I'm a little bit confused with how to understand the relationships between spin angular momentum $S$, orbital angular momentum $L$, and the total angular momentum $J$ by visualizing those quantities. Classically, if we consider the motion of the Earth, I think $S$ is its rotation, $L$ would be its orbit around the sun, and $J$ is the combination of both. However if we consider the electron spin, I've seen the following diagram to illustrate their relations:

enter image description here

I'm wondering is there a way to understand the Earth's total angular momentum from this diagram? If not, can we draw a different diagram to show their relations?


In this picture, both orbital and angular momenta are treated as vector. As the third case illustrates, it is perfectly possible for the sum of two vectors to be smaller in length than the length of both constituents in the sum.

This third figure would correspond roughly to the case where the rotation of the Earth about its axis is reversed compared to what it is now, so that the Sun would rise in the West. Then the $\vec S$ for Earth would be mostly antiparallel to the orbital angular momentum of Earth about the Sun.

The big difference of course is that, for the “quantum vectors”, only some projections about $z$ are possible, and only some lengths of the resulting vectors are possible so $\vec L$ and $\vec S$ must combine in specific ways so that their projections and lengths add up correctly.

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