page_title: Analemma
section_title: Earliest and latest sunrise and sunset
hierarchical_section_title: Analemma / Estimating sunrise and sunset data / Earliest and latest sunrise and sunset
caption_attribution_description: Deutsch: 9 Uhr MEZ auf etwa dem 8. östlichen Längengrad und auf etwa dem 50. nördlichen Breitengrad. Fiktive Fotomontage, die illustriert, welche Position zu dieser Zeit die Sonne über das Jahr am Himmel einnimmt. Würde man die Sonne etwa alle sieben Tage 9 Uhr MEZ fotografieren und die Fotos zusammenführen, würde dieses Muster sichtbar. English: Fictional Photomontage (actual positions of the sun are just estimated and have nothing to do with the German landscape) illustrating an analemma pattern in the sky as it would appear at 9:00 AM CET at roughly 50°N, 8°E. Were one to take a photo of the sun approximately each week for a year and combine the images taken, this pattern would be visible. Español: Fotomontaje ficticio mostrando un analema alemana en el cielo como aparecería a las nueve de la mañana (CET) a la posición geográfica aproximada de 50°N, 8°E. Si se hiciera una fotografía más o menos cada semana durante un año y luego se las combinara, este patrón sería visible.
context_page_description: In astronomy, an analemma is a diagram showing the position of the Sun in the sky, as seen from a fixed location on Earth at the same mean solar time, as that position varies over the course of a year. The diagram will resemble the figure 8. Globes of Earth often display an analemma.
  The north–south component of the analemma results from the change in the Sun's declination due to the tilt of Earth's axis of rotation. The east–west component results from the nonuniform rate of change of the Sun's right ascension, governed by combined effects of Earth's axial tilt and orbital eccentricity.
  One can photograph an analemma by keeping a camera at a fixed location and orientation and taking multiple exposures throughout the year, always at the same time of day.
  Diagrams of analemmas frequently carry marks that show the position of the Sun at various closely spaced dates throughout the year. Analemmas with date marks can be used for various practical purposes.
  Analemmas have been used in conjunction with sundials since the 18th century to convert between apparent and mean solar time.
context_section_description: The analemma can be used to find the dates of the earliest and latest sunrises and sunsets of the year. These do not occur on the dates of the solstices.
  With reference to the image of a simulated analemma in the eastern sky, the lowest point of the analemma has just risen above the horizon. If the Sun were at that point, sunrise would have just occurred. This would be the latest sunrise of the year, since all other points on the analemma would rise earlier. Therefore, the date of the latest sunrise is when the Sun is at this lowest point (29 December, when the analemma is tilted as seen from latitude 50° north, as is shown in the diagram); however, in some areas that use daylight saving time, the date of the latest sunrise occurs on the day before daylight saving time ends. Similarly, when the Sun is at the highest point on the analemma, near its top-left end, (on 15 June) the earliest sunrise of the year will occur. Likewise, at sunset, the earliest sunset will occur when the Sun is at its lowest point on the analemma when it is close to the western horizon, and the latest sunset when it is at the highest point.
  None of these points is exactly at one of the ends of the analemma, where the Sun is at a solstice. As seen from northern middle latitudes, as the diagram shows, the earliest sunset occurs some time before the December solstice – typically a week or two before it – and the latest sunrise happens a week or two after the solstice. Thus, the darkest evening occurs in early to mid-December, but the mornings keep getting darker until about the New Year.
  The exact dates are those on which the Sun is at the points where the horizon is tangential to the analemma, which in turn depend on how much the analemma, or the north–south meridian passing through it, is tilted from the vertical. This angle of tilt is essentially the co-latitude (90° minus the latitude) of the observer. Calculating these dates numerically is complex, but they can be estimated fairly accurately by placing a straight-edge, tilted at the appropriate angle, tangential to a diagram of the analemma, and reading the dates (interpolating as necessary) when the Sun is at the positions of contact.
  In middle latitudes, the dates get further from the solstices as the absolute value of the latitude decreases. In near-equatorial latitudes, the situation is more complex. The analemma lies almost horizontal, so the horizon can be tangential to it at two points, one in each loop of the analemma. Thus there are two widely separated dates in the year when the Sun rises earlier than on adjoining dates, and so on.
caption: Diagram of an analemma looking east in the Northern Hemisphere. The dates of the Sun's position are shown. This analemma is calculated, not photographed.
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