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#### 5.3.2.3 Kinetic energy, Gravitational potential, Potential energy

Applying the equation (66), we can derive the equation defining the kinetic energy of the free object moving in a line of the spaceflow speed :
(192)

where
m
stands for the object's rest mass,
czg
stands for the speed of light in the Zct zone, and,
Wkn/m
stands for the object's kinetic energy with respect to the chosen frame.
Obviously it must be :
(193)

Further substituting from equation (193) and (184) to equation (192), we obtain :
(194)

Since
(194a)

we also have:
(194b)

and,
(194c)

Defining the boundary condition in equation (194) : vzn/mk=0 at rlmxk approaching the infinity,
we can derive from equation (194):
(195)

The equation (195) gives the kinetic energy with respect to the chosen M-frame, of the object of the rest mass m, falling from infinity, that is, of the object moving at the same speed as the speed of the falling spacetime structure (the speed of the spacetime structure is the upper limit of the speed the free object may reach, but in a sufficiently long distance from the infinity this limit may be considered to be achieved). Neglecting the relativity factors this speed (vx/m) may be determined vx/m= vm/x. Respecting the equation (186), we can see that vn/mk=+ vm/x at radius rlmxk. It means, to leave the gravitational field the object needs the same kinetic energy as defined by the equation (195). This is why we may define the gravitational potential as :
(196)

and the gravitational potential energy of the orbit rlmx2 with respect to the orbit rlmx1 as :
(197)

where
U2
stands for the gravitational potential at the radius rlmx2 and,
U1
stands for the gravitational potential at the radius rlmx1.
Thus :
(198)

The potential and potential energy calculated according to the equations (196) and (198), give results close to the results calculated in accordance with the conform physics. Unlike to the conform physics however, the difference of the kinetic energy of the object in free fall, between two orbits (rlmx2 and rlmx1) does not match the respective difference of the potential energy in general. Applying the equation (194b), we can derive :
(199)

where
Wk2-1
stands for the difference of the kinetic energy of the object in free fall, between the two orbits (rlmx2 and rlmx1), and,
vn/m1
stands for the frame intrinsic object's speed at the radius rlmx1.
The equation (199) shows that the difference of the kinetic energy depends not only on the radia of the respective orbits, but also on the initial speed vn/m1 (or, in general, vn/mk ) of the object at the initial radiusrlmx1 (or, in general, rlmxk). In case only, when vn/mk=vm/x, the difference of the kinetic energy matches with the difference of the potential energy, since in this case we have :
(200)

Analysing the equation (194b), we can derive that for the gravitational objects from nucleons to stars this equation may be simplified, with sufficient accuracy, in the following way :
(201)

We can derive from the equation (201) the difference of the kinetic energy between two orbits (the orbit at the common radius rlmx and the orbit at the radius rlmx1) :
(202)

The equation (198) may be modified in the same way as the equation (201) was derived from equation (194b) :
(203)

We can see from equation (202), that, accepting a very low inaccuracy, the difference of the kinetic energy of the free object, between two orbits, may be considered as defined by the position only of the two orbits. (The analysis shows, that this equality cannot be applied to the gravitational objects of a very high mass along with a very high mass density). The difference of the kinetic energy of the free object matches with the potential energy between the same orbits (see equation 203).
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