Can a babylonjs object rotate around the world axis while revolving around itself like threejs?

Is it necessary to set a parent node?

Of course. You can use the same method as the threejs demo you showed, or use a parent - create two nodes, one is the code, one is a transform node:

Babylon.js Playground (babylonjs.com)

You can also use a pivot, although the parent method @RaananW suggests is much easier

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