Math in the Physical Sciences

Astronomy and Math

What type of geometric path does the Sun seem to take in the Earth’s sky?

The Sun’s apparent path in the Earth’s sky is called an analemma, or the measurement of the Sun’s declination over the year. In fact, if one recorded the position of the Sun in the sky at the same time every day, the Sun would appear to follow a figure-eight path, the analemma—a feature often seen on globes of the Earth. Astronomers also use another way to note the path of the Sun: the difference in time between the clock and the position of the Sun (clock versus Sun times) is called the equation of time. For those living in the Northern Hemisphere, if one notes the Sun’s position is to the east, the equation of time is negative; if the sun is to the west, the equation of time is positive.


The illustration at the top shows what happens during a lunar eclipse, when the Moon passes through the shadow of the Earth (M-1 to M-2). Below that is what happens during a solar eclipse, when the Moon comes between the Sun and the Earth, casting a shadow on the Earth’s surface. A and B points show where a total eclipse would be, and the region between the Cs would experience a partial eclipse.

Why does the Sun take such a different path across the sky each year? There are two main reasons: first the Earth’s rotational axis (the Earth’s rotation creates the day and night) is tilted 23.5 degrees in relation to the plane of its orbit around the Sun. Second, the Earth does not orbit the Sun in a circle, but orbits in an ellipse (oval-shape). Because of the tilt and the orbit, over a year the Sun’s path seems to move in a figure-eight. (It’s interesting to note here that because of the tilt and orbit of the other planets in the solar system, they, too, have analemmas all their own, which are different from the Earth’s.)


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