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In astronomy, analemma can mean on of two things. The first is a book by the ancient astronomer Ptolemy. Most commonly, analemma is a curve representing the angular offset of a celestial body from its mean position on the celestial sphere as viewed from another celestial body relative to the viewing body’s celestial equator. It is usually meant to refer to the position of the Sun as viewed from the Earth since no one has ever physically observed the event from any other celestial equator. Since we know that Earth’s average solar day is almost exactly 24 hours, an analemma can be traced by plotting the position of the Sun as viewed from a fixed position on Earth at the same time every day for an entire year. The resulting curve resembles a figure of eight.
There are three things that affect the size and shape of an analemma: axial tilt (the angle between an object’s rotational axis, and a line perpendicular to its orbital plane), eccentricity (a measure of how much an orbit’s shape deviates from a circle), and the angle between the apse line (an imaginary line defined by an orbit’s eccentricity vector) and the line of solstices. So, analemma can be determined by the orbit of the viewing celestial body in these ways: an object with a perfectly circular orbit and no axial tilt, the Sun would always appear at the same point in the sky at the same time of day throughout the year and the analemma would be a dot, an object with a circular orbit but axial tilt similar to Earth’s, the analemma would be a figure of eight with northern and southern lobes equal in size, an object with eccentricity similar to Earth’s, but no axial tilt, the analemma would be a straight east-west line along the equator.
Some sculptors have taken advantage of the Earth’s analemma to build analemma calendars. Analemma calenders are a common feature at science museums and planetariums. They exploit the fact that the Sun travels in a predictable pattern over the course of a year and trace the projection of an object’s shadow to measure time (weeks and months). They are very interesting pieces of art.
There is a good article about analemma here. It includes what is believed to be the analemmas of other planets. Here on Universe Today we have a great article about the path of the Sun. Astronomy Cast offers a good episode about optical astronomy.