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5.2 Gravity of Earth globe

5.2.1 Gravity above the earth surface

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 gzx/m =gx/m=gox/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 Zct spaceflow acceleration gzx/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 rlmx = rlm), 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 vx/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 go) by means of the equations (131) and (132), applying the substitution rlmx = rlm :

at cg = const:
(138a)

at cg 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, Re=6,378x106m as a radius rtm (see equation (107a)):

(139)

Respecting that cg=c on Earth surface, it must be:
(140)

The acceleration due to gravity on Earth surface is considered as verified in general:
(141)

where
Me
stands for the mass of the Earth globe. It is accepted Me=5,977x1024 kg
stands for gravitational constant =6,673x10-11m3kg-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 vm/x from equation (143) and for rx from equation (144) to equations (114) and (131) and respecting that:

and, consequently rlmx=rtmx=Re, we obtain
(145)
(145a)

Further, respecting the equations (108), (110), (133), (137) and (138a), we receive:
(146)
(146a)
(146b)
(147)
(147a)

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