Have you ever wondered how fast you are spinning around Earth’s rotational axis?  Probably not, but now you can find out anyway!  This graph shows the tangential speed of a point on Earth’s surface for a given latitude due to Earth’s rotational motion – it does not include speed due to our revolution around the sun! Tangential (linear) speed is the magnitude of the velocity vector, which points tangent to Earth’s surface in the same plane as the circle of latitude.

I’ve plotted the dependent variable (speed) on the x-axis; though this is unconventional, it allows the map in the background to be placed in the traditional north-pointing-up orientation.  So if you don’t know the latitude of your location, you can pick it out on the map and then trace a horizontal line to where it intersects with the curve. To the scientists and non-US readers, sorry that the speed axis is in mph; I converted from km/h because most of the people who read this are from the US.

Those who remember their trigonometry will notice that this graph is nothing more than a slight variation on the cosine function – because I have switched the axes, it could be thought of as cosine reflected over y=x, or arccos if it had no range restrictions and could plot below the x-axis.

Though this is an approximation, in an effort to be as accurate as possible, I used the length of a sidereal day (23 hrs, 56 min, 4 sec), which is a full 360° rotation of Earth. Because Earth is an oblate spheroid rather than a sphere, I varied the radius as a function of latitude when calculating the tangential speed. The polar radius is 3950 miles and the equatorial radius is 3963 miles; I approximated the radius at other latitudes via a linear interpolation. This has no visible effect on the curve, though. Using the average radius of the earth (3959 miles) as a constant changes the global tangential speeds by <1 mph. Topography of the Earth is equally unimportant for this level of accuracy because the difference between a mountain peak and the bottom of the ocean is trivial compared to the radius of the Earth. If, hypothetically, Mt. Everest’s peak (5.5 miles above datum) and the deepest part of the Mariana Trench (6.8 miles below datum) were both located along the equator, the difference in tangential speed caused by the 12.3 mile elevation difference would only be about 3 mph, or less than a third of a percent of the equator’s 1040 mph tangential speed.

Posted on 23 January, 2014

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