Time & Measurement

The Planispheric Astrolabe as an Observer-Frame Projection Engine

Period and origin

Hellenistic origin, developed in the Islamic world from the eighth century and in Latin Europe thereafter

What it was built to do

To answer questions about altitude, azimuth, sidereal and solar time, rising, setting, meridian transit, seasonal hours and direction by superposing two coordinate systems of the celestial sphere on one plane.

How the mechanism works

Stereographic projection maps celestial circles to circles or lines and preserves angles. A movable rete represents the rotating stellar sphere and ecliptic; a latitude-specific tympan represents the observer’s horizon, altitude circles and azimuth circles. Their relative rotation is the computation.

Input

An observed altitude, or a date and time, set by rotating the rete against the tympan.

Transformation

Stereographic projection of two celestial frames onto one plane, composed by the relative rotation of the two plates.

Output

The remaining unknowns of the same configuration, read directly off the graduated limb and the tympan’s circles.

What is evidenced

Established: the artefact or the documentary record carries this directly.

What it demonstrates

That a transformation between reference frames can be built into a shape, so that solving for one quantity is a matter of alignment rather than calculation.

All mechanisms