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January 4th, 2018, 02:21 PM   #1
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From: Milan

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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 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 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 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 , 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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February 20th, 2018, 11:08 PM   #2
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Sorry about delay.
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