Methods and sources
Where each number on this site comes from, and what it has been checked against. Each tool's own page has a fuller method section.
Sky positions, sun and moon
Sunrise, sunset, twilight, moonrise, moonset and moon phases come from astronomy-engine, an open-source astronomy library. Twilight and moon times were checked against the US Naval Observatory for several dates and locations: dusk and dawn agree within 2 minutes, and moonrise and moonset within 1 minute. All 149 moon phases from 2026 to 2028 agree within 1.3 minutes.
Target altitudes for whole nights use a faster method: positions are precessed from J2000 to the current date and turned into altitude with local sidereal time. This matches the full calculation to within 0.02°. Atmospheric refraction is left out, which makes objects near the horizon appear slightly lower than they are.
Astronomical darkness means the sun is more than 18° below the horizon.
Target data
Positions, sizes, types and magnitudes for the 272 targets come from OpenNGC (CC BY-SA 4.0). Common names follow the ones imagers use. The best months on each target page count hours above 30° in astronomical darkness on the 15th of each month, from 45° N and 35° S.
Exposure calculator
Sky brightness in magnitudes per square arcsecond is converted to photons using 10,080 photons per second per square centimetre per nanometre for a magnitude 0 source, with 81% combined optics and filter transmission. On a color sensor, broadband light is split three ways by the color filter array. The shortest useful sub is the length at which read noise adds a chosen share, 5% by default, to the total noise. Dark current is ignored.
Untracked exposure
The NPF rule of Frédéric Michaud (Société Astronomique du Havre, 2010). Results were checked against published examples: for a Sony A7R III at 19 mm f/2.8, PhotoPills' "Accurate" mode gives 5.88 s and this site 5.84 s; Galactic Hunter's simplified-rule example for 24 mm f/2 with 4.3 µm pixels gives 8.3 s and this site 8.29 s. Trail length in pixels uses the sidereal rate of 15.041 arcseconds per second times the cosine of the declination.
Back focus
Filter glass is counted as adding a third of its thickness to the required distance, the result of t(n - 1)/n for glass with a refractive index near 1.5. Spacer combinations are searched exhaustively and checked against the tolerance using exact values, not rounded ones.
Dew point
The Magnus formula with the constants of Alduchov and Eskridge (1996) over water, and the World Meteorological Organization's Magnus constants over ice for the frost point. Results match published dew point tables, for example 9.3 °C at 20 °C and 50% humidity, and stay within 0.35 °C of the exact thermodynamic value from -40 to 50 °C.
Camera presets
Pixel size, resolution, quantum efficiency, read noise and back focus for the astronomy cameras come from each manufacturer's manual or specification page. Where a read noise figure is only shown on a chart, the tool marks it "about". Read noise varies between individual cameras, so measured values for your own camera are better if you have them.
Images
Photographs are from ESA/Hubble under CC BY 4.0, with the credit shown unaltered beside each one.
Testing
The calculations are covered by automated tests that run before every update, including the published cross-checks above, tests for both hemispheres, daylight saving changes, polar day and night, and a thousand random back-focus gaps. The site is only packaged for upload when every test passes.
Found a problem
Write to info@theastromanual.com with what you entered and what you expected. Confirmed errors are fixed and noted here.