The force that balances the motion between Earth and Moon, according to Logical gravity.

For Logical Deductions the centrifugal force Fc is a real force that equilibrates with the radial component of logical gravity force (fq1); as long as the tangential component (fq2), which is always perpendicular to the axle earth-moon, keeps the moon moving around the Earth.

Where: XXXX

being:

fc = centrifugal force

fq = logical gravity force

Mearth = Earth’s mass

Moon = Moon’s mass

D = Distance between the center of both Earth and moon

G = Gravitational constant

= Angle that fq forms with the axle Earth-Moon

fq1 = Radial component of fq

fq2 = Tangential component of fq

Final conclusion

The Logical gravity is the only one able to explain the motion around the Earth.

Thus, we have proved the veracity of Logical Gravity that jointly with centrifugal force creates the mechanism responsible for dynamic balance between stars.

There is an orbital motion at velocity v between Earth and Moon. If v=0, it would means that they are standing still among themselves.
Thus, the energetrons emitted from Earth that arrived at Earth would describe the trajectory TL of average length D at velocity c in a time t, exerting a gravity force F0 on the center of moon in direction of the center of Earth.
At the same way that energetrons emitted from moon will exert a force F0 from the center of Earth in direction of center of moon, where:

Being:
F0 = gravity force exerted between Earth and Moon if there was not a relative velocity v between them.
MEarth = Earth’s mass
MMoon = Moon’s mass
D = distance from the center of Earth to the center of moon.
T = Time energetrons describe the trajectory D at velocity c
G = Gravitational Constant
G’ = Gravitational Constant, being G’ = G/c2

Through energetrons emitted by Earth in all directions, the observer on it thinks he is standing still on position T and sees those energetrons that will reach moon on L describing the TL trajectory of average length D, at velocity c, in a time t. When such energetrons arrive at its destiny, due to the orbital velocity v of moon and the aberration effect, they change their trajectories of an angle exerting over such new trajectory a gravitational force Fv, where:

In a way analogous to the previous case, considering an observer on the moon, he sees energetrons emitted from moon exerting a gravitational force Fv forming an angle with the axle Earth-Moon.

Stable balance of moon in the Earth’s orbit

As we have seen by Logical Deductions that the gravity force Fv that Earth exerts over Moon forms an angle with the axle Earth-Moon, then we can decompose the gravity force Fv that Earth exerts over Moon into two components:

Fgr (radial gravity force) in the axle Earth-Moon;

Fgt (tangential gravity force)

The force Fgr is on balance with Fc (centrifugal force) that appears on the moon due to its orbital motion v.

The force Fgt is always perpendicular to the axle Earth-Moon and it is responsible for changing the direction of linear motion. Thus, “Logical Deductions” obey the 2 nd Newton’s law because the resultants of the force exerted on the moon are not zero. Therefore, it justifies its circular motion.

In a way analogous to the preview reasoning, there is a gravity force Fv that Moon also exerts over Earth.

The algebraic consistence of radial gravitational force Fgr with the gravitational force (Fo) when v = 0.

We already know that gravitational force Fv is

where F0 is Newton’s gravitational force obtained considering as moon was standing still in relation to the Earth, it means:

On the other hand, according to the figure below, the radial gravitational force (Fgr) is:

We also know that:

and that we have the following trigonometric relation:

Thus, substituting (4) in (5) and then, in (3), we will have:

Finally, introducing (1) in (6), we will have:

Thus, we can conclude that the tangential component of gravitational force that Earth exerts over Moon and vice versa is equal to the gravitational force calculated by Newton’s formula.