Application of models mathematicians used in the phenomena of the orbit

Greetings back with you this navigator @newton666, in this occasion I bring them as it is the importance of the mathematical models used by the physics to explain his phenomena as that of the orbit, as a phenomenon of displacement or of movement exercised by body celestial, as one I marry very curiously in such a way that this one demonstrates giving geometric patterns of displacement of point with appearance of a circumference up to taking the elliptical form, the above mentioned phenomenon is described as a body or object realizes a movement about other, exercising a force in an essential part gravitational. They import something that adding is that it moves of oblique form, which the curvature of the object always orbiting will fall down under this one, it is for it the application of models mathematically for the collision of the explanation of this very particular physical movement.

Animation of two objects orbiting about a common center of masses, Source of image of mastery of Wikimedia Commons, Source Own work, Author User:Zhatt.

I took the freedom of complementing the following thing for the enrichment of learning on this hackneyed lover readership.

En Newton's words: " it is necessary to compare these reasons (the mathematical models) with the phenomena, so that it appears which conditions of those it appears which of these conditions of these forces correspond to every class of attractive bodies ”. That is to say, after having a generic theory on the force and his consequence for the movement, it takes place after look which of these mathematical models it corresponds (competant) to every class of phenomenon. Isaac Newton and the reconstitution of the divine palimpsest, for Sergio Hernan Orozco Echeverri, 2009 - Page 104.

Thank you this contribution helps us to understand by means of the laws of Newton's movement and the law of the universal gravitation, it is he allows us to calculate the movement of such a way as this phenomenon, influences two bodies his gravity state and to see how his orbit is with his behavior, of such a way it is considered that the sum of the forces will be equal to the mass for his acceleration; the gravity is proportional to the product of the masses and inversely proportionally to the square of the distance.

it are remembered that at first I commented on him as the movement of in circulation of an orbit it can depart from a geometric circular pattern up to behaving in the elliptical one, that owes for orbital speed and his magnitude of the speed, which can be is constant in the whole orbit of a circular way, represented with the following mathematical model:


Where v or r b is the orbital speed, G the gravitational constant, M the mass of the attractive body and r the radio of the orbit. An important fact that must to itself be known that the mass of the body does not affect in the speed exercised in this one.

For the case wherefrom a movement of elliptical behavior gives itself the speed according to the radiovector r, new paragraph that where a point in A initial, major semiaxis of the ellipse.

Another approach of analysis inside this one answered of es the change of the weight and of the depth documented of the following way:

En a deep mine the weight of a body than in the terrestrial surface, in effect: we have demonstrated that the intensity of the gravitational field in any interior point to a sphere, is equal to the produced one only for the material sphere of radio r and mass M. if ρ there is the average thickness of such a material sphere, the weight of a body of mass a m inside the mine (doing without the influences of the rotation of the Earth and without the diverse thickness of the subsoil), it is:

But being, we obtain

General physics for Santiago Burbano de Ercilla, Carlos Gracia Muñoz, page 248.

Author of the image @newton666

Is necessary to add also that of supporting in the use of a system of coordinated, that simplified under the scheme of centre of gravity of the system in study, where in the particular thing there is described this phenomenon of movement, like one of the most renowned example is that of the planets describe elliptical orbits, where the Sun in one of his searchlights of axes. Thanks to them it is possible to represent of way of vector, to represent the position of any planet with with regard to the Sun, we realize like in the field of the physics, for to study his phenomena they formulate his theory, in the language of a mathematical model, this way to describe every variable in study in this case of the phenomenon of the orbit of a dynamic way, which helps us to understand why the planets move about his orbit, during a fixed, definite quantity of time of ingenious line from the Sun, where geometrically it is possible to show a constant area of the orbital plane.

Types of terrestrial orbits, Source of image of mastery of Wikimedia Commons, principal Description terrestrial orbits used by the artificial satellites, Dates: 8 January 2016, Source Own work, Author: C records

One of the worries to the moment to construct a mathematical model in the orbital plane, is the elliptical movement she adds to herself that other variables of behavior of contingencies should be defined by you in perturbations, which demonstrates for the gravitational influence of other bodies that are in that one the orbital navigation. Of this worry it was a big contribution to add content of support in the theory of the general relativity, where relativista shows us the systematical way in the gravitational scheme, serving to focus better the study of a mass in the space forming curve joining the space and time, also it is important to mention it keeps on being geometrically a scheme Euclídea, reknowledge documented by the observation in the solar system, the consistency of the masses and speeds of the bodies take values determined in a geometric way of geodesic curves considered in the curve of the space and time, it is for it that Einstein prepared a mathematical general model to tackle his theory with most of the gravitational behavior and his effect on the orbital movement in the space and the time in the body that they take part in this phenomenon.

Hope that it should be of his taste and of big educational and informative contribution, on the mathematics, the physics of our environment and his universe.

Bibliographical References

Isaac Newton and the reconstitution of the divine palimpsest, for Sergio Hernan Orozco Echeverri, 2009 - Page 104.

general Physics for Santiago Burbano de Ercilla, Carlos Gracia Muñoz, page 248.