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Principle of Equivalence

This principle states that gravitational mass and inertial mass are equivalent.
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The statement of the theorem

Consider a test mass mm undergoing free fall in a gravitational field. The Principle of Equivalence states that the trajectory of this mass is independent of its internal composition and structure. Mathematically, this implies that the equation of motion derived from the gravitational force F⃗g\vec{F}_g is identical to the equation of motion derived from an inertial force F⃗i\vec{F}_i in an accelerating reference frame:\n\nd2xdt2=g⃗andd2xdt2=a⃗inertial\frac{d^2 x}{d t^2} = \vec{g} \quad \text{and} \quad \frac{d^2 x}{d t^2} = \vec{a}_{\text{inertial}} \n\nThus, the gravitational acceleration g⃗\vec{g} is locally indistinguishable from the acceleration a⃗\vec{a} of the reference frame.