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#### Basic parameters of the sun's gravitational field

The basic parameters of the Sun's gravitational field, namely its frame intrinsic radius and space-flow speed, not influenced by the relativistic relationships, should be calculated fro the equations (169) and (170). Using these equations we have :
(253)

(254)

where
r 'x
stands for the frame intrinsic radius of the Sun's gravitational field, not influenced by relativistic relationships,
v 'm/x
stands for the frame intrinsic space-flow speed of the Sun's gravitational field, not influenced by relativistic relationships,
stands for gravitational constant = 6,673x10-11m3kg-1 s-2 ,
T 'g
stands for the time constant of the Sun's gravitational field, not influenced by relativistic relationships = 570,48 seconds and,
m
stands for the mass of the Sun = 1,989*1030 kilograms
The relativistic behaviour of the space-flow mechanism, creating gravitational field, results in a slight modification of the basic parameters, that could be neglected in common calculations, but not in the precise calculations. This "relativistic modification" is defined by means of the factor p, by the equations (237), (244) and (246). Since the factor p varies with the radius, it must be determined for each orbital zone (e.g. for the mean radius of the planet's trajectory) separately. See Tab13b-1.
Tab13b-1
Planet Mean radius (m) p rx (m) vm/x (m/sec)
Mercury 5,897000E+10 0,999104 4,423318E+08 7,746738E+05
Venus 1,082070E+11 0,999339 4,422626E+08 7,747343E+05
Earth 1,496000E+11 0,999437 4,422335E+08 7,747599E+05
Mars 2,286600E+11 0,999545 4,422019E+08 7,747876E+05
Jupiter 7,787600E+11 0,999753 4,421404E+08 7,748414E+05
Saturn 1,429000E+12 0,999818 4,421214E+08 7,748581E+05
Uranus 2,872000E+12 0,999872 4,421056E+08 7,748719E+05
Neptune 4,497600E+12 0,999897 4,420980E+08 7,748786E+05
Pluto 6,045000E+12 0,999911 4,420939E+08 7,748822E+05
Comet Halley 1,005740E+13 0,999931 4,420880E+08 7,748873E+05

#### Calculation example for the planet Mercury

Given parameters
The initial radius at which the planet Mercury reaches the upper culminating point (Aphelion)
rk=7,1740*1010m
The initial Zcr vertical speed (Zcr ... in units of the chosen frame)
vol=0
The initial Zcr orbital speed (Zcr ... in units of the chosen frame)
vook=3,37220*104m/sec
Calculated parameters
Substituting for rx, vm/x, rk and vook to equation (227), we can calculate the initial Zct orbital speed (Zct ... length units in the frame at the radius at which Mercury occurs, time units in the chosen reference frame)
vzok= 3,806988*104
Substituting for rx, vm/x, rk and vzok to equation (216), we can calculate the final radius rf at which planet Mercury reaches the lower culminating point (Perihelion)
(255)

Since rk > rf, the radius rk represents aphelion (determining the greatest distance from the Sun) and, the radius rf represents perihelion (determining the minimal distance from the Sun).
Applying equation (216a) we receive for the excentricity of the Mercury's trajectory :
(256)

The apparent space density.
Applying the equation (224-1) we can calculate the apparent space density in the range of radia between rk and rf. See Fig16.

Since the gravitational space density rx/rlmx in range of radia rk - rf reaches values 6,1680*10-3 - 9,5758*10-3 (rx/rk - rx/rf), that is smaller than the apparent space density, the condition (224b) is fulfilled. Therefore the apparent density as shown on Fig16 stays valid all over the Mercury's trajectory.
The orbital Zct speed (the speed expressed in length units of the frame of the radius at which Mercury takes place and in time units of the chosen frame)
Applying equation (210) we can calculate the Zct orbital speed vzo for the range of radia rk - rf. See Fig16a.
The space deformation density.
Applying the equation (248), we can determine the space deformation density in range of radia rk - rf. See Fig16b.
The Zcr orbital speed (that is, orbital speed in length and time units of a chosen frame) in a deformed spacetime structure.
The Zcr orbital speed in a deformed spacetime structure is defined by the equation (249). The curve of Zcr, orbital speed (vood) vs radius, in the range of radia rk - rf, is shown on Fig16a.
The angle speed in a deformed spacetime structure is defined by the equation (250a). The curve angle speed vs radius, in the range of radia rk - rf, is shown on Fig16c.
The vertical Zct vzl speed (that is, the speed expressed in length units of the frame of the radius at which Mercury takes place and in time units of the chosen frame), on condition that the initial speed vzlk=0, according to the equation (213), is shown on Fig16d in the range of radia rk - rf.
The vertical Zcr speed vol
The vertical Zcr speed vol (that is, orbital speed in length and time units of a chosen frame) according to the equation (229), is shown on Fig16d in the range of radia rk - rf.
Time interval Tod of motion from the aphelion rk to the perihelion rf
Since the integral

is very complicated, it was calculated by the numerical method :
Tod=3,80125*106 seconds
The angle , the radius Sun - Mercury carries out during motion from the aphelion rk to the perihelion rf.
Since the integral

is very complicated, it was calculated by the numerical method :
Calculation of the parameters of Mercuru's trajectory for the motion from perihelion to aphelion
For the upward motion of the planet Mercury, from the perihelion to the aphelion, the initial Zcr orbital speed vook in non deformed spacetime structure shall be calculated from the parameters of downward motion, as the speed voo according to the equation (226) at the perihelion :
The radius rf from the calculation of the downward motion shall be now declared as the initial radius - rk.
rk=4,619260*1010 m
Applying the equation (227) we receive
vzok=5,912491*104 m/sec
Applying the equation (216) we receive
rf=7,1740*1010 m
All other parameters as calculated fot the downward motion will become identical with those fot the upward motion, including:
- The time interval Tou of the motion from the perihelion to the aphelion,
Tou=3,801025*106 sec
- The angle , the radius Sun - Mercury carries out during motion from the perihelion rk to the aphelion rf,
Siderical period of Mercury (period of rotation)
(257)
The advance of culminating points (perihelion or aphelion advance) within one revolution
(258)
The advance of culminating points (perihelion or aphelion advance) within 100 years
(258a)
The trajectory of the planet Mercury

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