Sun and Calendar · 5 of 9

The Analemma

Why does the Sun, photographed at the same time each day, draw a figure-8?

Photograph the Sun at the same time every day for a year and it draws a figure-8. What makes it tall, and what makes it wide and lopsided.

You’ll be able to say what makes the analemma’s figure-8 tall, and what makes it wide and lopsided.

8 steps · about 6 min

Before this: Celestial Coordinates (8 min), The Ecliptic (8 min), The Sun and Your Clock (4 min)

Where and which day

Working out the Sun’s day from where you are…

Where

Which day

Date

Time

Kept for this guide only, until you change it here — your map settings, and every other guide, stay as they are.

Print, play outside or present

Present on a big screen

Scan with a phone's camera, or open

Sources

Meeus, Astronomical Algorithms, 2nd ed. (1998), ch. 25 and 28 — the Sun's position and the equation of time
US Naval Observatory — dates of the equinoxes and solstices
Hughes, Yallop & Hohenkerk, "The equation of time", MNRAS 238 (1989) — its extremes and its two causes

← GUIDES

More below ↓

With a keyboard, focus the sky, aim it with the up and down arrow keys, and press Enter to drop the pin at the centre of the view; or press Show me.

You are here

Settings

Screen

Night mode Turns every page red, to keep your eyes adjusted to the dark.

High contrast Bolder constellation lines, larger and brighter names on the sky, and stronger text and edges everywhere. Starts on if your device asks for more contrast.

Reduce motion The camera cuts to where it is going instead of flying there, and panels and sheets appear without sliding. Starts on if your device asks for less motion.

Battery saver Draws the sky thirty times a second at most: smoothness traded for battery.

Night brightness Dims the screen below your phone’s lowest setting, down to a fifth, while night mode is on.

Clock and voice

Clock How every time is written. Until you choose, your language’s own clock decides.

D describes What D says about the view on the sky: one sentence, or in full with the field, the constellation and five names.

Sounds Quiet tones as you use the map: a tick as you drag the clock past a mark or dusk, a chime for the star you pick — higher for hotter stars — and a low swell while a figure is out of the dome. Made in your browser, and off until you turn them on.

All settings and your progress

Photograph the Sun at the same clock time every day for a year. Does it stay put? Here it is at local mean noon, your own longitude's noon. It climbs, sinks and sways, and the line it leaves is the analemma.

Its height you know from The Sun's Year: it is the season. The figure is 47° tall: twice 23.44°, the tilt of the Earth's axis. Its north end is the June solstice, its south end December's, and the two points where it crosses the celestial equator, just south of the waist, are the equinoxes.

↺ Why height is the season, from The Sun's Year

Its width is how far the Sun runs ahead of the clock or behind it: up to 16 min early in early November, 14 late in mid-February, and on the meridian only four days a year. The figure folds the year in half: you cannot read a date off it.

Unroll it. Each noon keeps its distance from the meridian and gets a row of its own, and the figure-8 opens into a curve: the equation of time, that lead and lag day by day. Touch the curve to read any date.

It is two waves added together. The dashed one is the ellipse: fastest in early January, the Sun falls behind the clock through spring and runs ahead of it by autumn. The dotted one is the tilt, twice a year; the next two steps show why.

Pin the view to the stars, and run a month of Suns along the ecliptic.

Near the solstices the Sun's daily degree runs straight east. Near the equinoxes the ecliptic crosses the celestial equator at a slant, so part of each degree goes north or south instead. Noon comes early, then late, twice a year.

Make one: mark a post's shadow tip at the same clock time each week. Then Build an Analemma.

Tall, from the tilt of the axis
Wide and lopsided, tilt plus ellipse
On the meridian only four days a year