- 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
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.
- 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
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.
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.
- By means of a frame intrinsic radius rtm. This radius is measured
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:
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:
Taking into consideration very low ratio vm/x/cg, we may write
for the space above earth surface:
- 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:
and, for earth gravitational field:
- By means of a frame intrinsic radius Rlm, standing for the distance
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
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:
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:
The total space densities may be derived from equations (105) and
- 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.
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),
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):
Taking into consideration the influence of the prospective change of the speed of light, we would have to solve
- 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).
- stands for the lower limit of the measured interval
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:
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 :
The equation (161) gives the following results for rlm=
Re=6,378 * 106 m: