Question Game object and particle system change of relative proportions when camera moves

I am using the traditional Particle System. I have a particle system producing a cyan ring that should coincide with the circumference of a real sphere ( the sphere is not a particle system ). Both are in hierarchy under an empty object.
My problem is that until the camera remains at the same distance used to build the particle system ( and to scale everything ) everything works as expected ( picture 1 ), but when the camera ( it could be on a character ) approaches or gets far from the sphere, the ring ( ie the particle system ) and the sphere lose their alignment and the sphere tends to appear much larger. Picture 2. The sphere is semi-transparent but the issue can be clearly seen.