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As the Earth rotates on it’s axis, the Equator remains aligned, but the line of ancient sites describes a sine wave as a result of it’s tilt relative to the Equator. The line of the ecliptic may be observed describing a similar wave by spinning a globe that has a line of the ecliptic. The wave may also be visualized by drawing the line of ancient sites on a flat projection of the Earth.

Image © Cosmi 3-D World Atlas

The wavelength is equal to the circumference of the Earth. The amplitude of this wave, measured from the middle of the wave (the equator), is 30° of latitude. Recall that the 30th parallels are ½ of the height of each hemisphere, or ½ of the radius of the Earth.

Since the height of the wave is equal to ½ of the Earth’s radius, the ratio between the wavelength and it’s amplitude is 4π. Measuring the amplitude from the top of the wavelength to the bottom (from 30° N to 30° S), the amplitude is equal to the radius of the Earth, and the ratio between the wavelength and the amplitude is 2π.