Basic Mechanics of Planet-Satellite Interaction with special reference to Earth-Moon System

TL;DR

This paper revisits Darwin's analysis of the Earth-Moon system, using modern data to model the Moon's recession and Earth's rotational changes, and proposes a novel application of day-length variations as an earthquake precursor.

Contribution

It provides a refined theoretical model of Earth-Moon interactions incorporating evolving Earth's moment of inertia and extends the mechanics to simulate other planet-satellite systems.

Findings

Theoretical graph of day-lengthening matches observational data in the post-Cambrian era.

Deviations in ancient data suggest Earth's moment of inertia has evolved.

Proposes using day-length variations as indicators for seismic activity.

Abstract

In1879 George Howard Darwin theoretically analyzed the outward spiraling orbit of Moon and the subsequent lengthening of the Mean Solar Day. The author redid the same analysis based on the fact that Moon was receding at the rate of 3.8 cm per annum. Basic Mechanics of Earth-Moon is worked out and various system parameters are optimized to fit the given boundary condition obtained by Apollo Mission and other modern means of observations. Based on this theoretical formulation the theoretical graph of the lengthening of the Mean Solar Day with respect to time is drawn and is compared with the observational graph of the same based on pale ontological data, paleo tidal data and iron-banded formation. The observational data on Mean Solar Day is found to follow the theoretical smooth curve in post-Cambrian Era but is found to deviate in the remote past. This deviation is corrected by taking the evolving form of Moment of Inertia of Earth. The deviation of the observed data prompts the Author to suggest that the lengthening of the Mean Solar Day curve could possibly be used as an analytical seismograph for the impending earthquakes and sudden volcanic eruptions. The Basic Mechanics of E-M system is generalized to lay the foundation of simulation software for any Planet-Satellite pair in our Solar System.