The spherical distance, also called the great-circle distance, between two points 
and 
on a sphere is the distance
of the shortest path along the surface
of the sphere (paths that cut
through the interior of the sphere
are not allowed) from 
to 
, which always lies along a great
circle.
For points 
and 
on the unit sphere centered
at the origin, the spherical distance is given by
 |
where 
denotes a dot product and 
denotes the principal
value of the inverse cosine (Brannan et
al. 1999, p. 344).
