I have a sphere and 2 points on it. I know everything about these points to be able to define them in 3 dimensional space with both cartesian coordinate system and polar coordinate system (x, y and z position of the points; angles and radius).

I need to find the shortest distance between this point on the sphere's surface.

  • 1
    $\begingroup$ It is the great circle distance. In order to find this, use the formula $s=r\theta$ where $s$ is what you are required to compute, $r$ is the radius of the sphere, and $\theta$ is the angle subtended by the arc connecting the two points at the center of the sphere. $\endgroup$ Jul 12, 2016 at 13:38
  • $\begingroup$ @Karthik Figuratively, you are asking to walk from Point A to B along the surface of the sphere? What if we connect A and B through the sphere, won't that be shortest? $\endgroup$
    – MonK
    Jul 12, 2016 at 13:43
  • $\begingroup$ Sorry my mistake, I did not read the last part of the question! :) $\endgroup$
    – MonK
    Jul 12, 2016 at 13:46

1 Answer 1



If $\mathbf {p_1}$ and $\mathbf {p_2}$ are the two points, note that $|\mathbf {p_1}|=|\mathbf {p_2}|=r$ ( the radius of the sphere).

Now find the angle $\alpha$ betveen the two points using the dot product: $$ \alpha=\arccos (\frac{\mathbf {p_1}\cdot \mathbf {p_2}}{r^2}) $$

and the distance between them is $ d=r\alpha$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.