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Modified uncertainty principle and non-commutative variables mayphenomenologically account for quantum gravity effects, independently of theconsidered theory of quantum gravity. We show that quantum fluids enableexperimental analogs and direct tests of the modified uncertainty principleexpected to be valid at the Planck scale. We consider a quantum clock realizedby a long-lasting quantum fluid wave-packet orbiting in a trapping potential.We investigate the hydrodynamics of the Schr\"odinger equation encompassingkinetic terms due to Planck-scale effects. We study the resulting generalizedmechanics and validate the predictions by quantum simulations. Wave-packetorbiting generates a continuous amplification of the quantum gravity effects.The non-commutative variables in the phase-space produce a precession and anacceleration of the orbital motion. The precession of the orbit is stronglyresembling the famous orbital precession of the perihelion of Mercury used byEinstein to validate the corrections of general relativity to Newton's theory.In our case, the corrections are due to the modified uncertainty principle. Theresults can be employed to emulate quantum gravity in the laboratory, or torealize human-scale experiments to determine bounds for the most studiedquantum-gravity models and probe Planckian physics.

Quantum-gravity-slingshot: orbital precession due to the modified  uncertainty principle, from analogs to tests of Planckian physics with  quantum fluids