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## 5.3 Gravity of a common cosmic object

### 5.3.1 Gravity at zero speed above the surface of a common cosmic object

In the chapter 4.9 we found quantity of a mass to be proportional to a spaceflow quantity. Therefore the equation (101) may be modified:
(162)

where
K
is constant, and,
m
stays for mass of the gravitational object
Applying equation (138b) at rlmx=rlm, we can derive:
(163)

It will be shown later, that, except of the case when vm/x approaches very closely the speed of light (in the orbital frame of the space density = 1), the equation (163)may be used in form:
(163a)

This is why (see also equations (138a) and (146b) ) we may write:
(164)

Applying equations (162) and (164) we can derive:

(165)

Since K is constant, the ratio rx/vm/x must be constant as well. Applying equations (142) and (144), we receive:
(166)

(167)

where Tg
stands for the time constant of a gravitational field. This constant must be considered as an universal constant not dependent neither on a mass, nor on a spacetime density of a spacetime structure surrounding mass. Physically may be interpreted as a time interval, the any orbit of the spacetime structure would take to meet singularity point, provided that the respective orbital spacetime density remained the same on its way to a singularity.
Applying equations (165) and (166) the equation (162) may be rewriten to an universal form:
(168)

Solving the equations (166) and (168), we obtain:
(169)

(170)

Remark:
Generalizing the equation (162), we may write:

Applying equations (165), (166) and (167) we can calculate the proportionality factor between mass and the flow of the space falling into it:

The validity of equations (169) and (170) is usually restricted on a relatively small region around a cosmic object. This is because the spacetime density in a system to which a cosmic object belongs is determined by a dominant cosmic object of the system, as it is Sun in the solar system.

The equations defining the spaceflow speed and its acceleration above the surface of a common gravitational object, can be derived by substitution of the basic gravitational parameters:
rx from equation (169), and
vm/x from equation (170),
to equations (114), (108) (131), (132), (137), (138a), and (138b) .

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