The Sun and the Mighty Eight

Throughout the lockdown, I enforced a practice on myself — to wake up early in the morning and do yoga. I am proud of myself that I have been doing great till now. I wake up in the morning around 5 AM, do yoga, and watch the sunrise. I realized something.

The sun doesn’t rise from the same location every day!

At some point, it rises from the northeast and sometimes southeast and only a very few times exactly from the east. This doesn’t stop here; the pattern repeats every year if observed from the same place!

Analemma 2014, Hong Kong. Picture by: Matthew Chen

When we take a picture of the sun from the same location and same time but different days of a year and superimpose them, we get an ‘8’. They call this an Analemma which is a Greek word that literally means ‘support’ or sometimes ‘pedestal of sundial’. This ‘8’ can tell us a lot about the shape of the earth’s orbit around the sun and its axial tilt. Analemma is not exactly an ‘8’ but a one-sided elongated version of an ‘8’.

The orbit of the earth is not exactly a circle and possesses some eccentricity — the measure of the deviation of the curve from circularity — which should actually result in an ellipse if the axial tilt of earth was 0 degrees.

Since the earth is tilted by 23.5 degrees, the elliptical pattern is disrupted. How?

The value of obliquity gets added up to give us the shape that we observe. Since the orbit is elliptic and the sun lies in one of the foci of the ellipse, the earth gets to pass 4 interesting points. These points lie around the extreme ends of the major and minor axes of the ellipse. Points on the major axis result in solstice — summer at perihelion when the sunlight is directed at Tropic of Cancer and winter at aphelion when the sunlight is directed at Tropic of Capricorn (with reference to the northern hemisphere). While the points on the minor axis result in equinoxes — vernal and autumnal depending on the hemispheres. The point where the loops cross is when we observe equinox and either end of the loops is when we observe solstice.

Image Source: Forbes

Observed from the northern hemisphere, the lower part seems elongated while from the southern hemisphere, it is the opposite. You may only observe either of the loops from the poles — the top one from the north and the bottom one from the south both being vertical. The case in the poles is due to the period when that region doesn’t receive sunlight. This results in only one loop of the ‘8’ visible in the poles. The analemma tends to tilt while going away from the poles. At the equator, the analemma lies to its sides, making it look like an ‘ill-shaped infinity’.

Martian Analemma. Image Source: APOD-NASA

While this is the case observed from earth, the shape of analemma depends on the orientation of the planet from which the sun is observed. It is the same for other solar systems too. Depending on the eccentricity and axial tilt, you may also get weird shapes like a raindrop or a straight line! I know you may wonder if we can get some cool batman logos as an analemma. One cannot jump to a conclusion that it is possible or it is completely ridiculous because nature has so much to reveal itself :)

Moral: Cool results require patience and keen observation!

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