Mark the Sun at the same clock time each clear day and the marks draw a figure-8. That path is the analemma. Up and down is solar declination: Earth’s axis leans 23.44° to its orbit, so the noon Sun climbs and falls through the year — the same lean as the seasons desk. Left and right is the equation of time: how many minutes the true Sun sits ahead of, or behind, mean solar time. Two things make that drift. The tilt again, because the Sun’s path along the ecliptic does not project evenly onto the celestial equator. And the orbit’s shape: eccentricity 0.0167, so Earth moves faster near perihelion, in January, and slower near aphelion, in July. Kepler’s second law is that uneven speed — a line from the Sun to Earth sweeps equal areas in equal times. Solstices sit at the top and the bottom. Equinoxes sit near the middle of the figure, close to the crossing and not on it. Southern Hemisphere seasons are the flip of the Northern labels on this page. Pair it with the solar map and the Annual Dial.
Classroom schematic — an approximation for the shape of the lesson, not a USNO almanac, not a precision ephemeris, and not a tool for setting a sundial or aiming a telescope. Not a photograph series, not a weather forecast, and not astrology. Declination uses the relation NASA GISS writes as arcsin of (sin ε times sin of solar longitude), with ε = 23.44° from NASA’s Earth Fact Sheet. Longitude on this page is a uniform mean sun plus the first term of the equation of the center, 2e sin M, with that sheet’s eccentricity 0.0167. The equation of time is four clock minutes per degree of (mean longitude minus right ascension), which is how NASA GISS defines it: true solar time minus mean solar time. The calendar is the non-leap classroom year on the seasons desk: about March 20, June 21, September 22, and December 21, with perihelion on day 4. NASA GISS publishes an Earth equation of time between −14.2 and +16.3 minutes. Those published bounds are not the readout on this slider. Minutes here are stretched sideways so the loop is readable; a real noon photograph is a tall, thin figure.
Interactive · Declination and equation of time
North up · minutes stretched so the loop is readable · schematic
Figure-8 · schematic
This day
Equator and zero minutes
Dec 21
Literacy · words for the loop
Analemma
A 2007 NASA Astronomy Picture of the Day calls it the figure-8 you get by marking the Sun at the same time each day through the year. Solstices are the top and the bottom, the northernmost and southernmost places. The 20 September 2026 picture adds that equinoxes are middle points of the analemma, not the intersection point. NASA GISS defines the same curve as a plot of the equation of time against solar declination, and says Earth’s is a figure-8.
Solar declination
How far north or south of the celestial equator the Sun sits. NASA GISS writes it as arcsin of (sin ε times sin of the Sun’s seasonal longitude). ε is the obliquity. On the Earth Fact Sheet the obliquity to orbit is 23.44°. NASA Science rounds that lean to 23.4° and names it as the cause of the seasons. The up-and-down of this figure is that swing. The seasons desk walks the same tilt around the Sun.
Equation of time
True solar time minus mean solar time. NASA GISS says that difference, in angle, is the gap between the right ascension of a fictitious mean sun and the right ascension of the true Sun, and that for Earth it varies between −14.2 minutes and +16.3 minutes. A positive minute on this desk means the true Sun is ahead of mean solar time. The fact sheet lists the length of the day as 24.0000 hours — that is the mean solar day the clock averages. The equation of time is the leftover after the average is taken. This slider’s minutes are the classroom truncation in the note above, not the GISS bounds.
Obliquity
The tilt of Earth’s equator to its orbit. The Earth Fact Sheet lists obliquity to orbit as 23.44°. The same number is the inclination of the equator on that sheet. It sets the height of the analemma and the seasons. It is not the Moon’s 5° orbital tilt on the eclipses desk.
Eccentricity and Kepler’s second law
The Earth Fact Sheet lists orbit eccentricity 0.0167, perihelion 147.095 million km, aphelion 152.100 million km, and orbital speed 30.29 km/s at the fast end, 29.78 km/s on average, and 29.29 km/s at the slow end. NASA Space Place puts perihelion in January at 91,400,000 miles and aphelion in July at 94,500,000 miles, and says the Northern Hemisphere is in winter at the closer distance. An archival NASA GSFC lesson states Kepler’s second law: the radius vector sweeps equal areas in equal times, so a planet moves fastest at perihelion. That January rush, lined up near the December solstice, is why the lower loop of this schematic is the wide one. The J2000 block on the fact sheet lists mean longitude 100.46435° and longitude of perihelion 102.94719°, so Earth was near perihelion at that epoch. This page does not integrate those elements.
Sources · public NASA education
Cited, not invented
NASA APOD — 20 September 2026, Analemma over the Callanish Stones — if you photograph the Sun from the same spot at the same time through a year, the composite is an analemma. The causes of the figure-8 are the tilt of Earth’s axis and the ellipticity of Earth’s orbit. At the solstices the Sun is at the top or the bottom. Equinoxes correspond to middle points of the analemma, not the intersection point.
NASA APOD — 4 December 2007, Analemma Over New Jersey — an analemma is the figure-8 from marking the Sun at the same time each day throughout the year. Solstices are the top and bottom, the northernmost and southernmost excursions. The tilt of Earth’s axis and the variation in speed as Earth moves around its orbit produce the curve.
NASA NSSDCA — Earth Fact Sheet — obliquity to orbit 23.44°; orbit eccentricity 0.0167; length of day 24.0000 hours; mean orbital velocity 29.78 km/s; maximum 30.29 km/s; minimum 29.29 km/s; perihelion 147.095 × 106 km; aphelion 152.100 × 106 km. J2000 mean orbital elements on the same page: eccentricity 0.01671022, mean longitude 100.46435°, longitude of perihelion 102.94719°. The schematic uses 23.44° and 0.0167. It does not propagate the J2000 elements.
NASA Science — Earth facts — axis of rotation tilted 23.4° with respect to the plane of Earth’s orbit; that tilt causes the yearly cycle of seasons.
NASA GISS — Mars24 technical notes — solar declination equals arcsin[(sin ε)(sin Ls)]. The equation of time is true solar time minus mean solar time, the difference between the right ascensions of the fictitious mean sun and the true Sun. For Earth that equation varies between −14.2 min and +16.3 min. The parametric plot of the equation of time against solar declination is the solar analemma; Earth’s is a figure-8. The Mars minute range on that page is not used here.
NASA Space Place — What causes the seasons? — perihelion 91,400,000 miles in January; aphelion 94,500,000 miles in July; Northern Hemisphere winter occurs at the closer distance. The axis keeps pointing the same way through the year.
Classroom picture of declination against the equation of time. The curve is a first-order teaching truncation on a 365-day calendar: mean longitude measured from day 79, true longitude equal to that mean plus 2e sin M with e = 0.0167, declination from the GISS arcsin relation with ε = 23.44°, and the equation of time equal to four minutes per degree of (mean longitude minus right ascension). Perihelion is day 4, the early-January marker shared with the seasons desk. Not USNO, not a precision ephemeris, not a photograph, and not for setting a sundial or aiming a telescope. Earthrise preview: NASA / Bill Anders (public domain).