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### (Gravitational acceleration)

Standing (means: not moving with respect to a singularity point) in a common distance rlmx from a singularity, we can detect, in our own frame, that the spacetime structure is falling into a singularity at a speed vx/m (frame intrinsic spaceflow speed), and is beeing just accelerated at an acceleration g (frame intrinsic acceleration of the spaceflow speed).

Again, standing in a common frame (in a distance rlmx from singularity), and observing the spacetime structure flowing through our own frame, we could detect (if, for example, the quantum of the spacetime structure was dyed) by the length instrument calibrated on our frame (frame of the observer), and the clock calibrated on the chosen frame (frame corresponding to the distance rlm from the singularity point), that the spacetime structure is falling into a singularity at a speed vzx/m, following the equation (114),or, (115) different than the frame intrinsic speed according to equation (110). This speed may be considered as a real con-spacetime speed of the spacetime structure through a common orbital frame (in its own units), respecting changes of the space and time densities relating to a chosen reference frame.

The acceleration of the motion of the spacetime structure in frames of the Zct zone (contemporary with the chosen frame) may be defined as a derivation of the speed vzx/m by time of the chosen frame:
(127)

where
gzx/m
stands for the Zct spaceflow acceleration.
The speed vzx/m is defined by equation (114). To calculate the derivation dvzx/m/drlmx, however, we would have to know the derivation of the speed of light , cg, by the radius. For the time being we do not know it.
The derivation dvzx/m/drlmx can be resolved in a following way:
• in case of a constant speed of light cg:
(128)
• in case the speed of light cg varies along with a radius (space density):
(129)
The derivation drlmx/dto may be expressed:
(130)

Solving the equations (114), (127), (128), (129) and (130), we have:
in case of a constant speed of light cg:
(131)
in case the speed of light cg varies along with a radius (space density):
(132)
The three spaceflow speeds we have been dealing with in chapter 5.1.3, may be expressed as the speed of the space flow that has passed the same distance lm expressed in the same frame intrinsic units, within the same frame intrinsic time interval tm, but expressed as:
galilean projection of the time interval tm into Zct frame, giving time interval

for the speed vzx/m,
frame intrinsic time interval
tm
for the speed vx/m,
galilean projection of the time interval tm into Zcr frame, giving time interval

for the speed vox/m
That is,
(133)

In a similar way as the acceleration gzx/m was defined, we may define:
• gx/m
as the frame M intrinsic spaceflow acceleration, and,
• gox/m
as the Zcr spaceflow acceleration (the acceleration of the space flow, expressed in length and time units of a chosen frame).
We came to conclusion, in chapter 5.1.1, that the speed vm/x does not change with the radius. Respecting the equation (110), we can say, that
• the frame M intrinsic space flow gravitational acceleration in case of a constant speed of light will be:
(133a)
• the frame M intrinsic space flow gravitational acceleration, in case the speed of light varies with the radius,
will depend on the derivation dcg/drlmx
According to equations (133) and (107) we have
(134)

Respecting the definition formula of the Zcr spaceflow acceleration,
(135)

and the derivation (from equation (134))
(136)

we receive, by substitution from eq. (134) and (136) to equation (135), the equation defining the Zcr spaceflow acceleration:
(137)

Summarizing the results of the chapter, we can say:
1. Measuring the acceleration of the space flow by means of the meter calibrated on the spacetime structure belonging to a respective point (radius), and by means of the clock calibrated on a spacetime structure of the chosen frame (like of the frame on Earth surface), we obtain the results corresponding to equation (131) or (132). This acceleration acts in direction of the space flow (accelerating it).
2. Measuring the acceleration of the space flow by means of both, the meter and clock, calibrated on spacetime structure belonging to a respective point (radius), we would come to conclusion, that the space flow moves without acceleration, or, with acceleration (if any) due to change of the speed of light with the radius.
Note: The spaceflow acceleration due to change of the speed of light might become significant in gravitational fields of the big cosmic bodies (like stars) or in gravitational fields of the bodies of a very high mass density (like nucleons).
3. Measuring the acceleration of the space flow by means both meter and clock calibrated on the chosen frame, we would find out that the acceleration is constant (acc. to equation (137)), but acting in opposite to the direction of the space flow (slowing down the spaceflow speed).
Note: The acceleration of the body moving in gravitational field will be described in subsequent chapters.
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