Static Mantle Density Distribution 2 Improved Equation and Solution

Abstract

Tian-Quan Yun

Using Archimedes Principle of Sink or Buoyancy (APSB), Newton’s universal gravity, buoyancy, lateral buoyancy, centrifugal force and Principle of Minimum Potential Energy (PMPE), this paper improves the derivation of equation of static mantle density distribution. It is a set of mutual related 2-D integral equations of Volterra/Fredholm type. Using method of matchtrying, we find the solution. Some new results are: (1) The mantle is divided into sink zone, neural zone and buoyed zone. The sink zone is located in a region with boundaries of an inclined line, angle α_0=35°15’, with apex at O(0,0) revolving around the z-axis, inside the crust involving the equator. Where no negative mass exists, while positive mass is uniformly distributed. The buoyed zone is located in the remainder part, inside the crust involving poles. Where no positive mass exists, while negative mass is uniformly distributed. The neural zone is the boundary between the buoyed and sink zones. The shape of core (in sink zone) is not a sphere. (2) The total positive mass is equal to the total negative mass. (3) The volume of BUO zone is near twice the volume of SIN zone. (4) No positive mass exists in an imagine tunnel passing through poles (the z-axis)

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