Exercise:

The Moon is at declination -14°.
What will be its hour angle at moonrise
(when the top edge of the Moon first appears over the horizon),
at a latitude of +56°20'?

At moonrise, the true altitude of the Moon is a = +0°7'
(allowing for semi-diameter, horizontal refraction and geocentric parallax).

Use the formula
cos(H) = { sin(a) - sin(φ) sin(δ) } / cos(φ) cos(δ)
where φ= +56°20' and δ = -14°.

This gives cos(H) = 0.38,
so H = 67.8° or 292.2°
= 4h31m or 19h29m.

To decide which,
note that the Moon is to the east of the meridian,
so H = 19h29m.

(This is 8 minutes later than sunrise,
when the Sun is at the same declination.)

Back to "geocentric parallax".