2018/07/06 by Thomas Dubos, Dubos, Thomas
Earth and Planetary Sciences · Engineering · Environmental Science · Physics and Astronomy · #Atmospheric and Oceanic Physics (physics.ao-ph) #Climate variability and models #Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Physical sciences #Geophysics and Gravity Measurements #Solar and Space Plasma Dynamics #Spacecraft Dynamics and Control #astro-ph.EP #physics.ao-ph
paper · pdf · doi:10.48550/arxiv.1807.02405
11 pages
arxiv created 2018/07/06 · openalex publication_date 2018/07/06 · arxiv updated 2018/07/09 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
Certain geometric approximations such as the widely used traditional shallow-atmosphere, spherical-geoid (TSA-SG) and the deep-atmosphere, spherical-geoid (DA-SG) approximations boil down to the specification of a spatial metric tensor. In order to eliminate the leading-order errors due to the SG and TSA approximations, a sequence of three metric geometric approximations of increasing accuracy at high altitudes is obtained. Their metric tensors possess a simple, closed-form analytical expression. The approximations capture to leading order the oblateness of the planet, the widening of atmospheric columns with height, the horizontal and vertical variations of gravity and the non-traditional part of the Coriolis force. Furthermore, for the first two approximations, the horizontal metric is conformal (proportional) to the spherical metric, which simplifies analytical and numerical formulations of the equations of motion.