Mount Fundamentals and Tracking Stability

This journal is the Week 7 companion document in the Austronomic foundational series, which approaches amateur astronomy as a systems-oriented engineering and scientific discipline. It examines the equatorial mount as the mechanical foundation of any astrophotography system, responsible for counteracting Earth's rotation with sufficient precision that starlight accumulates without trailing across the imaging sensor during each sub-frame exposure.The journal derives the sidereal angular velocity from first principles in Equation (1), expressing the rate that every equatorial drive must reproduce as a function of the sidereal day T_sid = 86164.1 s. Equation (2) converts periodic error amplitude in arcseconds into pixel-plane displacement as a function of image scale, establishing the instrument-independent relationship delta_px = A_PE / s that governs mount selection for any telescope-camera combination. Equations (3) through (6) develop an approximate mount PSF contribution framework under the assumption of Gaussian guided residuals, expressing RA and DEC tracking residuals as independent FWHM components and deriving the star elongation indicator RND = (r − 1) / (r + 1), where r is the DEC-to-RA residual ratio. Equations (7) and (8) model the approximate unguided RA displacement as a function of sub-frame duration and derive the crossover time t_c below which open-loop tracking produces less angular displacement than the guided noise floor, identifying a regime relevant to planetary and lucky imaging.Nine tables classify equatorial and alt-az mounts by geometry, drive technology, performance tier, and representative market examples spanning thirty instruments across six classes from camera trackers to direct-drive observatory systems. The classification uses a single consistent class spine, Classes 0 through V, across three independent attribute dimensions: payload capacity, tracking accuracy, and mechanical resilience. A mount selection matrix keyed to image scale synthesises these dimensions into a planning framework, distinguishing unguided peak displacement budgets from guided RMS tolerances and FWHM broadening estimates, which are not interchangeable criteria.A key finding is that improved polar alignment substantially reduces the DEC tracking residual for any mount class by reducing the frequency of DEC corrections and the engagement of DEC backlash, without requiring hardware change. Mechanical backlash, structural flexure, and guide-star seeing noise remain as residual DEC error sources regardless of alignment quality.A reproducible experimental procedure uses Sirius for raw periodic error logging under disabled corrections and the Sombrero Galaxy field (M104) for imaging-level validation. The procedure includes site-selection guidance for southern Victoria, dual-target rationale, signal-to-noise thresholds distinguishing the unguided logging regime from the closed-loop guiding regime, and quantitative validation criteria linking the measured centroid excursion amplitude to the Equation (2) prediction.This journal is produced as part of a 12-week educational series. Week 7 follows Week 6, which established atmospheric seeing as the resolution floor imposed by the turbulent air column above the telescope, and prepares the ground for Week 8, where camera sampling theory, the Nyquist criterion applied to the seeing-limited PSF, and the MTF framework are developed.