Is there a way to get the offsets needed for $\phi$ and $\theta$ so I can place a grid of spheres with radius $r_1$ without having the spheres collide. All of the spheres will be placed with the same r in a spherical coordinate system $[\phi,\theta,r]$
If I had a Cartesian coordinate system I would simple have used a offset of $2r_1$ for my x and y coordinates.
This will be used by a program to dynamically create a grid of spheres on a spheres surface.
How about a "cubo-octohedron.
place the centers of your spheres at $(2,0,0), (0,2,0), (-2,0,0), (0,-2,0), (1,1, \sqrt 2),(-1,1, \sqrt 2),(-1,-1, \sqrt 2), (1,-1, \sqrt 2), (1,1, \sqrt 2),(-1,1, -\sqrt 2),(-1,-1, -\sqrt 2), (1,-1, -\sqrt 2)$
Each sphere can have radius $1$ And each center lies on a sphere of radius 2.
in spherical it would correspond to $(\theta, \phi) = (n\frac {\pi}{2}, 0), (n\frac {\pi}{2}+\frac {\pi}{4}, \pm \frac {\pi}{4})$