How to make a sphere with low transparency in the middle and higher transparency toward the edge?

like this

 

With shaders. Assign something like dot product between surface normal and vecotr towards camera to alpha channel.

 

Obviously it can be successful, thank you.

 

You could also fake it. A billboard should be indistinguishable from a real model.

 

The keywords that might help is Fresnel or ndotv also known as don't aka like neg said a dot product between view and normal

Also the billboard can be done with texture but if you need 3d intersection and infinite resolution, bypass the texture and compute a ray intersection with a specs, extract normal and relative position, compare with depth buffer, use the screen aligned composant of the normal to extract Fresnel values without the dot.

 

Do you mean to make a picture rotate with the camera?

 

Yes - always faces the camera. Usually done by shader.

 

I used the pow function to modify the gradient curve and got an approximate effect.
What you said is so thorough and I learned a lot,
thank you