The distance between a pair of points on the unit sphere:

The distance between a pair of points on the unit 3-sphere:

Take several points on the equator of the sphere:

Show that they are all equidistant from the north pole:

SphericalDistance accepts exact numerical inputs:

SphericalDistance accepts arbitrary-precision numerical inputs:

SphericalDistance works with symbolic inputs:

Calculate a rectangular DistanceMatrix and display the results with ArrayPlot :

SphericalDistance accepts points in GeoPosition [{lat,lon}] notation:

Use GeoPosition lists of points:

Generate three points in an octant of the unit sphere:

Find edge lengths of the corresponding spherical triangle:

Verify the spherical triangle inequality:

Define a parametric trajectory in spherical coordinates:

Represent the curve as a series of points and plot:

Estimate the curve's arc length:

Take the angular coordinates for the vertices of an octahedron:

Compute distances from one point to all others:

Find the symmetric matrix of distances between any pair of points:

Calculate an angular distance along the great circle :

Calculate the same distance along the great circle :

Both results are just the difference of component values:

Choose two points on a sphere:

Convert to Cartesian coordinates on a unit sphere:

Compare the results of SphericalDistance and VectorAngle :

The result of EuclideanDistance is always less than the result of SphericalDistance :

Locate two stars in the constellation Orion:

Calculate their angular separation in radians:

Compare with the result of AstroAngularSeparation :

Specify coordinates using GeoPosition :

Compute the GeoDistance on an ellipsoidal Earth:

Divide by Earth's average radius to a comparable result:

Calculate a symbolic distance between arbitrary points on a sphere:

Compare with the result of VectorAngle , simplified over the reals:

Different usages of SphericalDistance may return different results:

Check that both results are equivalent:

List spherical coordinates for the vertices of a tetrahedron:

Plot the tetrahedron with arcs between its vertices:

Verify all points have equal angular separation: