A new approach to the derivation of the law of universal gravitation from Kepler’s laws

Everyone knows that the inverse square law follows from Kepler’s third law. Let us prove more: the law of universal gravitation follows from Kepler’s third law.

MIX Reality Based Media Prototype For Learning Physics of Gravity And Kepler’s Law

Gravity and Kepler’s Laws are materials that study natural phenomena, events or phenomena that reveal all the secrets of the universe. Based on the observations of several schools, there are difficulties for students understanding gravity and Kepler’s laws because they can not directly present 3D learning media in interactive classes. This study aims to develop a mixed reality-based media prototype for learning gravity physics and Kepler’s laws using special VR box glasses and markers to display 3D objects equipped with audio explanations, 3D animations, and evaluation questions. The research was conducted using the ADDIE development model (Analyze, design, develop, implement, and evaluate). To make it easier for students to use mix reality applications, the mix reality software design employs blender version 2.78, unity 5.1, Photoshop, the vuforia AR extension for unity, and the c # programming language. The trial of the feasibility of mix reality media was conducted by averaging the results of the validator’s assessment of each aspect of the assessment. Mixed reality media prototypes can help students understand gravity and Kepler’s laws.

KEPLER – NEWTON – LEIBNIZ – HEGEL

Kepler’s Laws of planetary motion (following the Copernican revolution in cosmology), according to Leibniz and his follower Hegel, for the first-time in history discovered the keys to what Hegel called the absolute mechanics mediated by dialectical laws, which drives the celestial bodies, in opposition to finite mechanics in terrestrial Nature developed by mathematical and empirical sciences, but that are of very limited scope. Newton wrongly extended and imposed finite mechanics on the absolute mechanics of the cosmic bodies in the form of his Law of one-sided Universal Gravitational Attraction, by distorting and misrepresenting Kepler’s profound laws and in opposition to Leibniz’s more appropriate “Radial Planetary Orbital Equation”. The still-prevailing error by Newton (notwithstanding his well known manipulation of science for selfish ends), not only shows the limitation of mathematical idealism and prejudice driven modern cosmology in the form of Einstein’s theories of relativity; but also, have made gaining positive knowledge of the cosmos an impossibility and has impaired social/historical development of humanity by reinforcing decadent ruling ideas. Hegel’s Naturphilosophie is not only a protest against the misrepresentation of Kepler’s Laws in particular; his Enzyklopädie der Philosophischem Wissenschaften is the negation and the direct rebuttal of Newtonian physics and Philosophiæ Naturalis Principia Mathematica, in general. Modern natural science ignores Leibniz and Hegel at its own peril! Kepler’s phenomenological laws of planetary motion and the dialectical insights of Leibnitz and Hegel opens the way for gaining positive knowledge of the dynamics, structure and the evolution of the cosmic bodies and other cosmic phenomena; without invoking mysteries and dark/black cosmic entities, which has been the pabulum of official astrophysics and cosmology so far.

Pedal equation and Kepler kinematics

Kepler's laws is an appropriate topic which brings out the significance of pedal equation in Physics. There are several articles which obtain the Kepler's laws as a consequence of the conservation and gravitation laws. This can be shown more easily and ingeniously if one uses the pedal equation of an Ellipse. In fact the complete kinematics of a particle in a attractive central force field can be derived from one single pedal form. Though many articles use the pedal equation, only in few the classical procedure (without proof) for obtaining the pedal equation is mentioned. The reason being the classical derivations can sometimes be lengthier and also not simple. In this paper using elementary physics we derive the pedal equation for all conic sections in an unique, short and pedagogical way. Later from the dynamics of a particle in the attractive central force field we deduce the single pedal form, which elegantly describes all the possible trajectories. Also for the purpose of completion we derive the Kepler's laws.