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### 5.1.4 Transformation equations of the radia in a gravitational field.

There are three orbital frames of the gravitational field outlined in Fig11. In all three frames the same frame intrinsic radius (or, the frame intrinsic distance from the gravity centre) rlm must be measured, according to equation (107a):
Fig11
The relations between radia in a gravitational field

By the instrument not breathing with space, and calibrated :
For frame 1, we can measure radia :

• r1lmx2, defining position of the frame 2 in units of the frame 1
• r1lmxn, defining position of the frame N in units of the frame 1
For frame 2, we can measure radia :
• r2lmx1, defining position of the frame 1 in units of the frame 2
• r2lmxn, defining position of the frame N in units of the frame 2
For frame N, we can measure radia :
• rnlmx1, defining position of the frame 1 in units of the frame N
• rnlmx2, defining position of the frame 2 in units of the frame N
In accordance with equation (107a):
(117)
where
stands for the space density of the frame 2 with reference to frame 1.
Therefore:
(118)
Again, in accordance with equation (107a):
(119)
where
stands for the space density of the frame 1 with reference to frame 2.
It must be:
(120)
Substituting for the space density from equation (120) into equation (119), we receive:
(121)
And again, according to equation (107a):
(122)
It must be:
(123)
Substituting from equations (118) and (122) to equation (123), we receive:
(124)
Since acc. to equation (107a):
(125)
substituting for space density from equation (124) to equation (125) we have:
(126)

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