SITE HOME HOME PREVIOUS NEXT

### 5.3.6 Gravitational acceleration inside gravitational objects

#### 5.3.6.1 Gravitational acceleration created by object itself.

In a common case, when under the radius rlmx occurs the sphere of the mass m, the average mass density may vary in large extent. Due to this fact it might also happen that the certain layer under the radius rlmx becomes "hidden", e.g. situated out of the own interface area (of course the mass particles of which the object is consisting have their own interface area, because of their high mass density). Such event arrives when the space density in the layer becomes lower than the space density of other gravitational object. We can see on Fig26 and Fig31 that inside a cosmic body such condition arises in a space close to the centre of gravity, if this space is filled by the mass of the high mass density. In such case the mass distribution in a respective layer is governed by the space density originated now by other governing object, and the gravitational acceleration in such layer has to be re-calculated from the hidden gravitational field of the respective layer to the open gravitational field of the other object, in accordance with the chapter 5.3.4.2.

The gravitational acceleration on the surface of the spherical object of mass m, under the radius rlmx inside the major gravitational object must be in conformity with the equation (182):
(545)

or, substituting for vm/x from the equation (170) :
(546)

where
gzx
stands for the Zct gravitational acceleration at the radius rlmx of the object of mass m under radius rlmx.
Applying the equations (189) and (190) at vn/mk=0 (the mass under radius rlmx does not move with respect to the centre of gravity) and at rlmxk=rlmx (since rlmxk means the radius at which vn/mk=0), we receive :
• the frame intrinsic acceleration acting at a common radius rlmx :
(547)
• and, the Zcr acceleration, acting at a common radius rlmx or, at a respective mass m :
(548)
The equations (546), (547) and (548) define the gravitational acceleration in a spaceflow line not only under the surface of the gravitational body, but also above its surface, in a space at which the frame intrinsic mass density approaches zero, however in case only,when the respective object does not move with respect to the centre of gravity. We can see that the frame intrinsic gravitational acceleration (we can measure it directly in a respective depth) is identical with the Zct gravitational acceleration, that cannot be measured directly, however it represents the important quantity for calculation of the gravitational potential and energy.

The example

SITE HOME HOME PREVIOUS NEXT