Why Altitude setting equals local Latitude

Aligning the axis of an Equatorial Mount to the Celestial Pole is necessary to prevent field rotation distortion around the edges of an Astro Image taken during long exposures. This physical alignment of pointing the Equatorial Axis, or Right Ascension (RA) axis, to the point in the sky that stars appear to rotate around, is called Polar Alignment.

The alignment points the horizontal direction of the Mount's RA axis to True South, (or True North in the Northern Hemisphere) and then adjusts the RA Axis altitude angle from the horizon, as the Latitude angle for the current location on Earth.

This alignment is performed by first, pointing the tripod to the pole, then fine adjustment by adjusting altitude or azimuth bolts on the base of the mount.

Two explanations are presented. One based on logic and one based on geometry.

Logic Explanation

The first drawing paints a simple picture for the 1st point with terms and colour-coded lines also used in the following drawings.

The drawing depicts an equatorial mount positioned at the South Pole and RA the Axis of the mount pointing straight up at 90 degrees to the South Celestial Pole (SCP).

The next drawing has the equatorial mount positioned on the Equator with the RA axis of the mount horizontal pointing at 0 degrees towards the SCP.

The last drawing has the equatorial mount positioned on the globe, somewhere between the Equator and the South Pole with the RA axis of the mount pointing towards the SCP.

For every position around the globe between the Equator and the South Pole, the Latitude angle and the Altitude angle of the mount to a level horizon are the same.
(The same is true for the Northern Hemisphere - just swap South for North in the explanations)

Geometry Explanation

The first drawing paints a simple picture with terms and colour-coded lines for the following drawings.

The drawing depicts a position in the Southern Hemisphere of a German Equatorial Mount with its RA Axis aligned with the South Celestial Pole (SCP)

The next drawing is rotated and simplified to set up the explanation in the next drawing.

In order to understand the last drawing, the following attempts to show the geometry needed to understand why certain angles equal other angles.

This last drawing maps the geometry onto the second drawing to show the relationship between the angles and why the Altitude angle at the base of the mount needs to be adjusted to the Latitude angle for the RA axis to point to the SCP.

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