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Dec 01, 2023Open Access
Up to now, there is a long time problem that dot product has no corresponding division. In order to solve this problem, in this paper, indefinite dot quotients are introduced as extensive inverse operations of dot products, which solve the problem in 3dimensional space that the quotient of a number and a vector on dot product does not exist from another angle. Some basic properties, and some expected operation properties, and two forms of geometric expressions and six coordinate formulas of ind...
Mar 01, 2023Open Access
It has to be noted that Albert Einstein used the extremal property of geodesic line when developing the general theory of relativity (GTR). In the following years, after the development of the GTR, it became known that the expression for a geodesic line can be replaced by the EulerLagrange equation. In the present work, the extremal property of the separatrix of a mathematical pendulum is used to develop a new approach to the general theory of relativity. The pendulum separatrix satisfies the E...
Nov 30, 2022Open Access
In this paper, in order to solve the problem that cross product has no corresponding division in natural space, indefinite cross divisions are firstly introduced as the inverse operations of cross products, which solve the problem from another angle. Then a lot of basic properties of indefinite cross divisions are obtained, such as the Conversion Formulas between left and right indefinite cross quotients, and linear operation properties, where some are expected and some are special. Especially, ...
Oct 21, 2021Open Access
This paper introduces a new way to calculate gravity force from mass total energy, instead of from matter of mass. By introducing total energy (E1 and E2) of the two objects into Newton’s gravitational theory, Newton’s gravitational formula can be modified from F = GM _{1}M _{2}/r ^{2} as F = GE _{1}E _{2}/(C ^{4}r ^{2}). E _{1} and E _{2} are the total energy of the two objects and C is the light speed. Then this formula can be furt...
Jan 22, 2021Open Access
To transfer a satellite or a spacecraft from a low parking orbit to another orbit requires one of the many orbital transfers. These orbital transfers need to determine some orbital elements of the initial and final orbits as perigee and apogee distances. The transfers compete to achieve the transition with minimal consumption of energy, transfer time, as well as the highest accuracy of transition. In the present research, certain mathematical procedures implementable with the help of computers w...
Sep 29, 2018Open Access
A snapshot of the circular speed as a function of the radius in a spinninghomogeneous spherical universe was obtained using a massdependent characteristicacceleration in the Modified Newtonian Dynamics (MOND paradigm as a modified 2nd law of Newton) with and without considering the impact of the relativistic speed. To consider the impact of the relativistic speed the Extended Newtonian Theory (E ...
Dec 19, 2017Open Access
Intuition of many
different unsolved problems and questions remains the “sorest troubles” in
basis and applied sciences particular in physics today. Also presented physical
models doesn’t describe world’s
framework aright and these make lots of defects to understand sciences and
solve scientific problems. Therewith no one can formulate the complicate relation(s)
between all existences’ and sciences’ components. However, ...
Nov 14, 2017Open Access
The topic undertaken in this paper (and probably in some other papers if required for possible future debates) is multibranched and with various interrelations. It is concerned with the identification and correction of miscellaneous misinterpreted concepts, and with what may appear as some embezzling phenomena, in classical and relativistic mechanics. These include revising the concepts of the indepen ...
Aug 11, 2017Open Access
In this paper it is proposed that the mass of the bodies has its origin and nature in the reciprocal gravitational interactions between them; and also by some kind of effect over the size of the celestial bodies due to the very big distances in space, as seemed each other at a distance. In a Dynamic Theory of Gravitation [1], it is proved that the fundamental velocity is the escape velocity due to the apparent size of the interact ...
May 17, 2017Open Access
In this paper, it is proposed that the size of the classical
electron, which is a stable elemental particle with the smallest concentration
of matter in Nature, can be used to
explain the very big size of the Universe.
In order to reach that objective, the ...
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