The density falls off pretty steeply at the “edge”, so the exact definition only makes little difference for the radius: https://www.researchgate.net/figure/Density-vs-radius-for-a-...
Two-body gravitational attraction is observed to be an inverse square power law; gravitational attraction decreases with the square of the distance.
g, the gravitational constant of Earth, is observed to be exponential; 9.8 m/s^2.
Atmospheric pressure: https://en.wikipedia.org/wiki/Atmospheric_pressure#:~:text=P... :
> Pressure (P), mass (m), and acceleration due to gravity (g) are related by P = F/A = (m*g)/A, where A is the surface area. Atmospheric pressure is thus proportional to the weight per unit area of the atmospheric mass above that location.
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> 40–1 The exponential atmosphere