SITE HOME HOME PREVIOUS NEXT

### 5.2.2 Measurement of the radia above Earth globe surface

Situated in any orbital spherical area in a gravitational field, we may define our position:
1. By means of a radius rtmx, corresponding to an orbital space density in a direction perpendicular to a spaceflow speed, with reference to a chosen orbit. Radius rtmx of the same orbit reaches different value, depending on a chosen orbit in which the radius is measured (see chapter 5.1.4). The size of an orbital spherical area (in units of a chosen reference orbit) may be calculated:
(149)

The radius may be measured by means of an instrument not breathing with space.

We can hardly measure radius rtmx by direct measurement, except of its value rtmx=Re on earth surface. Since the speed vm/x have been found many times smaller than the speed of light, we may consider the equation rtmx=rlmx=Re as sufficiently accurate on earth surface, and, equation rtmx=rlmx as sufficiently accurate for orbits above earth surface.

2. By means of a radius rlmx, corresponding to an orbital space density in a line of a spaceflow speed, with reference to a chosen orbit. This radius stands for the distance between singularity point and respective orbit, expressed in units of a chosen orbit, and reaches different value, depending on a chosen orbit in which it is measured (see chapter 5.1.4). It could be measured in a corridor only, made through the Earth globe, in which the same space density had been created as it is a longitudinal space density in a respective orbit.

We can measure the radius rlmx by the same way as the distance between Earth and its Moon had been measured, and brought Sir Isaac Newton to a diccovery of the law of universal gravitation, which conforms with equation (130) for the earth gravitation. See Fig.11.

Fig.11 Measurement of the radius rlmx

Knowing the radiusRe, distance AB, and angle alpha, we can simply calculate the distance CD and the radius rlmx.

Despite we provide measurement with instruments breathing with space, we measure the distance AB with a very high accuracy, because it practically lays in a spacetime structure and the same space density as which our instrument is calibrated for.

Also the angle alpha is measured with sufficient accuracy, considering that our speed vm/x is very small with respect to speed of light.
3. By means of a frame intrinsic radius rtm. This radius is measured (and calculated) by means of measuring of the length of line of an orbit circumference, by an instrument breathing with space. The size of an orbital area (in scale of the orbit own space density) may be calculated:
(150)

Any our orbital spherical area is constantly passed through, by X-frame spacetime structure, falling into a singularity. The observer from X-frame, just passing our orbital area, detects that M-frame is moving in opposite direction at a speed vm/x. The relativistic spacetime density in a direction perpendicular to the spaceflow speed is determined by equation (105). Therefore the galilean projection of the radius rx into our orbital frame will be:
(151)

Taking into consideration very low ratio vm/x/cg, we may write for the space above earth surface:
(152)
4. By means of a radius rlm measured by an instrument not breathing with space, in a line of a spaceflow speed. This radius stands for the distance between singularity point and respective orbit, expressed in units of an orbit itself.

The relativistic density in a line of a spaceflow speed is determined by equation (105). We can derive in a similar way as in c), that:

(153)

and, for earth gravitational field:
(154)
5. By means of a frame intrinsic radius Rlm, standing for the distance between singularity point and respective orbit, measured by the instrument calibrated in the chosen frame, but breathing with the spacetime structure in all points of the radius line. See Fig.12.

Fig.12 The example of a spacetime structure of which radius Rlm consists
The structure of the radius Rlm is shown exaggerating the principle of the matter. In fact, the size of the spacetime structure packet is innumerably times lower with respect to the radius. This size is constant, of course, if measured by an instrument breathing with space. In accordance with equation (153) it may be expressed as:
(155)

Note: The equation (155) says, that, if an increment's length of the rlmx (representing certain number of the spacetime packets) is measured, by the ruler, in the chosen frame, and then, the same number of the spacetime packets, in the same line, is measured in a common orbit by the same ruler, it will show the same increment's length.

But, creating radius Rlm, every spacetime packet must contribute to the radius by the same percentage of its magnitude. It means, the contribution of the packet from any orbit to the radius Rlm must be understood as a galilean projection of a packet's size into M-frame of a chosen orbit. Therefore:
(156)

where
stands for the total space density in a spaceflow line (having its origin both in relativistic and geometric reasons) in a respective orbit,
stands for the total space density in a spaceflow line in a chosen orbit.
The total space densities may be derived from equations (105) and (107):
(157)

(158)

These space densities may be applied in case only, if all mass of which gravitational field we are examining, is concentrated in a singularity. In case we were searching for a radius in a gravitational field of a cosmic object of a real size, like Earth, we should have to take into consideration, that the basic parameters of a gravitational field, rx and vm/x are decreasing under cosmic body surface along with decreasing mass into which the spaceflow structure flows.
Substituting for the total space densities from equations (157) and (158) to equation (156), we receive:
(159)

Taking delta increments as differentials, and, assuming the constant speed of light, or, restricting the validity of the equation on the interval of a constant speed of light, we obtain by integration of equation (159):
(160)

where
Llm
stands for the distance between the radia rlmxk and rlmx, measured by means of a measuring tape, that was calibrated inside of the chosen frame (that is, in the horizontal direction on the chosen orbit).
rlmxk
stands for the lower limit of the measured interval
Taking into consideration the influence of the prospective change of the speed of light, we would have to solve the integral:
(160a)

Trying to find out the height Llmx above the Earth surface (rlmxk= rlm=rx), we usually measure it by the method described on (Fig 11). By this method we receive the difference between radius rlmx and radius rlm=rx on Earth surface:
Llmx=rlmx-rlm

In case, however, if measuring tape was used, calibrated in a horizontal position on Earth surface, and then one its end was taken up to a height Llmx, we could read on its scale, just reaching the Earth surface, the value of the height Llm. Above Earth surface (in general, at rlmx > rlm) it must be :

(161)

The equation (161) gives the following results for rlm= Re=6,378 * 106 m:

Llmx(m) 103 105 106 2*106 4*106 6*106 8*106 1*107 5*107 1*108
Llm(m) 9992,2 99224 928943 1739629 3105025 4229036 5184323 6014992 13899093 17948612
Llmx/Llm 1,00078 1,00782 1,07649 1,14967 1,28823 1,41876 1,54311 1,662513 3,59736 5,57146

SITE HOME HOME PREVIOUS NEXT