How to use it
- Enter the aperture, the clear diameter of the main lens or mirror, in millimetres or inches.
- Keep 550 nm (green-yellow, where the eye is most sensitive) or enter another wavelength.
- To check a double star, enter its separation in arcseconds from a catalogue.
Formulas
- Dawes: θ = 116″ ÷ D(mm), which is 116 ÷ 25.4 ≈ 4.57″ ÷ D(in).
- Rayleigh: θ = 1.22 × λ ÷ D radians, × 206,264.8 for arcseconds.
- Smallest detail on the Moon: θ in radians × 384,400 km (the mean distance).
The double star check says “can be split” above the Rayleigh limit, “borderline” between the two limits and “too close” below the Dawes limit.
Worked example
A 100 mm refractor at 550 nm:
- Dawes 116 ÷ 100 = 1.16″;
- Rayleigh 1.22 × 550 × 10⁻⁹ ÷ 0.1 = 6.71 × 10⁻⁶ rad, × 206,264.8 = 1.384″;
- on the Moon 1.16″ spans 1.16 ÷ 206,264.8 × 384,400 = 2.16 km.
An 8-inch (203.2 mm) telescope reaches 0.571″ (Dawes) and 0.681″ (Rayleigh); a pair 0.6″ apart is borderline for it.
Tips
- Aperture is everything for resolution: twice the diameter halves the limit. Magnification only makes the detail big enough to see.
- Unequal pairs are harder: the limits assume two stars of similar brightness; a faint companion next to a bright star needs more.
- A central obstruction (in reflectors) changes the diffraction pattern slightly, but the formulas still give a good guide.