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We introduce a type of symmetry breaking and associated order parameter inconnection with Laplace-Runge-Lenz vector of Kepler orbit through an extendedspatial dimension and Ensemble view. By implementation of a small extra spatialdimension and embedded infinitesimal toral manifold, it has been shown thatemerging of LRL vector under SO(4)symmetry is in analogy with a variety ofexplicit and spontaneous symmetry breaking situations and related Goldstonebosons such as phonons and spin waves. A theorem introduced to generalize thisconcept of breaking symmetry. The diffeomorphism of circular orbit(geodesic)toelliptic one proved to be equivalent with a covariant derivative and relatedparallel displacement in this extended four dimensional spatial space.Respectto ensemble definition this diffeomorphism breaks the O(2) symmetry of initialorbit and Hamiltonian to Z2 resulting in broken generators in quotient spaceand associated Goldstone boson as perturbing Hamiltonian term leading to aperpetual circular motion on 2-torus comparable to the perpetual motion idea inTime Crystal of Wilczek. This leads to an introduction of gravitational gaugepotential under the symmetry of Cartan sub algebra of su(2).

On Laplace-Runge-Lenz Vector as Symmetry Breaking order parameter in Kepler Orbit and Goldstone Boson