I'm trying to find the resulting location of a point on a sphere in spherical coordinates or Cartesian. Based on velocities from the perspective of an object on the sphere. So given the: location on the sphere (in spherical or Cartesian) zy - plane rotation of the point up direction of the point is always away from the origin velocity from the perspective of the object How do I find the resulting new location on the sphere. I am not sure what math to use, or what keywords to search in google. Made an illustration below.