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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.

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 4
π. 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.

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