Parallactic Angle in terms of Hour Angle and Zenith Distance

Theorem

Let $x$ be a point on the celestial sphere.

Let $q$ denote the parallactic angle of $x$.

Then:

$\sin q := \dfrac {\cos \phi \sin t} {\sin \zeta}$

where:

$\phi$ is the terrestrial latitude

$t$ is the hour angle

$\zeta$ is the zenith distance.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): parallactic angle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): parallactic angle