Assuming the even distribution of the Earth mass along with a space angle, we may consider
the Earth mass as concentrated into a singularity in the middle of the Earth globe, for the
investigation about the gravity over the Earth surface.
The formula, derived by Sir Isaac Newton, defining the acceleration due to gravity in the Earth globe gravitational
field is generally accepted:
(138)
In this formula, however, the change of the space and time density was not taken into account. The space and time
were considered as the homogenous quantities, not deformed by the thickening of the spacetime structure with the
decreasing radius. To speak in words of this paper, in Newton's theory it is assumed g_{zx/m}=g_{x/m}=g_{ox/m}.
In fact, the theory of the spacetime geometry presented in this work is quite new idea, and was not yet verified.
Such verification is simple in principle. It might be carried on by comparison of the contemporary time intervals
in the different orbital frames, and, by comparison of the height above Earth, measured by the mechanical
instrument, with the same height measured by light ray (or better, by means of the angular measurement as presented
in next chapter).
Anyhow, we can tell that the Newton's formula was verified in a relatively small region above Earth surface, where
the consequence of the change of the space and time densities hardly can be found out. During the space research
within last 40 - 50 years however many informations have been available, confirming inaccuracy of the Newton's
formula in higher heights.
The Z_{ct} spaceflow acceleration g_{zx/m} according to equations
(131) and (132) must be identical
with the frame intrinsic acceleration influencing an object situated in a chosen frame (at the radius
r_{lmx} = r_{lm}), but in case only, we are dealing with the frame intrinsic acceleration
acting on the object of a zero speed with respect to a chosen frame. This is because the frame intrinsic gravitational
acceleration of the object depends not only on radius, but also on object's speed (we came to conclusion in
chapter 5.1.5, that the frame intrinsic acceleration of the object approaching the speed v_{x/m}
reaches zero.)
This is why we may express the frame intrinsic gravitational acceleration of an object situated at a zero speed in the
chosen frame (this gravitational acceleration will be indicated g_{o}) by means of the equations
(131) and (132), applying the substitution
r_{lmx} = r_{lm} :
at c_{g} = const:
(138a)
at c_{g} variable:
(138b)
Since any common orbital frame may be declared as a chosen one, we are coming to conclusion that the frame intrinsic
acceleration influencing the objects, not moving with respect to the gravitational object, is defined by equations (138a)
and (138b). The speed of light dependency on radius, in equation (138b) however, evidently must be applied with
reference to the space density, since it might give the only physical reason for the change of the speed of light. It means
that, examining the gravitational field of the object different from Earth globe, the same speed of light c = 2,997924 * 10
^{8} ms^{-1} has to be expected in the orbit of the same space density as it is on Earth surface.
It will be derived in the chapter chapter 5.3.2.2 that for the Earth globe gravitational field the
equation (138a) may be applied with sufficient accuracy.
Our meters for direct measurement evidently do breathe with spacetime structure. Therefore considering the fact
that the radius of the Earth globe was determined from the Earth globe circumference length
(not by direct measurement through the globe), we may consider the radius of the Earth globe
on its equator, R_{e}=6,378x10^{6}m as a radius r_{tm}
(see equation (107a)):
(139)
Respecting that c_{g}=c on Earth surface, it must be:
(140)
The acceleration due to gravity on Earth surface is considered as verified in general:
(141)
where
M_{e}
stands for the mass of the Earth globe. It is accepted M_{e}=5,977x10^{24}
kg
stands for gravitational constant =6,673x10^{-11}m^{3}kg^{-1}
s^{-2}
Solving the equations(138a), (140) and (141), we receive:
(142)
The equations(140) and (142) show the basic parameters of the Earth gravitational field. These
parameters may be modified for practical calculations in a following way:
Respecting that:
we have:
(143)
being equal to the escape speed of the Earth gravitational field,
and, respecting that:
we have:
(144)
representing the radius considered as a radius of the Earth surface orbit.
Substituting for v_{m/x} from equation (143) and for r_{x} from equation (144) to equations (114) and
(131)
and respecting
that:
and, consequently r_{lmx}=r_{tmx}=R_{e}, we obtain
(145)
(145a)
Further, respecting the equations (108), (110),
(133), (137) and (138a),
we receive: