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Plane Geometry Description of Mechanical Energy Curves

Alexander Garron
Organization: Sand Box Geometry

Wolfram Technology Conference 2013
Conference location

Champaign, Illinois, USA

Galileo, born 7 years before and dying 12 years after Kepler, was well aware of Keplerís solution concerning complexity about orbit parameters of our sister planet Mars. He refuted till his death, Keplerian elliptical planetary motion as much too complicated. Though a heliocentric advocate as was Kepler, he held that natural curves of an orbit must be circular. This paper explores Galileoís concept of circular heliocentric planetary motion. I develop a standard model means to build a CURVED SPACE DIVISION ASSEMBLY (CSDA) using two plane geometry curves, a unit circle and its construct unit parabola, creating a plane geometry function needed to measure g-field energy curves. It turns out that g-field inverse square energy curves are spherical, can be constructed using NASA sourced observation parameters, build a standard model space and time square, once constructed provide analytics for orbit momentum around our sun and across the g-field time curve, all within reach of STEM HS math. CSDA analytics require Mathematica utility to find slope of orbit energy tangents as means to measure changing orbit kinetic energy. Linear slope and metered time curves have always been used in HS physics to determine instantaneous velocity (momentum). It turns out Galileo is also correct. Both curves, his circles and Keplerís ellipse, can be used to explain orbit mechanics.

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