Statistics – Methodology
Scientific paper
Feb 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009adspr..43..460s&link_type=abstract
Advances in Space Research, Volume 43, Issue 3, p. 460-466.
Statistics
Methodology
1
Scientific paper
At 4.56 Ga, the accretion of the slowly rotating Solar Nebula led to the formation of Sun and its Planets in the plane of disc of accretion. Moon was formed by accretion from a circumterrestrial disk of debris generated by the glancing angle impact of the young Earth by a Mars size planetary embryo at about 4.5 Ga at a distance of 15,000 km. The Moon since then has migrated to the present position of 384,400 km from the center of the Earth. In course of this outward migration it has slowed down the spin rate of Earth and caused the lengthening of diurnal day length from 5 h initially to 24 h presently. The basic mechanics of Earth Moon System has been worked out and theoretical determination of lengthening of day curve is carried out. This theoretical lengthening of day curve is compared with the observed lengthening of day curve based on paleobotanical evidences, ancient tidalites and Australian Banded Iron Formation. There is a remarkable correspondence between the two curves except for intermittent deviations due to geographical and geophysical factors. Based on the theoretical curve of lengthening of day, an empirical formula for the lunar orbital radius expansion is determined. Based on this empirical formula, simulation software is developed that gives the correct evolution of the semi-major axis (a) of our Moon for any time span from the inception to the time chosen under study. For mathematical simplicity the system is considered to be a two body rotating system throughout its evolutionary history of 4.5 Gyrs. This simulation draws the Moon’s spiral trajectory from its inception to any subsequent epoch. The terminal epoch is an input to the simulation software to arrive at the spiral trajectory of the Moon from the inception to the given epoch. The basic mechanics of Earth Moon System and this simulation can be generalized to lay the foundation of simulation software for any Planet Satellite pair or any Sun-Planet pair in our Solar System or Star-Planet pair in any Extra-Solar System. The basic dynamics has been found to be valid for Star Planet pair also. So this Simulation Methodology can as well be applied to study the migratory evolution of Gas Giants also.
Ishwar Bhola
Rangesh N.
Sharma Bharat K.
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