Analemma Help

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The analemma is the path of the sun you would record if you took a picture of the sun every day at the same time of day during the whole year.

Analemma in sky

The analemma on the globe shows the position of the Sun as it would be in the sky at noon each day.


The default settings of the animation are set to the actual parameters for the analemma on the Earth. The settings can be changed with the sliders.

Even though the displayed Earth is not to scale compared to the Sun, the obliquity, eccentricity and perihelion are displayed to scale. So the same analemma shape would be traced no matter what the displayed size of the earth was. 


Obliquity is the same as the axial tilt of the Earth. Which is the same as the angle of the ecliptic that the sun travels on. The orbital plane that is shown is the ecliptic plane. The 23.4° is always the top and bottom limits to the analemma because that is the tilt of the Earth. The analemma always has the highest point at the tropic of Cancer and the lowest point at the Tropic of Capricorn.

The blue disk is the Ecliptic Plane that the Sun makes its yearly orbit. The dotted yellow circle is the path that the Sun is seen to travel once a day. The radius of this circle changes every day as the Sun gets closer or farther away from the Earth.



The orbits of all the planets are not perfect circles, but are ellipses instead. Eccentricity is the amount the orbit deviates from a perfect circle. The eccentricity of the Earths orbit is 0.0167 which is only 3%.

Using the formula:

(from center of ellipse)


The Earth (or Sun) is at one focus of the ellipse. When the eccentricity changes, the position of the foci of the ellipse changes as well.

The display if from the point of view of the Earth. The Sun is on an ellipse around the Earth, but it is mathematically equivalent to the Earth ellipse around the Sun.


The perihelion is the point where the Earth is closest to the Sun in its orbit. Where the perihelion of the orbit is in relation to the tilt of the planet makes a big difference in the shape of the analemma. Mostly it would change whether the short loop of the analemma is on the top or bottom, or evenly on both. A circular orbit would always be even on the top and bottom of the figure 8.


The perihelion changes over thousands of years because the orbital ellipse rotates around the Sun. This is called apsidal precession.
apsidal precession

Right now, perihelion is at January 3.  Thirteen days off of the December 21 soltice.

Why the loops on the analemma are not equal:


The fact that there is a perihelion and aphelion causes a different projected shape on the Earth.

In July, the Sun is projected at the top of the analemma.

In January, the Sun is projected at the bottom of the analemma. The closer distance and faster speed is going to change the shape of the analemma.

It's only coincidental that aphelion and perihelion are near the top and bottom of the figure 8. The perihelion changes position over thousands of years.

Because of the eccentric orbit and perihelion, the Sun is in the northern hemisphere about 8 more days than it is in the southern hemisphere.

On the elliptical orbit the perihelion is marked with a small box:



You can stop and start the animation with the Animation checkbox.


This will reset all the setting back to the actual parameters for the Earth.

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