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#### 5.3.3.7 Orbital trajectories round the characteristic radius of gravitational field

As it was derived, while at radia greater than the characteristic radius rx the free motion of an object in a gravitational field is defined by equations (225).....(229), at radia less than the radius rx, the free motion is governed by equations (225a).....(229a). The parameters and appearance of the trajectories are considerably influenced by this fact, especially due to different distribution of the space density in that two cases.
On Fig13e-1 we can see four trajectories, all starting at the same aphelion rk=4*108 m (below radius rx), with the different excentricities, reaching down to the radius rf=1,1837*107 m (that is, below rx). It is to be pointed that such motion would be realistic only provided that the mass of the Sun was compressed into the volume of sphere of the radius less than rf. The actual radius of the Sun is 6,959*108 m.

Fig13e-1

Trajectory
e=0,0976
Trajectory
e=0,4192

Parameters
rk=4*108 m
vook=5,5*105 m/sec
rf=3,288599*108 m
e=0,0976
To=3,790650*103 secs

Parameters
rk=4*108 m
vook=4,5*105 m/sec
rf=1,636793*108 m
e=0,4192
To=2,606312*103 secs

Trajectory
e=0,7565
Trajectory
e=0,975952

Parameters
rk=4*108 m
vook=3*105 m/sec
rf=5,544063*107 m
e=0,7565
To=2,069060*103 secs

Parameters
rk=4*108 m
vook=1,5*104 m/sec
rf=1,183759*107 m
e=0,9425
To=2,080688*103 secs

On Fig13e-2 we can see two trajectories, both starting at the same aphelion rk=1*109 m (over radius rx), with the different excentricities, reaching down to the radius rf=3,94444*107 m (that is below rx). It is to be pointed that such motion would be realistic only provided that the mass of the Sun was compressed into the volume of sphere of the radius less than rf.

Fig13e-2

Trajectory
e=0,5491
Trajectory
e=0,9241

Parameters
rk=1*109 m
vook=3*105 m/sec
rf=2,910727*108 m
e=0,5491
To=8,010336*103 secs

Parameters
rk=4*108 m
vook=6*104 m/sec
rf=3,944432*107 m
e=0,9241
To=4,918258*103 secs