We reveal all linear order inertial and gravitational effects on a non-relativistic Dirac particle (mass m) on the Earth up to the order of 1/m in the Foldy–Wouthuysen-like expansion. Applying the result to Penning trap experiments where a Dirac particle experiences the cyclotron motion and the spin precession in a cavity, i.e. a geonium atom, we study modifications to the g-factor of such as the electron. It is shown that each correction from gravity has different dependence on the cyclotron frequency and the mass m. Therefore, their magnitude change depending on situations. In a particular case of an electron g-factor measurement, the dominant correction to the observed g-factor comes from effects of the Earth’s rotation, which is δg/2 ≃ 5.2 10−17. It may be detectable in the near future.