Moving a Object3d based on the camera rotation in a imaginary circle

I’m not good at math, if someone can help to achieve this behavior will save my day.

I have a Sprite that have to be positioned as close as possible to the camera. So the idea is to draw an imaginary circle (the red one) and if the camera rotates then we should relocate the Sprite.

Two screenshots to understand better:


Basically I’m trying to achieve an offset like to the Sprite. But apparently is not possible natively.
Here is my other post:

Not sure if this is a better approach than the pivot point mentioned by @Mugen87. At the end I just want to represent the life of the soldier in my game. But I’m struggle with this for several weeks.