Geodesics of a metric tensor describes the motion of a test particle in the gravitational field of a central mass by a second-order differential equation. A resolution gives the trajectory the shortest distance, demonstrated by variational principles, and carries out parallel transport of the velocity tensor, according to the covariant derivative. The characterization by geometric principles makes the kinematic effect resolvable, but untangling the dynamic cause in Christoffel's symbol remains intricate. The canonical representation of the equation in its geometric purpose introduces terms that disturb mechanical understanding. Geodesics also appears in the derivative of the Lorentz invariant, which conditions parallel transport to the conservation of the invariant velocity modulus. The vectorial elaboration of this equation involving geodesics reduces the tensor system to a closed scalar sentence. The correspondence between terms can be inferred from the reciprocity between space and time in the metric tensor by the variational pattern.Considering the covariance isometry property, we establish equivalences between the terms of the geodetic equation and expose the dynamics of geodetic acceleration in a concise equation.