Can an Electron Orbit Around Another Particle?

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Chaos' lil bro Order
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Hello,

While thinking about how an electron has an orbital momentum around a nucleus as well as an intrinsic momentum (spin), I was wondering if there is any sense in asking if the electron itself may in turn have an orbitting particle of its own.
 
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Electrons are consider fundamental in the sense that they are not made of other smaller particles, i.e. they are not composite like protons and neutrons, which are composed of quark triplets.