The Rotational Speed at Latitude calculator computes the rotational speed on the surface of the Earth based on the Earth's Rotation Rate and the latitude.
INSTRUCTIONS: Enter the following:
Rotational Speed (S): The calculator returns the Rotational Speed in miles per hour. However, this can be automatically converted to other velocity units (e.g. meters per second or kilometers per hour).
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This equation computes the rotational speed (S) of a point on the Earth defined by its latitude (`alpha`). This equation assumes a round Earth approximation and uses the WGS-84 value for the .
First we recognize the circle that is the equator and the circle created by the rotation of a point on the Earth at a non-zero latitude describe circles in parallel planes. Thus the radius of that circle at a specified latitude and the radius at the equator can be rotated in those parallel planes to be parallel lines -- as drawn in the figure at the left. The black line at the equator is parallel to the red radius of dimension Rlat.
These two radii crossed by the radius drawn diagonal from the center of the Earth to the specified latitude, form two internal opposite angles, `alpha`. We know from basic geometry that the two internal angles (`alpha`) in the figure are equal. The top red line of the triangle is then the cosine of the angle, `alpha`, multiplied by the length of the right triangle's hypotenuse:
Rlat = Re•cos(α) where Re is 6378137.0 m
Next, knowing the circumference of the circle whose radius is Rlat is given bylat we have the distance a point rotates each day at the latitude given by `alpha`.
Then we can compute the instantaneous velocity of a point on the globe at the specified latitude, α, by dividing the distance traveled in one day (in one rotation of the globe) by the number of hours in a( 23.9344699 hours). A is the true period of a 360 degree rotation of the Earth in space. This takes into account the difference in from solar day attributed to the Earth's flight around the Sun.