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Spherical TrianglesHello Everybody! :D 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 ALatitude 45° 27' 50.95" N Longitude 9° 11' 23.98" E Also I have POINT B which is the Antipode: POINT BLatitude 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 semi-circle)- and the distance to go back from Point B to Point A is also 180° (second semi-circle)Now let's say I have POINT C with the following coordinates: POINT CLatitude 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 CARRIVE IN POINT B (completing the first semi-circle of 180°)COME BACK IN POINT A (completing the second semi-circle of 180°)My problem is to find the formula to calculate the coordinates of the 2 Points which are half-way (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 semi-circle of 180°)PASS TO POINT N (at 270°)COME BACK IN POINT A (completing the second semi-circle 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 :unsure:, 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 |

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