot with a camera on a fixed tripod will depend on the focal length of the lens being used and the location of the object in the sky. Objects along the celestial equator trail the quickest while objects near the north or south celestial poles trail more slowly.

Formula 17    Star Trail Length on a Fixed Tripod

TL = FL * T *(2Pi/S) * Cos(D)

Where:

  • TL = Trail Length in mm
  • FL = Focal length of lens in mm
  • T = Exposure length in seconds
  • Pi = 3.14159265 (the ratio of a circle's circumference to its diameter)
  • S = Length of sidereal day in same units as exposure (86,164 seconds in a sidereal day)
  • D = Declination of the star

Example - What is the length of trailing for a star on the celestial equator with a 50mm lens for a 30 second exposure?

TL = FL * T *(2Pi/S) * Cos(D)

TL = 50 * 30 * (2*3.14159265/86,164) * 1
(note: the cosine of zero declination at the celestial equator is 1)

TL = 50 * 30 * 0.0000729 * 1

TL = 1,500 * 0.0000729 * 1

TL = 1,500 * 0.0000729

TL = 0.10935mm


The length of a star trail for a star on the celestial equator with a 50mm lens and a 30 second exposure is 0.10935 mm.

How do we relate this to the real world? Lets look at the star size at the focal plane.

First, let's convert the 0.10935 millimeter trail to microns so we can relate it to the size of the star that is formed by the lens.

0.10935 mm equals 109.35 microns.

A 50mm lens working at f/4 can produce an airy disc that is about 5.3 microns in diameter. Usually we can't achieve this size - mostly because the seeing makes stars larger. So let's say a faint star shot with a 50mm lens at f/4 forms an airy disk that is about 10 microns in diameter.

If our trail is 109 microns, and a star should be 10 microns, then the trail will be roughly 11x the star's diameter. This would produce noticeable trailing.

How much trailing can you get away with and still be acceptable? That is partially a personal decision. But let's say you don't want the star to be trailed more than twice its diameter.

If we double our 10 micron star size, we would get 20 microns.

So we would need an exposure that is 109/20 times shorter. 109/20 = about 5.5. The original exposure was 30 seconds, so 30/5.5 = 5.5 seconds.

This is a worst case scenario with a star on the celestial equator where there is maximum trailing per unit of time. For stars closer to the celestial pole, you could use longer exposures to achieve the same amount of trailing.

If you don't mind accepting longer trails, you can also expose longer.




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