Radial and Nonradial Effects of Radial Fields in Frenet Frame

2014

ILCPA

Self Cite

Operationally complete representation of work done and the corresponding to it potential energy within the usual radial/center-bound, nonrotating gravitational force fields comprises two extra terms: linear nonradial and angular nonradial, in addition to the usual radial term. Since these nonradial terms have negative signs, they suggest presence of potentials corresponding to repulsive forces generated by the very same, usual radial attractive force field. The extra linear nonradial term depends on exposure of an orbiting satellite to the distribution of mass within the field, whereas the extra angular nonradial term also depends on that as well as on exposure of the satellite to density of matter of the mass source that generates the usual, locally dominant radial/center-bound attractive gravitational force field.

Section: International Letters Of Chemistry Physics and Astronomy Vomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Operationally Complete Work Done Suggests Presence of Extra Potentials Corresponding to Repulsive Forces

2014

ILCPA

Self Cite

“…by deciding the inner meanings of mathematical concepts and inferences by using dictionary of any language alone), because it is the synthetic matching of structures and corresponding to them operational procedures that permits drawing valid conceptual inferences. To draw conclusion that radial force fields cannot have any nonradial interactions may sound good from a purely linguistic standpoint, yet mathematically it is not only possible but in fact, it is unavoidable in general [9].…”

Section: Equalized Mass Marks the End Of Natural Philosophymentioning

confidence: 99%

“…Yet the operationally wrong and conceptually faulty formula (2) is used in all textbooks and lectures [4] despite the fact that -according to ingenious Frenet-Serret (FS) formulas of differential geometry -the formerly omitted nonradial term rdF is unavoidable in general [9].…”

Section: Recapitulation Of Misdefined Potential Energymentioning

confidence: 99%

“…Since the necessity to take density of matter into account has been confirmed by experiments [2], [3] as well as by purely mathematical analyses of gravitational interactions [9], [8], it may be beneficial to briefly highlight some problems created by ignoring the Newton's ingenious definition and then concisely recapitulate the developments that actually resolved those problems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

With Equalized Mass, its Density of Matter can Affect Radial Gravitational Interactions TOO

2015

ILCPA

Self Cite

It is shown that if all stars and planets were made out of the same material substance, such as water, for example, then their density of matter, which is conventionally defined as the ratio of their actual mass to an equivalent mass of water, must be taken into account also in the usual radial Newtonian law of gravitation. The idea of equalized mass supports the concept of quantity of matter involving density of matter as well as the bulk/mass that Newton envisaged. It has been proved necessary to explain formerly unexplained experimental results, including discrepancies between predictions based on general theory of relativity (GTR) and actually recorded data. The equalized mass is not meant to turn us back and embrace post-Newtonian theories of gravitation, but to complement the (radial-only by design) GTR for the phenomena that are only partly radial and partly nonradial. A certain new pull-and-twist equation of orbital gravitational interactions is proposed.

Mathematical Expansion of Special Theory of Relativity Onto Accelerations

2021

JFMA

Self Cite

The special theory of relativity (STR) is operationally expanded onto orthogonal accelerations: normal and binormal that complement the instantaneous tangential speed and thus can be structurally extended into operationally complete 4D spacetime without defying the STR. Thus the former classic Lorentz factor, which defines proper time differential can be expanded onto within a trihedron moving in the Frenet frame (T,N,B). Since the tangential speed which was formerly assumed as being always constant, expands onto effective normal and binormal speeds ensuing from the normal and binormal accelerations, the expanded formula conforms to the former Lorentz factor. The obvious though previously overlooked fact that in order to change an initial speed one must apply accelerations (or decelerations, which are reverse accelerations), made the Einstein’s STR incomplete for it did not apply to nongravitational selfpropelled motion. Like a toy car lacking accelerator pedal, the STR could drive nowhere. Yet some scientists were teaching for over 115 years that the incomplete STR is just fine by pretending that gravity should take care of the absent accelerator. But gravity could not drive cars along even surface of earth. Gravity could only pull the car down along with the physics that peddled the nonsense while suppressing attempts at its rectification. The expanded formula neither defies the STR nor the general theory of relativity (GTR) which is just radial theory of gravitation. In fact, the expanded formula complements the STR and thus it supplements the GTR too. The famous Hafele-Keating experiments virtually confirmed the validity of the expanded formula proposed here.