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Celestial Equator Star Trail Length
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The following two formulas calculate the length of the trail for a star on the celestial equator based on the exposure time for a camera on a fixed tripod that is not tracking the stars. This is the worse case scenario as stars closer to either celestial pole will trail less in the same amount of time.
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Formula 18 Star Trail Length based on Exposure Time and Focal Length
TL = FL * E * 0.00007
Where:
- TL = star trail length in millimeters
- FL = focal length in millimeters
- E = exposure time in seconds
- 0.00007 = 2*Pi/length of a sidereal day in seconds (2*3.14159265/86,164 = 0.0000729 rounded to 0.00007)
Example: What is the length of a star trail for a star on the celestial equator when shot with a 50mm lens and a 60 second exposure?
TL = FL x E x 0.00007
TL = 50mm x 60 x 0.00007
TL = 3000 x .00007
TL = .21 mm or
TL = 210 microns
A star on the celestial equator will trail 210 microns when exposed for 60 seconds with a 50mm lens.
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Formula 19 Exposure Time and a Specific Star Trail Length
E = (TL/FL) / 0.00007
Where:
- TL = star trail length in millimeters
- FL = focal length in millimeters
- E = exposure time in seconds
Example: What exposure time is needed to keep the length of a star trail on the celestial equator to 30 microns when shot with a 50mm lens?
E = (TL/FL) / 0.00007
E = (0.03/50) / 0.00007
E = (0.0006) / 0.00007
E = 8.5 seconds
To keep the star trail size to 30 microns, the longest we can expose a star on the celestial equator with a 50mm lens is 8.5 seconds.
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Approximate Exposure Times for No Trailing
| 50 mm Lens |
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| Star Declination |
Exposure |
| 0 degrees (on the celestial equator) |
8.5 seconds |
| 30 degrees (60 degrees from the celestial pole) |
12.5 seconds |
| 60 degrees (30 degrees from the celestial pole) |
25 seconds |
| 24 mm Lens |
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| Star Declination |
Exposure |
| 0 degrees (on the celestial equator) |
17 seconds |
| 30 degrees (60 degrees from the celestial pole) |
25 seconds |
| 60 degrees (30 degrees from the celestial pole) |
50 seconds |
Maximum exposures for other focal lengths can be interpolated and extrapolated from the above chart.
Of course, a 24mm lens has quite a wide field of view. If the North celestial pole is included, say on the edge of the field, the entire field will encompass as range of declinations, roughly from 90 degrees at the celestial pole, through 60 degrees about halfway through the frame to 30 degrees dec at the edge of the frame. A photo like this would have a different amount to trailing in different parts of the frame.
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