Circumference at a Given Latitude Date: 01/26/2001 at 17:52:23 From: Lynn Subject: Circumference - at latitude of globe I know the circumferance of the earth at the equator in miles. How can I calculate the circumference of a line around the earth (a circle) at 40 degrees north latitude? Date: 01/26/2001 at 20:37:52 From: Doctor Fenton Subject: Re: Circumference - at latitude of globe Hi Lynn, Thanks for writing to Dr. Math. If you're familiar with trigonometry, a point on the circle of latitude at latitude L has as its radius one leg of a triangle with center at the center of the Earth, one vertex at the point, and the other vertex on the polar axis: P is the point on the latitude circle, O is the center of the Earth, and Z is the point on the polar axis the same distance above the equatorial plane as P. polar axis | | radius at latitude L Z |---------P | / | / | / | / | / | / | / L |/_______________ Equatorial radius O By geometry, Angle OPZ is also L, the same angle as the latitude. OP is the same as the equatorial radius, if you consider Earth a sphere, so ZP -- = cos(L) OP and ZP = OP*cos(L). The circumference at latitude L is 2*pi*ZP = 2*pi*OP*cos(L) = (equatorial circumference) * cos(L). So, just multiply the equatorial circumference by the cosine of the latitude, and you will have the circumference at that latitude. If you have further questions, please write again. - Doctor Fenton, The Math Forum http://mathforum.org/dr.math/

Circumference at a Given Latitude Date: 01/26/2001 at 17:52:23 From: Lynn Subject: Circumference - at latitude of globe I know the circumferance of the earth at the equator in miles. How can I calculate the circumference of a line around the earth (a circle) at 40 degrees north latitude? Date: 01/26/2001 at 20:37:52 From: Doctor Fenton Subject: Re: Circumference - at latitude of globe Hi Lynn, Thanks for writing to Dr. Math. If you're familiar with trigonometry, a point on the circle of latitude at latitude L has as its radius one leg of a triangle with center at the center of the Earth, one vertex at the point, and the other vertex on the polar axis: P is the point on the latitude circle, O is the center of the Earth, and Z is the point on the polar axis the same distance above the equatorial plane as P. polar axis | | radius at latitude L Z |---------P | / | / | / | / | / | / | / L |/_______________ Equatorial radius O By geometry, Angle OPZ is also L, the same angle as the latitude. OP is the same as the equatorial radius, if you consider Earth a sphere, so ZP -- = cos(L) OP and ZP = OP*cos(L). The circumference at latitude L is 2*pi*ZP = 2*pi*OP*cos(L) = (equatorial circumference) * cos(L). So, just multiply the equatorial circumference by the cosine of the latitude, and you will have the circumference at that latitude. If you have further questions, please write again. - Doctor Fenton, The Math Forum http://mathforum.org/dr.math/