January 4th, 2018, 02:21 PM  #1 
Newbie Joined: Jan 2018 From: Milan Posts: 1 Thanks: 0  Spherical Triangles
Hello Everybody! I'm not a student, I'm just trying to figure out how to calculate coordinates on a globe, and I would like to ask for some help. Let's say I have POINT A on the globe with the following coordinates: POINT A Latitude 45° 27' 50.95" N Longitude 9° 11' 23.98" E Also I have POINT B which is the Antipode: POINT B Latitude 45° 27' 50.95" S Longitude 170° 48' 36.02" W Given we are on a sphere (globe), from Point A to Point B for example I can draw 360 great circles, one for each single degree of the sphere:  and the distance to go from Point A to Point B is 180° (first semicircle)  and the distance to go back from Point B to Point A is also 180° (second semicircle) Now let's say I have POINT C with the following coordinates: POINT C Latitude 45° 26' 48.53" N Longitude 9° 1' 58.11" E Given these information, THERE IS ONLY ONE GREAT CIRCLE which: START IN POINT A GOES THROUGH POINT C ARRIVE IN POINT B (completing the first semicircle of 180°) COME BACK IN POINT A (completing the second semicircle of 180°) My problem is to find the formula to calculate the coordinates of the 2 Points which are halfway (90°) from Point A to Point B. Let's call these 2 Points as M and N: START in POINT A GOES THROUGH POINT C PASS THROUGH POINT M (at 90°) ARRIVE IN POINT B (completing the first semicircle of 180°) PASS TO POINT N (at 270°) COME BACK IN POINT A (completing the second semicircle of 180°) Which is the formula to calculate M and N? On a  plain surface  i would have used the simple proportion of triangles to calculate them, but given is a sphere I don't know the formula to be applied. I did some online search but I find a kind of difficult to figure it out. I have been out of school from 15 years now , so I would like to ask if somebody can help me. I hope my explanation is clear, thx a lot if you can help!!! Cheers 
February 20th, 2018, 11:08 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,865 Thanks: 1833 
Sorry about delay.


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