So, How to Build an Astrolabe: Tympan Plate – Tropics and the Equator

This week, build an astrolabe’s tympan—latitude—plate to represent the Equator, Tropic of Capricorn, and Tropic of Cancer

 

The beating metal heart of the astrolabe is the tympan plate. The center circular plate is made up of complex layers of arcs and circles. The tympan—sometimes referred to as a latitude plate—lies in the center of the astrolabe and represents the observer’s point of view. The tympan is engraved with the arcs to represent different features and places in the sky (almucantar, azimuth, twilight arcs, and unequal hours) for a specific latitude. Historically, an astrolabe might come with many different tympan plates for important latitudes that could be traded into the body when needed.

Astrolabe Parts - Highlighting Tympan Plate

The full three-dimensional view of the night sky can be translated into the flat metal circle through the use of spherical projection. Spherical projection to build an astrolabe can be achieved without math. Instead, the position of astronomical features like azimuth, almucantar, and the position of the poles are accomplished through a series of hand drawn circles and arcs.

Diagram of spherical projection

First, the base of the plate will require three concentric circles. These circles will make up the base of the plate and will represent the latitude position of the equator at 0°, the Tropic of Cancer at 23.4°, and the Tropic of Capricorn at -23.4°.

Tympan plate with Tropics and Equator highlighted

To begin, draw a circle.

 

This circle is not the tympan plate, but instead represents the Earth and will be split in half at the equator by a long line. This line will store the location of all projected points. In the North Hemisphere, projections are made from the southern pole (at the bottom of the circle) and lines will extend through important features along the circle until they intersect the line in the center that represents the equatorial plane.

Setup for spherical projection setup

The Tropic of Cancer and Capricorn are both lines that are created by projecting 23.4° from the center of the circle. The projection will extend from the center until it touches the edge of the circle.

Spherical projection with marks for Tropic of Cancer and Tropic of Capricorn

For plates in the Northern Hemisphere, the projected line will begin at the South Pole. From the South Pole, it will extend until it intersects with the important feature being measured. In this case, the line starts at the South Pole, crossing the equatorial plane, and intersects the right most point of the Tropic of Cancer.

Projection from South Pole setup

All lines projected from the South Pole must cross the line in the center of the circle that represents the equatorial plane since this is where the projection is created.

Tropic of Cancer projection setup line

Next, from the position where the projection line intersects the equatorial plane, a long line, perpendicular to the plane should be drawn directly down.

Full Tropic of Cancer spherical projection

The two parallel lines formed by the points where the equator intersects the plane will form the edges tangent to a new circle that will represent the projected position of the equator on the plate, centered on the middle of the celestial sphere.

Spherical projection for Northern Hemisphere from the South Pole

 

This process is repeated for the Tropic of Cancer, Tropic of Capricorn, and the Equator, forming three concentric circles. For features close to the South Pole—like the Tropic of Capricorn—the line should extend until it eventually intersects beyond the circle and intersects the equatorial plane.

 

The outermost circle—the Tropic of Capricorn—forms the edge of the plate, completing the base tympan plate that will be used for all latitudes in the Northern Hemisphere. The center of the plate represents +90° N.

 

The new three concentric circles representing the Tropics and the Equator are features that do not change based on latitude and will form the base of the tympan plate

 

Mathematically, if the obliquity of Earth is assumed to be 23.4°, then  the radius of each concentric circle can be found as:

 

Equations for Tropic of Cancer/Capricorn and the Equator

 

Southern Hemisphere:

For the purpose of simplicity, the construction steps for the plate will be built for the Northern Hemisphere, however, the same steps can be applied to the construction of the Southern Hemisphere with a few minor changes that will be noted.

 

For the base plate, the projection lines are built from the North Pole instead of the South. As a result, the center of the plate will represent  -90° S and the outermost circle of the tympan plate is the Tropic of Cancer instead of Capricorn. However, if this is not labeled, there would be no visible difference as both sit at 23.4° and -23.4° respectively.

Spherical projection for Southern Hemisphere from the North Pole