Analemma

Example of solar analem, showing the curve in the form of "eight" lying down, for an observer in the northern hemisphere.

In astronomy, the analemma (from the Greek ἀνάλημμα «pedestal of a sundial») is the curve that the Sun describes in the sky if every day of the year it is observed at the same time of day (time zone) and from the same place of observation. The analemma forms a curve that is usually approximately a figure-of-eight (8) or lemniscate shape. Analemmas can be observed on other planets of the Solar System, but they have a different shape from that observed on Earth, and can become curves different from an eight (on Mars it is very similar to a drop of water), although they have a common characteristic of always being closed. The axial component of the analemma shows the declination of the Sun while the transverse component provides information about the equation of time (which is the difference between apparent solar time and mean solar time). Sometimes, it is drawn on the globes.

Analemma Observation

Astrophotography

It is possible to obtain an analemma by putting a fixed camera (using a tripod) pointing at a given position in the sky (if possible a point on the ecliptic) and when the Sun passes through the center, take a picture; after 24 hours the operation is repeated, superimposing the photo of the previous day, and the procedure is repeated for each day of the year. In this way, a photo is obtained with a kind of 8 that represents an analemma. Analemmas are an important subject of astrophotography. An image that includes a total eclipse of the sun in one of its images is called a tutulema.

Gnomonic projection

Example of watch design with the layout of the system of time zones; you can see how each of the hours represents an analytics.

Another, simpler way is using a stick or stake driven into the ground, on a surface with which stable marks can be made over a period of one year. The stake will have a certain height h and its end will cast a shadow that ends at one end; If the position of the shadow is taken at a certain hour, and the same operation is repeated every 24 hours, the gnomonic projection of the analemma will be obtained for that instant. This projection makes it possible to create a type of sundial called a civil time sundial, where the straight lines of the scale become "eights" for each hour of the time zones.

Stereographic projection

A variant of this way of representing an analemma is representing it on a window pane (for example), setting an observation point, marking the position of the Sun seen from the observation point already established on the first day every 24 hours, and repeat the operation every 24 hours. The result is an analemma stereographically projected onto the window.

Etymology

The word "analemma" comes from the Greek to indicate the pedestal of a sundial, and comes from the Greek verb "analambanein", which means "to carry, resume, repair". The analemma is the pedestal that supports the sundial. Formerly the word "analema" appears in certain gnomonic treatises related to the special way of building a sundial, lowering the notable circumferences in such a way that there is an orthographic projection on the plane of the clock. For the ancients (until well late in the XVIII century) the word analemma meant the procedure for the geometric construction of sundials; this method was demonstrated geometrically and completely revised by the German mathematician Christoph Clavius, 1537-1612, Later this concept changed throughout history until the concept with which it is understood today.

History

Analema de Vitrubio, as described in Book IX of his "Re architectura".

Already in the Middle Ages, the need to determine the instant of the equinox to determine the first analemmas, which were calculated by Paolo del Pozzo Toscanelli in the year 1475, used the design of one of the first meridians capable of providing with great precision not only the noon event, but also the time of year. This meridian was built in the cathedral of Santa Maria del Fiore, Florence, Italy. The meridian was built on the ground in the form of a long strip of marble and a hole was made in a southern wall to allow a &# 39;point' light on the marble strip indicating the date of the year on a scale. The method of construction of these meridians was through an ancient geometric procedure called "analemma".

Mechanical advances in the 18th century made mechanical watches increasingly accurate, and with the advent of pendulum clocks it was possible to measure minutes of time with great precision. At this moment, the difference between solar time (measured by sundials) and time zone (measured by the regular machinery of mechanical watches) began to be perceived, which is given by the equation of time. It is possible that it was around this date that the word analemma gradually became confused from the procedure of the gnomonic to the representation in the space of the figure.

Features

Three orbital parameters affect the shape and size of the analemma: obliquity (23.45°), eccentricity, and the angle of the equinox with respect to the periapsis.