

Earth and Moon Rotation
Name: James
Status: Educator
Age: 30s
Location: N/A
Country: N/A
Date: N/A
Question:
I have read your answer to "How fast does the earth and
moon rotate."
What is the formula for determining the rotational speed for any given
latitude? I would like to use my latitude or one close to it for
my students.
Replies:
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%.
The formula is
C=2 x Pi x R x Cos((Pi x L)/180)
if you calculate the cosine of an angle in radians (many computer
spreadsheets use radians), or
C=2 x Pi x R x Cos(L)
if you calculate the cosine from the angle's measurement in degrees.
In this formula, Pi = 3.1415927..., L is the angle of latitude, and R is the
radius of the earth, 6378 km.
Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois
James,
This question is related to the one on "Earth Circumference" at different
latitudes that I
answered a few days ago. The radius (r) of a circle (that is parallel to
latitude) at any latitude (assuming the Earth to be a perfect sphere) is the
Earth's radius (3963.5 miles) times the cosine of the latitude angle. The
circumference at the latitude is then 2 x pi x r. The Earth
rotates once per 23 hours, 56 minutes and 4 seconds (approximately 24 hours).
By determining
circumference at any latitude and dividing it by the time in a day, you get the
rotational speed.
Dr. Cook
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Update: June 2012

