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Name: Lori
Status: Student
Age: 40s
Location: N/A
Country: N/A
Date: N/A 

What is the earth's rotational speed at different points on the globe?
What formula can I use to determine it?

To answer the question you are asking is trivially easy. The question I think you meant to ask is a little more involved, but not much.

The earth's rotational speed is one revolution per day. It doesn't matter where on earth you stand, that is the rotational velocity. I believe that you mean to ask the TANGENTIAL velocity of any point on the earth due to the earth's rotation. To compute this approximately, you need to know two things: the latitude of the point on the earth's surface, and the circumference of the earth. For ease of calculation, we will assume that the earth is a perfect sphere. This is a pretty good approximation; the surface IS extremely flat, and the oblateness at the equator is only a factor of about 0.3%.

I came up with a formula similar to the one you cite. One possible source of error in using this formula is that it converts the degrees of latitude into RADIANS, which you need to do if you're calculating cosines in a spreeadsheet. Some calculators default to calculating trigonometric functions of angles measured in degrees. If you are calculating the cosine of the angle in degrees, you don't need the factor of pi/180 used in the formula. Be aware that the formula as written gives the velocity in distance per DAY, and you need to explicitly multiply by day/24h to find the value in distance per hour. Doing that, I get 860.16 mi/h at 34 degrees latitude.

In doing this, I convert the latitude of 34 degrees to 0.593 radians. The cosine of an angle of 0.593 radians is 0.829; multiply this by your equatorial velocity number and you'll get 860 mph. If you make the mistake of calculating the cosine of 0.593 DEGREES, you'll find that it is 0.999946; multiplying this by the equatorial velocity gives 1037.48 mph. I'll bet that's what you did.

So, the short answer to your question is either that you shouldn't convert to radians when you use the formula, or that you should calculate the cosine from the latitude in radians.

Richard E. Barrans Jr., Ph.D.
Assistant Director, PG Research Foundation
Darien, IL USA

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