Planar Earth Version 4.31

Abstract

This thesis advances the concept of Planar Earth-a formal reinterpretation of the Earth's measurable geometry as a flat, stationary topographical framework-intended to refine how empirical observation, measurement, and modeling interact within the sciences. By distinguishing itself from archaic "flat-earth" traditions, the Planar Earth framework re-centers the planar assumption as an initial condition for testing, modeling, and verification rather than as a belief about ultimate cosmology. The project systematically compares planar and spherical assumptions across applied domains: surveying, civil and structural engineering, ballistics, flight navigation, hydrography, LiDAR mapping, and geomatics. Drawing on open-source datasets and technical literature-spanning USGS, NOAA, NASA, and DTIC archives-the investigation evaluates how often real-world measurements require curvature or rotation to achieve closure or accuracy within stated tolerances. Methodologically, Planar Earth employs a model-comparison framework, constructing paired mathematical descriptions-a spherical/rotational and a planar/static model-to quantify residuals between predictions and observations. Statistical measures and epistemic analysis together illuminate the scales at which curvature terms become indispensable, if at all, and where a strictly planar approximation remains functionally sufficient. Philosophically, the thesis contributes to the continuing discourse in the philosophy of scientific modeling: proposing that the form of Earth chosen for computation may reveal as much about human epistemology and instrument calibration as about the world's actual topology. Rather than seeking refutation or defense, the thesis aspires to methodological clarity-to show exactly how and why certain geometric assumptions are adopted, and to explore whether a globally coherent planar framework could, under modern data constraints, serve as an alternate reference model for terrestrial and celestial phenomena.