analemma

An analemma is a curve that describes the apparent position of the Sun in the sky over the course of a year, as observed from a fixed location on Earth. It is essentially a plot of the Sun's declination against its equation of time. If you were to mark the Sun's exact position in the sky at the same time each day, for an entire year, you would trace out a figure-eight shape. This shape is the analemma.

The analemma's shape is caused by two main factors. The first is the Earth's axial tilt, which is approximately 23.5 degrees relative to its orbital plane. This tilt causes the Sun's declination (its angle north or south of the celestial equator) to vary throughout the year, reaching its maximum and minimum values at the solstices. The second factor is the Earth's elliptical orbit around the Sun, which means its orbital speed varies. This variation in speed, combined with the axial tilt, leads to the difference between apparent solar time and mean solar time, known as the equation of time.

The equation of time describes the difference between the time shown by a sundial and the time shown by a clock. This difference fluctuates throughout the year, being positive when the Sun is ahead of the clock and negative when it is behind. The analemma visually represents this combined effect of axial tilt and orbital eccentricity on the Sun's apparent movement. It is a fundamental concept in astronomy and is used in the design of sundials and in understanding celestial mechanics.