5.3.5.2 Mass distribution of gravitational object created of several layers
of different frame intrinsic mass density.

In a common case let us have the gravitational object formed of the following layers of the frame intrinsic mass density :

1

on its surface, between radia R_{o} - R_{1}

2

between radia R_{1} - R_{2}

3

between radia R_{2} - R_{3}

n

between radia R_{(n-1)} - R_{n}

Fig28

Gravitational object formed of 3 layers of different frame intrinsic
mass density.

In this common case the differential equation (523) must be solved for the different
boundary condition in each layer :

1st layer

(534)

Solution for R_{1} < r_{lmx}
< R_{o}

(535)

where

(536)

Applying the equation (535) we can derive :

The space density:

(535a)

The average mass density:

(535b)

2nd layer

(537)

Solution for R_{2} < r_{lmx}
< R_{1}

(538)

where

(539)

Applying the equation (538) we can derive :

The space density:

(538a)

The average mass density:

(538b)

3rd layer

(540)

Solution for R_{3} < r_{lmx}
< R_{2}

(541)

where

(542)

Applying the equation (541) we can derive :

The space density:

(541a)

The average mass density:

(541b)

n-th layer

(543)

Solution for R_{n} < r_{lmx}< R_{(n-1)}

(544)

where

(545)

Applying the equation (544) we can derive :

The space density:

(544a)

The average mass density:

(544b)

The example

To calculate the mass distribution and related parameters under Earth surface, on condition that its outer radius
R_{o} = 6,378*10^{6} m, its total mass
M_{o} = 5,977*10^{24} kg, and, that the mass is created of the following 3 layers : 1st layer
Radia : R_{o} = 6,378*10^{6} m, R_{1} = 6,377*10^{6} m
Frame intrinsic mass density: 1000 kg/m^{3} 2nd layer
Radia : R_{1} = 6,377*10^{6} m, R_{2} = 6,378*10^{3} m
Frame intrinsic mass density: 2700 kg/m^{3} 3rd layer
Radia : R_{2} = 6,377*10^{3} m, R_{3} = 0 m
Frame intrinsic mass density: 7870 kg/m^{3}

Solution
Applying the derived equations, the mass distribution, the space density, and the average mass density under radius
were calculated in each layer : 1st layer (See Fig29)

Fig29

Mass distribution, space density and average mass density under radius
in 1st layer

2nd layer (See Fig30)

Fig30

Mass distribution, space density and average mass density under radius
in 2nd layer

3rd layer (See Fig31)

Fig31

Mass distribution, space density and average mass density under radius
in 3rd layer

We can see from Fig29, Fig30 and Fig31, that the space density is increasing with the decreasing radius in the upper two
layers (1st and 2nd layer), causing, that, in spite of fact that the frame intrinsic density in upper two layers is much less
than in the 3rd (inner) layer, the most of the Earth mass is situated in upper two layers. In the 3rd layer the space density
becomes decreasing with decreasing radius. At the radius approaching to zero, the space density is comming to zero as
well.

Note
At this low space density must exist the radius r_{lmx} = R_{cr}, representing the radius
of one spacetime cell (much bigger than the cell on Earth surface, when measured in units of the Earth surface frame).
Summarizing the mass between radia
R_{o} and R_{cr}, we have to come to conclusion, that the summarized mass
M_{s} is less than the total mass M_{t} of the gravitational object.
Under these circumstances we would have to admit,
that the mass amount of M_{t} - M_{s} must be situated in
this very last spacetime cell, or, more likely, in a different zone of the spacetime
continuum, spreading from the centre of gravity out to infinity. To determine the radius R_{cr}
(of course it must be very small with respect to R_{o}, and depending on the frame intrinsic mass
density), however, we should have to know the frame intrinsic radius of the spacetime cell.

The average mass density under radius reaches its maximum 2,087*10^{8} kg/m^{3} at the radius
R_{2} (on spherical area between the 2nd and 3rd layers). This very high mass concentration arises both due to
high frame intrinsic mass density and high space density.