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 (M_{1})
stands for mass of a superior (inferior) object
r_{xm} (r_{xm1})
stands for radius according to equation (169) of an object
M (M_{1})
R_{orl}
stands for radius r_{lmx} of an orbit around object M, at which object
M_{1} 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 :
The gravitational interaction originated by the exterior object M_{1} (M_{2})
has to be added to the gravitational interaction of the
examinated object M_{2} (M_{1}), to calculate the resultant gravitational interaction in
the gravitational field of the object M_{2} (M_{1}).
In case, the object M_{2} is situated inside the gravitational field of the dominant object
M_{1}, we can find out the contribution of the gravitational field of the object
M_{1} to the acceleration caused by the gravitational object M_{2}, 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 M_{2} is defined by gravitational
field of the object M_{1} (not M_{2}). Since the space density due to gravitational field
of the object M_{2} becomes higher now than the space density that is originated by the object
M_{1}, the gravitational field of the object M_{1} becomes hidden in this zone.
Therefore the acceleration due to gravitational
field of the object M_{1} must be re - calculated on space density of the gravitational field of the
object M_{2}.
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 v_{1}.
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 l_{1} frame
intrinsic meters within t_{1} frame intrinsic seconds, it will pass
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 v_{1} to v_{2}:
(506)
Examining gravitational effects of the dominant object M_{1} (of the mass M_{1}) in point P,
situated in a gravitational field of the inferior object M_{2} (of the mass M_{2}) (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-M_{1}, of the spacetime structure of the gravitational field
of the object M_{1} ,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-M_{1}, of the spacetime structure of the gravitational field
of the object M_{2} (due to gravitational field of the object M_{1}), that would have to be added (in vector
superposition) to speed v_{m/x2}, (representing the frame intrinsic speed in direction P-M_{2},
caused by gravitational field of the object M_{2}), if we wanted to know the total frame intrinsic speed of the
spacetime structure in point P,
r_{lmx1}
stands for the distance P-M_{1} in length units of the chosen frame, and,
r_{lmx2}
stands for the distance P-M_{2} in length units of the chosen frame.
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 M_{2} (due to gravitational field of the object M_{1}), that would have to be added (in vector
superposition) to speed v_{m/x2}, (representing the frame intrinsic speed in direction P-M_{2},
caused by gravitational field of the object M_{2}), if we wanted to know the total frame intrinsic speed of the
spacetime structure in point P of the gravitational field M_{2}.
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 M_{2},
(509)
Remark : Applying the equations (169), (170) and
(114) (or (115)), we can derive that the Z_{ct}
speed (in a direction P - M_{2}), of the spacetime structure inside gravitational field M_{2}, may be
expressed as :
(509a)
Comparing the equations (509) and (509a) we can easily derive, that inside the interface area of the gravitational field
M_{2} (like Earth) in a dominant gravitational field M_{1} (like Sun) the spacetime structure
Z_{ct} speed v_{zx/m1-2} reaches higher values than the M_{2} 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 M_{1}, and, the gravitational field M_{2}
would be deformed so much, that the parameters of the M_{2} 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
M_{2} 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 M_{2}, due to gravitational field of the object M_{1}, that has to be
added to the Z_{ct} gravitational acceleration in gravitational field M_{2}, in vector superposition,
to calculate the total Z_{ct} acceleration. The negative sign in equation (512) define the direction
P-M_{1} 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 M_{1} andM_{2}, the gravitational
acceleration reaches
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 M_{1} (in direction P - M_{1}) to gravitational acceleration
caused by object M_{2} (in direction P - M_{2}) 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 M_{1} 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 M_{1} (in direction P - M_{1}) to gravitational acceleration
caused by object M_{2} (in direction P - M_{2}) 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.