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 r_{lmx2} of the object M_{2}, we may modify
the equation (512):

(550)

Substituting for radius r_{x2} from the equation (169) to the equations
(549) and (550), we get :

(551)

where

m_{2}

stands for the mass under the radius r_{lmx2} inside the gravitational object M_{2}.

The Z_{ct} gravitational acceleration, caused by the object M_{1}, in a point P
under the surface of the gravitational object M_{2} (see Fig19) in a
distance r_{lmx1} from the object M_{1}, acting in direction P - M_{1},
is defined by the equation (551). The mass m_{2} 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 M_{2} (created of the mass of a constant
mass density) to the object M_{1} situated far away from the object M_{2}. The
object M_{2} has its own open gravitational field.

Solution

The total force attracting the object M_{2} to the object M_{1} is defined :

Substituting from the equations (553) and (554) to the equations (551) and (552), and considering the distance
r_{lmx1} between the object M_{1} and all particular points inside the object
M_{2} as identical, we can derive :

(555)

(556)

The example 2

To derive the equation for the total gravitational force attracting the object M_{2} (created of the mass of a constant
mass density) to the object M_{1} situated far away from the object M_{2}. The
object M_{2} 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 M_{2} to object
M_{1} does not depend in general on mass of the objects and on the distance between them only, but also
on the constant k_{2} or, on the mass distribution inside the object M_{2}. The constant
k_{2} 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.