4. UNIVERSAL POTENTIAL ENERGY of REPULSING

 

This book is saturated with criticism of known physical notions and theories. Specially it concerns to a modern physics. But it is more logical to a critic to start from classic notions.

At even and rectilinear motion of a body with speed V its kinetic energy is peer:

 W_k = mV²/2 (1).

That the body has the indicated energy, instead of any another is easy for testing by experiment. Let body will get in the calorimeter (device for measurement of a quantity of heat) and we shall determine, that at a stop of a body the allocated thermal energy in accuracy is peer to former kinetic energy on an equation (1), instead of to what to another.

Let's consider rotation of a body on a circumference of radius r with speed V. Apparently, that the energy of this body too will be determined by expression (1). It is easy for testing by cutting off a thread, which one retains a body on a circumference. The body will become to move uniformly and rectilinearly with the same speed V, т.е will gain kinetic energy W_k. We link to kinetic energy capacity of a body unrestrictedly to leave from view point. But the body, rotated on a circumference, does not leave anywhere and remains on same spacing interval from center of rotation, i.e. fixed concerning this center. This property of potential energy of a body: to have capacity to be turn intoed kinetic energy, stay put. Is linkable a body with center of rotation by a rod on which one a body can be displaced in a radial direction. To move up it to center, it is necessary to expend energy, and at deleting from center it is necessary a body to hold, since the energy is allocated. As a whole, at anyone movements and return of a body in initial point if to neglect friction, the energy of a body start initial value, that is a consequent of an energy conservation law. It too property of potential energy. If we shall raise and to lower shipment on a miscellaneous altitude, we shall come to the same conclusion. Thus, any body at motion on a curvilinear trajectory has universal potential energy of repulsing from center of curvature trajectory. For the greater clearness of this problem we shall consider motion of a space body m on an elliptical trajectory around of a central body M, which one is shown on a figure 1.

        

 

In a point 1 pericentre of orbit (if M - Sun, this point is called as a perihelion) body m has maximum speed, therefore greatest possible potential energy of universal repulsing and bound with it maximum centrifugal force. At the same time, spacing interval up to a central body in this point is minimum also customary potential energy, bound lift bodies m on a definite altitude from a central body M also is minimum. The energy conservation law requires, that the sum of universal potential energy of repulsing and customary potential energy at linear deleting of one body from another should be a constant. The zerolevel of customary potential energy can be accepted arbitrary, therefore in a point 1 it is possible to consider it to equal zero point. In a point 2 apocenter of orbit (if M - Sun, this point is called apogee of orbit) body m has minimum speed, but maxheight above a central body М. The sum of universal potential energy of repulsing and customary potential energy (attraction) will be peer to potential energy of repulsing a point 1, if in it energy of attraction conditionally we shall accept for zero point. Thus, at motion of a space body on elliptical orbit the sum of universal potential energy of repulsing and potential energy of attraction always remains to a constant. Potential energy of repulsing conditionally consider positive, and potential energy of attraction - negative. Certainly, it is conditionality, bound that these kinds of energy have opposite properties. It would be possible, on the contrary, potential energy of attraction to consider positive, but in this case there is a disadvantage at dialogue. It is possible customary table to call «object», but then it is necessary to everyone to explain, that your object is completely identical to our table. On the basis of above-stated, we can record the main equation of motion of a body on a curvilinear trajectory in a potential field (electrostatic or gravitational) for which one characteristicly, that the work of movement of a charge (electrical or gravitational) on a closed loop is peer to zero point. This equation looks like this:

E_(tie)= W_(rep) - W_(att) (2),

where E_(tie) - bond energy of two interacting bodies, W_(rep) - universal potential energy of repulsing of these bodies, and W_(att) - potential energy of attraction of bodies.

On indefinitely large spacing interval of any interplay between bodies there is no, therefore E_(tie), W_(rep) and W_(att) everyone is peer to zero point, accordingly, and their sum (total energy) also is peer to zero point. Such it also remains in any point of any trajectory on demand of an energy conservation law. Pay attention, that we here not mention at all kinetic energy of a body. It would appear from potential energy, when the body will confront with an encumbrance, but such case we here not envision.

To concretize an equation (2) for a case electrostatic or gravitational interaction, we shall decrypt in (2) values W_(rep) and W_(att).

Energy of attraction of two unlike electric charges q₁ and q₂ is determined by a Coulomb's law:

W_(att.e)=(q₁×q₂)/r (3),

where r - spacing interval between charges.

Energy of attraction between two gravitational charges (some masses m₁ and m₂) is determined by a law of universal gravitation of a Newton:

W_(att.g)=(G×m₁×m₂) /r (4),

where G - gravitational constant.

Equation (2) we shall apply to bodies of small mass driving on orbit around of massive bodies. It is most relevant in practice a case suitable for the description of an electron motion around of a nucleus or satellites around of a massive central body (of the Sun or planets). In this case it is possible to consider a central massive body fixed (though as a matter of fact both bodies are gyrated around of common center of gravity of a system), differently calculations considerably become complicated in damage to comprehension of the essence of process.

W_(rep) in considered interplays is identical (is universal) and numerically is peer to «kinetic» energy of a body on orbit:

W_(rep)=mV²/2 (5).

But we are interested by change of universal potential energy of repulsing depending on a radius of gyration, instead of speed of a body. Therefore we shall take advantage of a principle of conservation of moment of momentum:

L=mVr (6), where L=const.

Let's substitute (6) in (5) instead of V:

W_(rep)=L²/(2mr²) (7).

Now, in view of equations (7), (3) and (4), the equation (2) can be written to an obvious kind for electrostatic interplay:

E_(tie.e)=L²/(2mr²)-(q₁×q₂)/r (8)

And for a gravitational interaction:

E_(tie.g)=L²/(2mr²)-(G×M×m)/r (9).

The graph of change of bond energy of interacting (attracted) bodies is shown on a figure 2.

From equations (8) and (9) it is visible, that with decreasing of spacing interval up to a central body (arranged in a point 0) potential energy of universal repulsing are augmented more abruptly (in a denominator a square of spacing interval) than energy of attraction (in a denominator spacing interval in the first degree) therefore summary curve for bond energy will have a minimum (potential well). This condition of stable equilibrium and any elliptical orbits early or late are transformed in circumferential with radius r₀ at the expense of the gradual forfeit of exuberant energy to an equal difference between energy of repulsing and bond energy. From a figure 2 also it is possible to note, that the energy of repulsing is peer in steady position to bond energy and twice less energy of attraction (this conclusion in physics is called as a virial theorem).

At invariable mass of a body its product Vr remains to a constant (Vr=a), then (6) it is possible to copy so:

L=ma (10),

and the equations (8) and (9) will accept a kind:

E_(tie.e)=ma²/2r² - (q₁×q₂)/r (11),

E_(tie.g)=ma²/2r² - (G×M×m)/r (12).

Equations (11) and (12) is applicable for practically relevant cases: the rotation of an electron with a charge е and mass m_e around of a nucleus having the charge Z and some space body in mass m, revolving around of a central massive body M. The finding of a position of a potential well for these cases requires applying differentiation of equations (11) and (12), therefore we shall put at once end results for r₀ - spacing interval from a central body to the bottom potential wells:

r₀=(m_ea²)/(Ze²) (13) - for atom both

r₀=a²/GM (14) - for a space system.

It is understandable, that values a=Vr for an electron and space body miscellaneous.

If to substitute (13) and (14) in the applicable equations (11) and (12), we shall discover electron-binding energy with a nucleus or (for example) of Earth with the Sun:

E_(tie.e)=-(Ze²)²/(2m_ea²) (15).

E_(tie.g)=-(G²M²m)/2a² (16).

The negative values of bond energy demonstrate (conditionally) that energy, which one should be expended to eliminate a rotated body in perpetuity.

It is interesting to count up bond energy of the Earth with the Sun.

Orbital velocity of the Earth of 30 kms/sec=3×10⁶ cm/sec, spacing interval up to the Sun 1.5×10¹³ cm, therefore, a for the Earth is equal 4.5×10¹⁹ cm²/sec. Gravitational constant 6.7× 10-8 dynes×cm²×g^-2, Mass of the Sun 2×10³³ g, mass of the Earth 6×10²⁷ g. Substituting all these values in the formula (16) we shall discover bond energy: 2.7×10⁴⁰ ergs. True bond energy it is a little less, since orbit of the Earth not circumferential, and elliptical, i.e. the Earth has some exuberant energy, which one has not lost yet neck and crop.

Here it is necessary to note, that official physics does not know about existence of a potential well at electrostatic and gravitational interaction. Instead of a pit it has potential abyss and electrons should drop on a nucleus of atom, and satellites - on a central body. Why they do not drop official science explains by a rather artful way, which one here we shall not esteem, the nature is more simply, than the official scientists think of it. Here it is necessary to pay attention the reader to that circumstance, that the official scientists somehow explain any phenomena, because receive for it the salary. What price of these explanations you will understand, by reading the book. Will appear, that the majority of explanations not only is not explained observed phenomena, but also enter the reader in fallacy by different methods not compatible with the present science.

 Else about motion of a body on a circumference.

This motion is, as though, porch physics and by not understanding its essence cannot be gone into rooms.

The orthodoxes in this problem have got confused also others have complicated and prolong to create tangle in heads of millions schoolboys all over the world. Now this tangle in each head.

1. Power aspect of a problem.

At motion on a circumference on a body the attractive force to center of rotation acts and the centrifugal force of inertia acts (orthodoxes it name as dummy force to distinguish the stepdaughter from the native daughter - centripetal force). The forces these are always balanced at steady circular motion, therefore of resultant force is peer to zero point and does not cause on the second Newton's law of acceleration in a direction of operating of these forces. In a perpendicular direction the body is gone without undertaking work. The situation is completely similar to rolling of a bead on a horizontal surface. The force of weight of a bead is balanced by forces of reaction of a surface also applied to a bead, therefore in a direction of operating of these forces it is not displaced, and in a perpendicular direction moves not commit work. Let's sit on a carriage established on a girder, with center of rotation on one end. We trundles to other end with acceleration on the second Newton's law under operating of unbalanced centrifugal force yet pressed against in the limiter precluding throw off from a girder. In this position the centrifugal force is balanced by force of reaction of the limiter and any acceleration is not present. When we were freely displaced on a girder centrifugal force mV²/r caused acceleration V²/r, which one numerically coincides orthodox "centripetal" acceleration, but is directed to the counter side. On orthodox notions the attractive force acts on a body, and the "dummy" centrifugal force acts on "connection". Under operating of these unbalanced forces the body should drop to center of rotation (on their notions it and "drops"), and "connection" should fly away from center. It is interesting, if the orthodox will point site of the apposition of centrifugal force for the Earth.

2. Power aspect of a problem.

Each time cut off a thread on which one is bound a rotated body, we are convinced, that any energy is transformed into this moment in kinetic energy of a free body, and the law of conservation of angular momentum L=mVr is strictly executed, therefore body is gone on tangent to a former trajectory. As from time of creation of a world the rotated body was not moved anywhere, its energy we shall consider as universal potential energy of repulsing. In the given problem we have not dynamics, and clean statics. The force in this case is of derivative POTENTIAL energy on spacing interval. Really, by recording potential energy electrostatic or gravitational interaction of two bodies and differentiated on radius, we shall receive a Coulomb's law or law of world-wide attraction of a Newton. Let's make that most for a rotated body.

E=mV²/2, V²=L²/m²r², E=L²/mr², dE/dr=-mV²/r. We have received "law of inertia" for a rotated body.