This week, build an astrolabe’s tympan—latitude—plate to represent the Horizon, Almucantar, and Twilight arcs
Horizon and Almucantar Arcs
Engraved on the front plate of the astrolabe are a dense series of overlapping arcs. The curved lines and circles work together to form a map of the night sky. Each arc represents a piece of an imaginary circle that defines a specific spot in the night sky, similar to how longitude and latitude are imaginary circles on a globe that together define a specific place.
However, the overlapping arcs can also make the plate difficult to understand at a first glance. Only a small portion of the series of off-center circles and arcs represent the almucantar positions.
The almucantar is a type of imaginary circle that breaks up the sky vertically from the observer’s point of view. Each point in an almucantar circle is at the same altitude above the horizon. The almucantar circles run parallel to the horizon and split the sky from 0° at the horizon to 90° at the zenith directly above an observer.
Almucantar circles can be easy to confuse with latitude. However, while latitude is also made up of imaginary circles that run parallel and horizontal, latitude encircles the Earth, while almucantar circles are specific to an observer. 90° N in latitude is always the northernmost point on a sphere while 90° almucantar is directly above an observer and changes depending on the observer’s location on the Earth. 0° latitude is the equator, while 0° almucantar is the horizon.
10 different explorers standing in the same open field will have slightly different spots directly over their heads. 10 explorers with ten unique zeniths, but in a field will all share the same degree of latitude. So, while 90° is the North Pole with or without an observer, almucantar circles only exist in reference to an observer.
The almucantar arcs and circles are created with the same principle of spherical projection as the Tropic of Cancer, Tropic of Capricorn, and the Equator. The outermost arc represents 0° at the horizon, and continues inward, usually every 10° or 30° increments, until reaching the maximizing value of 90°.
Closer to the poles, and at a higher latitude, the observer’s night sky is more closely oriented to the top of the Earth and in line with the tropics and equators so the arcs will be more aligned. But at lower latitudes, and closer to the equator, it will be shifted more dramatically and cut the circles into arcs, pushing the arcs up against the edge of the plate.
Perhaps the most important step in creating almucantar arcs on an astrolabe (and the easiest step to make a mistake) is the first step and the initial setup. The observer’s latitude is measured from the pole, not the equator. If the observer is in the Northern Hemisphere, the latitude is measured from the North Pole, and in the South is measured from the South Pole. So, if an observer is standing at 40° latitude, roughly halfway up in the Northern Hemisphere, the angle is measured from the pole and down 40°.
If the latitude is measured from the equator, the projections it will produce will be incorrect. A latitude of 40° measured from the equator would become a latitude of 50° (when properly measured from the pole). As a result, the projections produced will not accurately reflect the observer’s actual position. This is an easy mistake to make, but it will negatively impact the entire plate’s accuracy.
Spherical projection will project lines from the pole through the equatorial plane until the projection line intersects the position of a feature on the globe. Previously, these features were where the tropics and equators touch the edge of the flat circle.
To find the places where the almucantar circles lie on the Earth, first measure from the pole. The angle will produce a line from the top of the globe, through the center, and to the opposite end. This is the longest line and represents the smallest almucantar circle at 0°. 0° is the same as a circle around the observer at the base of their feet, or, in other words, the horizon. For a observer at 40°, the horizon line would be:
Each almucantar circle between the horizon and the zenith are measured relative to the new horizon with a line extending through the center of the sphere to form two points of intersection on the sphere. For the almucantar circle at 30°, the arc is measured at 30° above the horizon:
Then, the almucantar circle at 60°, measured at 60° above the horizon:
And finally, the almucantar circle at 90°, measured at 90° above the horizon. This point is the zenith and lies directly above an observer. The position of the zenith is 90° above and perpendicular to the horizon and unlike other positions in the sphere is represented by a single point.
Aligned below the flat representation of the globe, a new circle will represent the tympan plate and is positioned to align the centers of both circles. The radius and size of the tympan plate was previously determined by the projections for the base plate and will represent the outermost tropic of the base plate—either as the Tropic of Capricorn in the Northern Hemisphere and the Tropic of Cancer in the Southern Hemisphere.
The spherical projection for the almucantar circles follow the same projection rules as the base plate for the tropics and equator previously discussed, with a line extending from the South Pole until it has touched both the edge of the almucantar and the equatorial plane. The center of the almucantar circle sits at 90°, a single point in the night sky and the projection will also be represented by a single point, aligned with the center of the plate.
Each additional almucantar circle below 90° will contain two points along the flat globe. Instead of a single point, two lines are projected from the South Pole. Two parallel lines will be drawn down from where the projections intersect the equatorial plate. The lines form the edges of the newly projected almucantar circle on the base plate. The center at the projected circle lies in line with the position of the zenith at 90°, so, at 0°:
Unlike the tropics and the equator, the shifted position of the almucantar circle means that some of the almucantar circles projected will lie outside of the base plate. Any circles formed by projections that lie outside the outermost of the base plate—representing the Tropic of Capricorn in the North and the Tropic of Cancer in the South—will be removed, leaving behind an arc instead of a full circle.
The projection rules apply for the almucantar circle at 30°:
And finally, at 60°:
All together, the four almucantar positions relative to the observer—0°, 30°, 60°, and 90°— will form three circles and one dot.
The horizon will form the largest circle for the positive almucantar circles and each additional almucantar circle above the horizon will be contained within it.
Typically, the almucantar is split into 10° increments. This allows for greater precision, but requires more projection lines and additional room for circles that can become difficult to read on smaller plates.
Southern Hemisphere:
Tympan plates made for observers in the Southern Hemisphere of the Earth will still be constructed with the same principles as the Northern Hemisphere. The only difference lies in where the projection lines are drawn. In the Northern Hemisphere, lines are projected from the South Pole, and in the Southern Hemisphere, the lines are projected from the North Pole
Twilight Arcs
Twilight Arcs are unique almucantar circles that represent the position of the sun when it rests below the horizon. During twilight, when the sun is below the horizon, there is still some time before the sunlight is completely gone. In the evening, this time is called dusk and in the early morning, it is called dawn.
The three types of twilight that are most commonly used are: civil twilight at -6°, nautical twilight at -12°, and astronomical twilight at -18°.
The twilight circles will form larger circles that sit below the existing almucantar circles. The projections for the twilight arcs are constructed below where the horizon (at 0°) lies. The first, civil twilight at -6°, is measured as an angle below the horizon.
Then, nautical twilight at -12° below the horizon:
And finally, astronomical twilight at -18° below the horizon:
The three almucantar circles for twilight are represented by lines on the flat model. This model will be used to generate projection lines and overlay on the tympan plate.
All projection lines in the Northern Hemisphere are first projected from the South Pole. Each line will continue until it touches the edge of the twilight arcs along the sphere and the equatorial plane.
First, as the smallest of the three circles, civil twilight:
And, then nautical twilight:
And finally, astronomical twilight:
Together, the twilight arcs form three circle that encircle the existing almucantar circles:
Unlike other arcs, twilight arcs are typically engraved as dashed lines to help distinguish them from the other arcs and prevent making the other arcs that lie below the horizon difficult to read.
Southern Hemisphere:
In the Southern Hemisphere, the construction will be mirrored across the center of the celestial sphere. The new position of the twilight hours will rest at 6° for civil twilight, 12° for nautical twilight, and 18° for astronomical twilight. The projections are drawn from the North Pole instead as:
The arcs are mirrored across the plate for the Southern Hemisphere from the Northern Hemisphere.
