Gravity inside of mass

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5.3.4 Mass object in gravitationald field of another object

5.3.4.1 Interface area

If a mass object orbits around cosmic object, or anyhow is situated in its gravitational field, it has its own open gravitational field, if its specific mass is high enough, to create the gravitational space density on its surface higher than the gravitational space density of a respective position in a gravitational field of a dominant gravitational object. If its specific mass is not high enough, it is without its own open gravitational field, despite its individual parts, like atoms and nucleons, have always their own open gravitational fields (because of their very high specific mass).
Note : To explain the fact that an object does not have its own open gravitational field, we must remind that the gravitational effects of such object are manifested by means of the hidden gravitational field (that is, the gravitational field of the respective object in a space of the density defined by the dominant object). The matter will be dealt with later.
The boundary between gravitational field of the object M_l and the superior gravitational field of the object M is defined as the interface area. See Fig18.
Fig18

Fig18 shows that the open part of the gravitational field, if any, of the mass object in a gravitational field of a dominant gravitational object is enclosed in an egg-shaped interface area, defined by:

D_l: lower interface limit
D_u: upper interface limit
D_a: central interface limit

Applying equations (107) and (170), we can derive conditions of the equality of a gravitational space density:

for lower interface limit
for upper interface limit
for central interface limit

where

M (M₁): stands for mass of a superior (inferior) object
r_xm (r_xm1): stands for radius according to equation (169) of an object M (M₁)
R_orl: stands for radius r_lmx of an orbit around object M, at which object M₁ is located.

Substituting for r_x and v_m/x from equations (169) and (170) into the equation (114), we can easily derive :

	(501)

It means, the expression v_zx/m represents the Z_ct (contemporary) speed of the spacetime structure, when the relativistic effect is ignored.Therefore, except of case when the mass of the gravitational object approaches zero, or infinity, we may write :

	(502)

Applying the equation (502) and the derived conditions of equality of the gravitational space density, we can determine the interface limits :

	(503)

	(504)

	(505)

5.3.4.2 Gravitational acceleration due to exterior objects.

The gravitational interaction originated by the exterior object M₁ (M₂) has to be added to the gravitational interaction of the examinated object M₂ (M₁), to calculate the resultant gravitational interaction in the gravitational field of the object M₂ (M₁).

In case, the object M₂ is situated inside the gravitational field of the dominant object M₁, we can find out the contribution of the gravitational field of the object M₁ to the acceleration caused by the gravitational object M₂, according to equations derived in chapter 5.3.2.2. However this calculation is based on condition that the space density of the respective point in the gravitational field M₂ is defined by gravitational field of the object M₁ (not M₂). Since the space density due to gravitational field of the object M₂ becomes higher now than the space density that is originated by the object M₁, the gravitational field of the object M₁ becomes hidden in this zone. Therefore the acceleration due to gravitational field of the object M₁ must be re - calculated on space density of the gravitational field of the object M₂.

Let us imagine the two following events :

An object or a spacetime structure itself moves in a background of the spacetime density (consequently, in a time density ) at the frame intrinsic speed v₁.
The same object or a spacetime structure itself passes from the background of the space density to the space density , without being affected by gravitational (or any other) interaction.

Under these circumstances we must admit that if an object, or a spacetime structure itself in a background of the spacetime density passes distance l₁ frame intrinsic meters within t₁ frame intrinsic seconds, it will pass
equation

in the background of the space density .

Therefore the inertial passage from the background of the space density to the background of the space density brings the change of the frame intrinsic speed v₁ to v₂:

	(506)

Examining gravitational effects of the dominant object M₁ (of the mass M₁) in point P, situated in a gravitational field of the inferior object M₂ (of the mass M₂) (see Fig19), we can derive :
Fig 19

	(506a)

	(506b)

Applying the equation (169) for r_x1 and r_x2, we receive :

	(506c)

and, substituting from (506c) to (242), we have:

	(507)

Examining the speed of the spacetime structure in point P, it must be :

	(507a)

where

v_x/m1: stands for the frame intrinsic speed, in direction P-M₁, of the spacetime structure of the gravitational field of the object M₁ ,in case, if the point P was situated in the space density _g1. This speed is defined by equation (170).
v_x/m1-2: stands for the frame intrinsic speed, in direction P-M₁, of the spacetime structure of the gravitational field of the object M₂ (due to gravitational field of the object M₁), that would have to be added (in vector superposition) to speed v_m/x2, (representing the frame intrinsic speed in direction P-M₂, caused by gravitational field of the object M₂), if we wanted to know the total frame intrinsic speed of the spacetime structure in point P,
r_lmx1: stands for the distance P-M₁ in length units of the chosen frame, and,
r_lmx2: stands for the distance P-M₂ in length units of the chosen frame.

Thus, respecting the equation (108), it must be :

	(508)

where v_zx/m1-2

stands for the Z_ct speed (speed in frame intrinsic length units and the time unit of the chosen reference frame), of the spacetime structure of the gravitational field of the object M₂ (due to gravitational field of the object M₁), that would have to be added (in vector superposition) to speed v_m/x2, (representing the frame intrinsic speed in direction P-M₂, caused by gravitational field of the object M₂), if we wanted to know the total frame intrinsic speed of the spacetime structure in point P of the gravitational field M₂.

We may write, respecting also the equations (169), (170), and (242a) :

where r_x2, defined by equation (169), stands for the radius in units of the orbital frame of the point P in gravitational field of the object M₂,

	(509)

Remark :
Applying the equations (169), (170) and (114) (or (115)), we can derive that the Z_ct speed (in a direction P - M₂), of the spacetime structure inside gravitational field M₂, may be expressed as :

(509a)

Comparing the equations (509) and (509a) we can easily derive, that inside the interface area of the gravitational field M₂ (like Earth) in a dominant gravitational field M₁ (like Sun) the spacetime structure Z_ct speed v_zx/m1-2 reaches higher values than the M₂ gravitational field own spacetime structure Z_ct speed v_zx/m2. If these two speeds were acting in the same (contemporary) spacetime structure, they would result (due to vector superposition) to the resulting speed approaching the Z_ct speed of the gravitational field M₁, and, the gravitational field M₂ would be deformed so much, that the parameters of the M₂ gravitational field should be considerably changed, in contradiction to the chapters 5.2.1, 5.2.2 and 5.3.1. This is why we must admit that the spacetime continuum makes the partial flows of the spacetime structure of the different densities (of the different time flows) possible to exist inside the same space zone, not affecting one another. The acceleration however, acting on mass in such space zone, is defined as the vector superposition of the partial accelerations from all partial spacetime flows.

The acceleration of the space flow, manifested by the speed v_zx/m1-2 in gravitational field of the object M₂ can be expressed as

	(509b)

Since

(510)

where v_ox/m1-2 stands for the Z_cr speed,
and (see equation (509)),

(511)

substituting from equations (510) and (511) to equation (509), we receive :

	(512)

The gravitational acceleration g_zx/m1-2 represents the Z_ct gravitational acceleration in gravitational field of the object M₂, due to gravitational field of the object M₁, that has to be added to the Z_ct gravitational acceleration in gravitational field M₂, in vector superposition, to calculate the total Z_ct acceleration. The negative sign in equation (512) define the direction P-M₁ of the acceleration.

In case when r_lmx2 / r_x2 = r_lmx1 / r_x1, occuring in all points of the interface area between gravitational fields M₁ andM₂, the gravitational acceleration reaches

	(513)

According to equations (170) and (166) :

	(514)

Applying r_x1/r_x2=v_m/x1/v_m/x2= r_lmx1/r_lmx2, we can derive for the ratio of the gravitational acceleration induced from object M₁ (in direction P - M₁) to gravitational acceleration caused by object M₂ (in direction P - M₂) in points of the interface area (like the ratio of the components of the gravitational acceleration on from Sun and Earth on the interface area around Earth):

	(514a)

The equation (251) is identical with the equation (182), confirming that the Z_ct acceleration g_zx/m1-2 becomes identical with acceleration g_zx/m1 of the gravitational field M₁ in all points of interface area.

In case when r_lmx2 = r_x2, occurring, for instance on Earth surface ( if the reference frame on Earth surface was taken as the chosen one), the equation (512) becomes

	(515)

and, applying the equation (138), we can derive for the ratio of the gravitational acceleration induced from object M₁ (in direction P - M₁) to gravitational acceleration caused by object M₂ (in direction P - M₂) in the chosen reference frame (like the the ratio of the components of the gravitational acceleration from Sun and Earth on the Earth surface):

	(515a)

This result is in compliance with the Newton's theory of universal gravitation, confirming that the gravitational effects of the Sun's gravitational field on Earth surface, calculated by spaceflow theory, are in correspondence with experiment. The contribution of the gravitational acceleration of the Sun to the gravitational acceleration of the Earth according to the equation (249) however, differs from the acceleration expected by Newton's theory along with the height above Earth.

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