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Radius of Earth at specific angle, need help

  1. Jan 24, 2012 #1
    I was going to post this on Earth-forum here but I thought that you guys here can help me better with this. I'm trying to get the radius of Earth on every latitude degree from 0° to 90°, knowing 0° at Equator is ~6378,137km and 90° at North/South Pole is ~6356,7523km (source Wikipedia). In Wikipedia there is formulas to calculate radius at any angle, but I dont have a clue how to calculate with it. Now to what I'm asking here:
    Can someone please explain to me (one that doesnt have even College education on mathematics) so that I could understand it? Best way to explain would be adding some examples like for 61° and 34°?

    Now, I have been struggling with this for a very very long time, and I am already being really thankful for the one that explains this to me.

    Wikipedia article:
  2. jcsd
  3. Jan 24, 2012 #2


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    No college math needed here, just how to use a calculator! The applicable formula is the first:
    "The distance from the Earth's center to a point on the spheroid surface at geodetic latitude"
    [tex]R= \sqrt{\frac{(a^2cos(\phi))^2+ (b^2sin(\phi))^2}{(acos(\phi))^2+ (bsin(\phi))^2}}[/tex]
    And you are given that a= 6,378.1370, b= 6,356.7523.

    So if, for example, [itex]\phi= 61^o[/itex], [itex]cos(\phi)= cos(61)= 0.4848096[/itex] and [itex]sin(\phi)= sin(61)= 0.8746197[/itex].

    So [itex]a^2cos(\phi)= 19722361[/itex], [itex]b^2sin(\phi)= 35341895[/itex], [itex]acos(\phi)= 3092.182[/itex], and [itex]bsin(\phi)= 5559.741[/itex] where I have rounded to 7 significant figures. Can you finish?
  4. Jan 24, 2012 #3
    I'm afraid and really sorry, but I think I cant finish, haha. I put numbers you had calculated on formula and I keep having number 435114,36..., double-checked. Thank you very much for the your explain this far, I get it to the point you have calculated it, but I'm afraid I have to ask you to tell me how to finish it?
  5. Jan 24, 2012 #4
    Oh, now I got it right, THANK YOU very very much, I'll be thankful for you for really long time!
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