## Geometric (Clifford) Algebra Calculation of the Trajectory of a Gas Molecule Desorbed from the Earth's Surface

**Authors:** James A. Smith

As a step toward understanding why the Earth's atmosphere "rotates" with the Earth, we use Geometric (Clifford) Algebra to investigate the trajectory of a single molecule that desorbs vertically upward from the Equator, then falls back to Earth without colliding with any other molecules. Sample calculations are presented for a molecule whose vertical velocity is equal to the surface velocity of the Earth at the Equator (463 m/s) and for one with a vertical velocity three times as high. The latter velocity is sufficient for the molecule to reach the Kármán Line (100,000 m). We find that both molecules fall to Earth behind the point from which they desorbed: by 0.25 degrees of latitude for the higher vertical velocity, but by only 0.001 degrees for the lower.

**Comments:** 15 Pages.

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### Submission history

[v1] 2017-02-08 19:17:35

[v2] 2017-02-09 19:34:42

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