5.3.6.2 Gravitational acceleration created by other object.
Applying the equation (512), and realising that the expression
(549)
means the space density at the radius rlmx2 of the object M2, we may modify
the equation (512):
(550)
Substituting for radius rx2 from the equation (169) to the equations
(549) and (550), we get :
(551)
where
m2
stands for the mass under the radius rlmx2 inside the gravitational object M2.
The Zct gravitational acceleration, caused by the object M1, in a point P
under the surface of the gravitational object M2 (see Fig19) in a
distance rlmx1 from the object M1, acting in direction P - M1,
is defined by the equation (551). The mass m2 to be used in the equation (551) is defined by the equation
(526) for the object created of the mass of the constant frame intrinsic mass density. For the
object consisting of the more layers of the different mass density the equation must be derived for each layer, by the way shown
in the chapter 5.3.5.2.
The example 1
To derive the equation for the total gravitational force attracting the object M2 (created of the mass of a constant
mass density) to the object M1 situated far away from the object M2. The
object M2 has its own open gravitational field.
Solution
The total force attracting the object M2 to the object M1 is defined :
Substituting from the equations (553) and (554) to the equations (551) and (552), and considering the distance
rlmx1 between the object M1 and all particular points inside the object
M2 as identical, we can derive :
(555)
(556)
The example 2
To derive the equation for the total gravitational force attracting the object M2 (created of the mass of a constant
mass density) to the object M1 situated far away from the object M2. The
object M2 has not its own open gravitational field. Both objects are situated slightly above Earth surface.
Solution
In this case the space density does not follow the equation
(549), but the equation defining the space density of the object that governs in a respective zone. Usually its value will be constant
for the objects of small volumes. For instance for the piece of a rock on Earth surface will be
= 1. Also the mass distribution in such case will
follow the conditions given by the governing object. Again for the piece of rock on Earth surface, the mass distribution will be
homogenous. On such conditions the equation (552) becomes :
(557)
(558)
Analysing the equations (556) and (558), we can tell that the total force attracting object M2 to object
M1 does not depend in general on mass of the objects and on the distance between them only, but also
on the constant k2 or, on the mass distribution inside the object M2. The constant
k2 is defined by the equation (525) and is directly proportional to the
frame intrinsic mass density. In a common case the two objects of the same total mass are attracted each by the different force, if the mass distribution inside the objects is not the same.
does not follow the equation
(549), but the equation defining the space density of the object that governs in a respective zone. Usually its value will be constant
for the objects of small volumes. For instance for the piece of a rock on Earth surface will be
