Edge-On Geometry Raises a Public Orbital Data-Center Radiator Model's Coded Equilibrium Temperature by 6.35 K

Edge-On Geometry Raises a Public Orbital Data-Center Radiator Model's Coded Equilibrium Temperature by 6.35 K: An Exact Earth View-Factor Correction, Its Decomposition, and a Verified Orbit-Coupled Transient Extension Third in a series on heat rejection for orbital data centers, following the thermodynamic-bounds preprint (10.5281/zenodo.20650893) and the AI1 design-point paper (10.5281/zenodo.20670772). A prominent publicly accessible first-principles model of orbital data-center radiator behavior — Andrew McCalip's open "Space Datacenters" model — estimates a sun-tracking bifacial panel's equilibrium temperature from a closed heat balance with an approximate Earth view factor (a cosine-of-tilt heuristic floored at 5% of the nadir value). This paper reproduces that model independently to floating-point roundoff, then changes only the view-factor approximation, holding every other model choice and constant fixed. At the model's own default geometry (orbit beta angle 90 degrees, 550 km) the panel is edge-on to Earth, where the exact per-face Earth view factor is 0.25777. The public code, however, produces an orbit-averaged per-face value of 0.02118 — even though its nominal 5% floor is 0.04237 — the extra halving arising from the floating-point treatment of cos(90 degrees) in the branch logic. Replacing the coded value with the exact tilted-plate-to-sphere view factor raises the coded equilibrium temperature from 335.75 K to 342.10 K. This +6.35 K correction to the public code as executed is decomposed: +5.77 K is the model-form geometric correction relative to the intended 5% floor, and +0.58 K is the floating-point branch artifact. The correction is positive at every sampled beta angle and largest at the default. The paper then extends the static balance to an orbit-coupled, time-dependent one-node radiator model and quantifies the averaging-load bias: at periodic steady state, energy balance forces the fourth-power mean to equal the steady value, so the arithmetic-mean temperature sits at or below it, while any nonzero periodic ripple has a peak above it. The operational penalty of a steady-state sizing is peak under-prediction (up to several kelvin for a light panel), not a mean offset. Every quantitative claim is reproduced by a paper-specific verification script pinned to the open software release (orbital-thermal v1.0.0), with the McCalip replication locked against a SHA-256-pinned Node oracle by the package test suite. The work is explicit about scope: it is cross-model verification — an exact geometry correcting an approximate coded geometry — and not validation against a flown radiator, for which no public data exists for this configuration. The supporting software, tests, frozen oracle, verification script, and figures are openly available at https://github.com/dan-lee-odinson/orbital-thermal-bounds (release v1.0.0).