Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If A and B are two points on the earth, how could I find any arbitrary point between them along the shortest distance side of their great circle path?

Points are in radians
longitude = 0 to 2pi
latitude = 0 to pi, 0 being at north pole
Points are not antipodal

I desire something where I specify a range 0.0 to 1.0, with 0.0 being point A and 1.0 being point B and 0.5 being the midpoint between them, with all other values being their corresponding points. Thanks!

Note: This is not homework. I'm 41yrs old and this is for a personal project I'm working on.

share|cite|improve this question
Good question. It is an embarrassment to the site that a climate has been created where users feel they have to post detailed personal disclaimers (even about subjects that are not taught in today's education system -- spherical geometry!) to avoid the accusation of posting homework. – T.. Nov 10 '10 at 23:24
Here's an idea: you first get the spherical distance of your two points, construct an equatorial arc of that length, and then rotate the arc such that the ends coincide with the original points. I don't have the time to work out the mathematics completely, but I don't see a reason why it shouldn't work. – J. M. Nov 10 '10 at 23:53

This aviation website has the information that you were looking for. The formula presented there returns the latitude and longitude of a point that is a fraction $f$ between points A and B except when they are antipodal just as you mentioned in the question.

share|cite|improve this answer
Nice! Note that safe implementations couch any use of inverse trigonometric functions in terms of the two-argument arctangent. – J. M. Nov 11 '10 at 0:26

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.