How to find an angle in spherical geometry.

[yungman]

Hi
I am not familiar with spherical geometry. I am working with elliptical polarization that involves using poincare sphere that present the latitude and longitude angle in spherical geometry. I need to find the great circle angle if given two points that each specified by their longitude angle $2\tau$ and latitude angle $2\chi$.

ie. If I am given the $\chi$ and $\tau$ of $M_{1}(\tau_{1},\chi_{1})$ and $M_{2}(\tau_{2},\chi_{2})$, how can I find the great circle angle between $M_{1}(\tau_{1},\chi_{1})$ and $M_{2}(\tau_{2},\chi_{2})$?

I really don't want to learn the details of spherical geometry, just want to learn the way of finding the angle as this is only a small part of antenna design.

Thanks

Alan

 

[Simon Bridge]

google for "great circle distance". eg. http://mathworld.wolfram.com/GreatCircle.html

If the great circle distance is $d$, then the angle (in radians) between the points is $\theta=d/R$ where R is the radius of the sphere.

 

[yungman]

Thanks for the reply, but what if if I have only the longitude and latitude angle of the two points, how can I find the great circle angle between the two points?

 

[Simon Bridge]

what if if I have only the longitude and latitude angle of the two points, how can I find the great circle angle between the two points?

Step 1: find the great-circle distance between the two points from the long and lat values.
Step 2: divide this by the radius of the sphere.

Anticipating your next question: see link in post #2.