Comprehensive Guide to Astrophotography Optics & Formulas
Because the Earth rotates around its celestial axis once every 23 hours, 56 minutes, and 4 seconds (a sidereal day), stars appear to move across the sky at approximately 15 arcseconds per second. To capture crisp, pinpoint stars without elongation, your camera's shutter speed must not exceed the physical threshold where a star's light trails onto adjacent sensor pixels.
1. The 500 Rule vs. The NPF Rule
The traditional 500 Rule was invented during the 35mm film era when standard print enlargements hid minor star movement:
With today's high-resolution digital sensors (24MP, 45MP, 61MP), 100% crop inspection immediately reveals trailing under the 500 Rule. The NPF Rule (devised by Frédéric Michaud and the Société Astronomique du Havre) accounts for lens aperture $N$, pixel pitch $p$ (in microns), and focal length $f$:
For a 14mm f/2.8 lens on a 24MP full frame sensor ($5.9\mu\text{m}$ pixels), the 500 Rule suggests 35.7 seconds, while the NPF Rule calculates 19.6 seconds. Shooting at 19.6s guarantees 100% pixel-level sharpness!
2. Star Trail Mathematics
For star trail photography, trailing is the desired aesthetic. The length of a star trail is directly determined by Earth's rotational speed ($15^\circ/\text{hour}$):
A 2-hour stack produces a dramatic $30^\circ$ circular arc around Polaris in the Northern Hemisphere or the Southern Cross in the Southern Hemisphere.
3. The Looney 11 Rule for Moon Photography
Because the moon has no atmosphere and is illuminated directly by sunlight, its brightness equals daytime on Earth! Under the Looney 11 Rule:
At f/8: Shutter Speed = 1 / (2 × ISO)
Shooting a full moon at ISO 100 with an f/8 telephoto lens requires a shutter speed of 1/200s or 1/250s. Overexposing the moon at multi-second exposures completely blows out crater detail!