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# How do you calculate parallel radius on a sphere.

Posted on 2013-12-01
Medium Priority
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I have a wire frame sphere with a diameter of 96 units.  I need a math pro to show and explain the formula to calculate the diameter of the circle created by a parallel at a certain degree of latitude.  For your example please use 30 degrees.  If you find a web page that has a calculator for this on it, that would be good enough also.
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Question by:pamsauto
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LVL 24

Expert Comment

ID: 39688051
Is the calculator at the following page you are looking for ("Calculate Circumference of the Earth at a given Latitude")?:

http://www.easysurf.cc/circle.htm#cetol1 >
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Author Comment

ID: 39688064
That is using the correct formula I would assume (but it could be working with the fact the earth is not a sphere), but I need to input the diameter of my own sphere.
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LVL 24

Expert Comment

ID: 39688069
Assume perfect circle.

Formula: C = 2 pi r cos(x),

where pi = 3.14159..., r = the earth's equatorial radius = 6378 km, and x is the angle of latitude.
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Accepted Solution

ozo earned 2000 total points
ID: 39688076
96*cos(30°)
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LVL 24

Expert Comment

ID: 39688504
The formula: C ("diameter of the circle created by a parallel") = 2 pi r cos(x).

2 pi r = 96 in your case.

You can use the formula for all "degree of latitude" and "spheres" of all sizes.  :-)
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LVL 84

Expert Comment

ID: 39688586
C = Circumference = pi * Diameter
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