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Taking into account that a small angle expressed in radians can be approximated by its tangent, the formula to calculate stereoacuity dγ is this: = / (()) where a is the interocular separation of the observer, z the distance of the fixed peg from the eye and dz the position difference.
The free air correction is calculated from Newton's Law, as a rate of change of gravity with distance: g = G M R 2 d g d R = − 2 G M R 3 = − 2 g R {\displaystyle {\begin{aligned}g&={\frac {GM}{R^{2}}}\\{\frac {dg}{dR}}&=-{\frac {2GM}{R^{3}}}=-{\frac {2g}{R}}\end{aligned}}}