Satellite Geodesy J2 Recovered from Hydrostatic Flattening and the Density Profile

This study computes the J2 gravity coefficient from stated inputs and places the result against both the published observational value and the density ceiling of Einstein-Cartan torsion gravity, in which spin-sourced torsion caps the effective density of neutron matter near 9.72e57 kilograms per cubic metre. The computation gives: J2 from the Clairaut relation 1.08140e-03; satellite J2 1.08263e-03; residual -0.11 percent; Radau polar moment factor 0.331; accepted polar moment factor 0.331. The standard geophysical account reproduces the measured behaviour of the external gravity field of the Earth within the uncertainty of its inputs, and the largest correction the ceiling could contribute at terrestrial densities is far below the precision of the observations, so the measurement is consistent with the frame while also naming the threshold at which it would cease to be. That a seventeenth-to-nineteenth-century hydrostatic argument reproduces a satellite coefficient to about a percent shows how strongly rotation dominates the long-wavelength gravity field, and it isolates the small non-hydrostatic remainder as the part that carries information about mantle dynamics. The study is a computation from stated assumptions, not a new measurement.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-12
DOI
https://doi.org/10.5281/zenodo.24147797
Primary Topic
Geophysics and Gravity Measurements
Type
article
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article

Satellite Geodesy J2 Recovered from Hydrostatic Flattening and the Density Profile

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Geophysics and Gravity Measurements
article

Satellite Geodesy J2 Recovered from Hydrostatic Flattening and the Density Profile

William Alexander Aldred
article en

Abstract

This study computes the J2 gravity coefficient from stated inputs and places the result against both the published observational value and the density ceiling of Einstein-Cartan torsion gravity, in which spin-sourced torsion caps the effective density of neutron matter near 9.72e57 kilograms per cubic metre. The computation gives: J2 from the Clairaut relation 1.08140e-03; satellite J2 1.08263e-03; residual -0.11 percent; Radau polar moment factor 0.331; accepted polar moment factor 0.331. The standard geophysical account reproduces the measured behaviour of the external gravity field of the Earth within the uncertainty of its inputs, and the largest correction the ceiling could contribute at terrestrial densities is far below the precision of the observations, so the measurement is consistent with the frame while also naming the threshold at which it would cease to be. That a seventeenth-to-nineteenth-century hydrostatic argument reproduces a satellite coefficient to about a percent shows how strongly rotation dominates the long-wavelength gravity field, and it isolates the small non-hydrostatic remainder as the part that carries information about mantle dynamics. The study is a computation from stated assumptions, not a new measurement.

Zenodo (CERN European Organization for Nuclear Research)
Geophysics and Gravity Measurements
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Satellite Geodesy J2 Recovered from Hydrostatic Flattening and the Density Profile — William Alexander Aldred · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS