Have you ever wondered how fast Earth is rotating about its axis? Well, since Earth is a sphere the answer to this question will depend on the exact location you are relative to the equator. In order to get a precise value for the speed you'll have to do some calculations, nevertheless you can intuitively understand that people at the equator are moving at maximum speed, whereas at the poles people are moving rather slowly.

When we need to calculate speed it all comes down to this simple formula:

v = d / t

where:

v = velocity
d = distance
t = time

We all know that irrespective of the place where we live, an Earth day always lasts 24h. This means that a single point on the surface of the Earth takes 24h to return to the same place covering a certain distance. Thus, we can replace t = 24h in our formula:

v = d / 24h

What about the distance? Unlike time, the distance we travel each day will depend on our position relative to the equator, or more precisely our latitude. In order to understand this, try picturing the Earth as a huge orange which you slice in thin slices, each of which is at a certain latitude. Now, instead of thinking about a globe rotating simply imagine this differently sized slices rotating, you can think of them as circles. The circle with the greatest circumference will obviously be the slice you cut at the equator, then as you move north or south the circumference of the circles will decrease reaching a minimum at the poles.

We live at a certain latitude, which means we live at a particular circle. When Earth rotates for 24h completing a day, the distance we travel is exactly the circumference of one of these circles. We know that the circumference of a circle is given by this formula:

c = 2 * Pi * r

However, how can we know what is the radius of the circle we live in? Since we know the radius of the equator, we can find the radius or our circle by multiplying it by the cosine of our latitude:

r = Req * cos(lat)

Replacing r = Req * cos(lat) in the circumference formula we obtain:

c = 2 * Pi * (Req * cos(lat))

As we've seen previously, the circumference (c) of the circle in which we live is actually the distance we travel, thus we can replace d = c in our initial v = d / t formula finally yielding:

vlat = 2 * Pi * (Req * cos(lat)) / 24

Which is the formula used to calculate Earth's rotational speed at a specific latitude. The latitude must be in radians, not degrees so you might have to convert your latitude in degrees with this formula:

radians = degrees * Pi / 180

Now as an example let's calculate the rotational speed at two distinct cities, Lisbon and Helsinki:

Req = 6378.14 km
Pi = 3.14159265...
Lisbon latitude = 38.72 degrees = 0.675791486 radians
Helsinki latitude = 60.17 degrees = 1.05016461 radians

Substituting in the formula we obtain:

Lisbon vlat = 1302.79 Km/h
Helsinki vlat = 830.60 Km/h

As expected, Lisbon which is closer to the equator is rotating faster than Helsinki which is closer to the north pole.

It's now over a week since I moved to Posterous and all I can say is that I'm loving it much more than I thought possible and I'm posting much much more often!