Sub-exposure length
How long should one sub be? Long enough that sky noise swamps read noise. Going longer buys almost nothing and risks lost frames. Estimated from your sky brightness, optics and camera.
Model: V-band sky photon flux 8.8×10⁵·10−0.4·SQM ph/s/cm²/arcsec², 85% optics transmission, filter bandwidth scaling; sub length = C·RN²/esky where C sets the read-noise penalty. Broadband at Bortle 7 really is that short. That's the math telling you to stack more subs, not stretch them.
Backfocus & spacing
Build your imaging train from the flattener/reducer flange to the sensor and see what spacer closes the gap. Filters push focus back by about a third of their thickness, which is accounted for automatically.
Rule of thumb: adjusted backfocus = required + filter thickness / 3 (n≈1.5 glass). Tolerance for most flatteners is roughly ±0.5 mm before corner stars complain.
Critical focus zone
The depth of focus inside which stars stay diffraction-sharp. Slow scopes are forgiving; fast astrographs demand precision. This tells you how much.
Classic formula CFZ = 4.88·λ·f². In average seeing the practical tolerance is ~2–3× wider, so treat this as the target for autofocus, not a cliff edge.
Untracked exposure (NPF rule)
Maximum exposure on a fixed tripod before stars trail. The modern NPF rule, with the old 500 rule alongside for comparison.
NPF t = (35·N + 30·p)/FL, stretched by 1/cos(dec) away from the celestial equator. Defaults are the Samyang 135 f/2 on the A7R II.
Planetary f-ratio
For lucky imaging, match the f-ratio to your pixel size, then this picks the Barlow that gets you there and shows how big each planet lands on the sensor.
Nyquist floor ≈ 3.6× pixel size; the sweet spot for OSC lucky imaging ≈ 5×. Defaults are the LX85 6" ACF with the ASI585.
Moon interference advisor
How badly will the Moon hurt tonight's target? Separation, phase and altitude combined into a verdict, and whether narrowband rescues the session.
Uses a compact lunar ephemeris (~0.5° accuracy, plenty for planning). Rules of thumb baked in: moonlight scatters strongly within ~30–40°, and 3 nm narrowband shrugs off all but a nearby full Moon.
Polar-alignment tolerance
How good does polar alignment actually need to be? Worst-case drift for unguided rigs, and worst-case field rotation for guided ones, both ways: max exposure from your PA error, and required PA error from your target sub length.
Worst-case bounds: unguided drift ≤ ω·δ; guided field rotation ≤ ω·δ/cos(dec), trailing measured at the sensor corner. Real pointing is usually kinder, so if the bound says you're fine, you're fine.