Five Most Important Equations in Practical Observational Astronomy

These are possibly the Five Most Important Equations in Practical Observational Astronomy

1. Inverse-Square Law for Brightness
   F = L / (4π d^2)
   Light or radio power from a point source declines as the square of the distance.
2. Magnitude–Flux Conversion
   m1 – m2 = -2.5 log10(F1/F2)
   m = -2.5 log10(F) + C
   Used for photometry and flux calibration.
3. Angular Resolution (Diffraction Limit)
   θ = 1.22 λ / D
   Sets the limit of how fine a telescope can resolve details.
4. Radial Velocity via Doppler Shift
   v_r = c * (λ – λ0) / λ0
   or ∆f / f0 = -v_r / c
   Used in spectroscopy and HI-line velocity work.
5. Signal-to-Noise Ratio (Radiometer Equation)
   SNR = (T_sig / T_sys) * sqrt(B τ)
   A core equation in planning and evaluating observations.
   Honourable Mentions:
   Parallax relation, air mass, coordinate transforms, blackbody law, fringe phase