Calculating Distances Along Parallels of Latitude

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As discussed, the equatorThe Equator is Zero degrees (0°) latitude. The Sun is directly overhead the equator at noon on the two equinoxes (March and Sept. 20 or 21). The equator divides the globe... More is the zero-degree Latitude that divides the earth horizontally into two equal parts. The diameter of the earth at the equator is about 12,756 kilometres while the radius is approximately given as 6,400 km and dented by R as shown in the figure above.

All other latitudes aside from the equator are smaller circles and their radius are denoted by the small letter r . This is because the radius at the equator is greater.

The radius of the parallel of latitude is r because it is a small circle while the radius of the equator is R because it is a great circle.

If we draw a line from the centre O to a latitude below (or above) to meet at a point on the circumference B, OB will also be equal to the radius of the equator R. Also, the angle subtended at O will be equal to the angle subtended at B (alternate angles).

Considering right angle triangle OAB

Cos θ = \( \frac {r}{R} \)

∴ r = R Cos θ

Note that the distance between two points along parallels of latitude lies on the arc length of