Geophysics

A Dynamic Model of Tidal Deformations of the Earth's Elastic Crust in the Central Force Field of the Earth-Moon System

Authors: Viktor Strohm
Comments: 8 Pages.

Traditional theories of Earth tides (such as the classical models of Clairaut, Love, and Darwin) describe geoid deformations via the differential potential of an isolated external disturbing body distributed across the volume of an elastic-plastic sphere. However, when attempting to interpret the physical meaning of forces acting on discrete crustal elements (mobile tectonic plates) within a real bound system, researchers inevitably encounter kinematic paradoxes—specifically, a theoretically unavoidable but empirically unobservable macro-displacement of the planet’s dense core toward its internal boundaries.The present work aims to describe the dynamics of the Earth’s shape variation based on generalizing the law of central forces and the kinematics of the system’s elliptical motion around the barycenter, as presented in [1]. The primary conceptual difference of the proposed approach is the transition from abstract scalar potentials to direct vector summation of actual gravitational accelerations acting on a rigid elastic shell of fixed thickness.The resolution of the apparent contradiction in the direction of individual particle force vectors during the transition from an abstract disk to the real Earth-Moon system lies within the framework of the classical three-body problem. As soon as we begin decomposing the monolithic mass of the planet M into an ensemble of discrete elements m_i, the system transforms into a hierarchical three-body configuration: two interacting bodies are located in immediate proximity (the analyzed crustal microparticle m_i and the residual mass of the planet M-m_i), while the third massive body (the Moon) is removed at a significant orbital distance.In such a formulation, the total force vector acting on each particle naturally decomposes into two components. The short-range (local) interaction binds the particle to the main mass distribution of the planet, directing its elastic retention vector strictly toward the center of the disk C (which, in a geocentric reference frame, manifests as radial compression in the lateral zones Y-Y' ). At the same time, the long-range (gravitational) field of the distant third body imparts the necessary centripetal acceleration to the entire bound system, directing the orbital force vector toward the system’s focus — the barycenter F. Thus, the formalism of force decomposition into focal and central components, proposed in [1] for the circle model O_E, receives a rigorous dynamic justification within the restricted three-body problem, linking the internal geodynamics of the lithosphere with Kepler's laws.
Category: Geophysics