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                         Gravity Spheres theory in terms of equations

          In the beginning of our presentation we compared the gravitational
     force field to magnetic force field. We did that in order to make
     visualization of gravity spheres easier. To define the gravity spheres
     theory in terms of equations, we, in a similar manner, pair it with
     electric field. We compare gravitational density of a unit of volume in
     gravitational field to a charge density of a unit of volume in electrical field.
          Gauss' law for vector electric field in vacuum is

                             ∇⋄E = ρ / ε

                             where:   ρ  -  charge density per unit volume
                                            ε  -  electric constant

          In a similar manner, Gauss' law for vector gravitational field would be

                            ∇⋄g  =  d / γ

                            where:   d  -  gravity density per unit volume
                                          γ  -  gravity constant

          That is the Maxwell equation number five.
 
          Let's find the value of the gravity constant.

          In the movie Contact a woman-scientist made a journey to Andromeda
     galaxy. To all observers, her trip appeared to be instantaneous,
     though to her it lasted about eighteen hours. During the public inquiry,
     she was asked by the panel, "Do you expect us to take what you said
     on faith?!"
          
          Developing our theory, we took several well known equations on faith.
     That saved us a bucket of time. These well known equations were
     developed by you and scientists like you. At the present time there are
     no tools to measure gravity in all its details. The only tools we have is
     math and logic. If you have anything to contribute to this theory, please
     do so.

          Gravitational field is a force field similar to any other force field.
     Perhaps it is more rarefied and weak, but it is still a force field. We
     already compared gravitational force field to magnetic and electric force
     fields. We will continue this process in parallel. Gravitational density
     (gilottis: gi) is similar to electric charge (coulombs). Gravitational
     intensity (in) is similar to electric current (amperes). Other units of
     measurement are the same: newtons, kilograms, meters, seconds, etc.
     We'll use the SI scale.

           The Ampere force law gives us

                  F = μ ∗ I∗∗2 ⁄ 2∗ π ∗ r                                             (1)

         The force is 2 ∗ 10∗∗-7 newtons per meter. With current of 1 A and
     distance 1 m, we compute the field's permeability, or magnetic constant μ

                  μ = 4 ∗ π ∗ 10∗∗-7
                 = 1.256637061 ∗ 10∗∗-6

          Gravitational force is 10∗∗39 times weaker than magnetic or electric
     force. Its value then is 2 ∗ 10∗∗-46 newtons per meter. Using the
     equation (1) with distance of 1 m and current of 1 A (or distance of 1 m
     and gravitational intensity of 1 in), we obtain gravitational permeability

                  μ = 4 ∗ π ∗ 10∗∗-46
                 = 1.256637061 ∗ 10∗∗-45  kg ∗ s∗∗4 ⁄ m

         Electric constant is

                  ε = 1 ⁄ μ ∗ C∗∗2                                                       (2)

              where μ is magnetic constant and C is the speed of light.

           Using gravitational permeability in equation (2) we obtain
     gravitational permittivity, or gravity constant
     
                  γ = 1 ⁄ 1.256637061 ∗ 10∗∗-45 x 8.987551787 ∗ 10∗∗16
                 = 8.854187823 ∗ 10∗∗27  kg∗∗-1 ∗ m∗∗-1 ∗ s∗∗-2

           Let's check whether the new constant fits. Define C from (2), use γ

                   C = 1 ⁄ √μ ∗ γ                                                         (3)
                   √μ ∗ γ = 3.335640952 ∗ 10∗∗-9
                    C = 299792458  m/s

           The equation (3) validates the gravity constant.

          We must verify the process of finding gravitational constants in terms
     of units. In our MATH pages we equated 1 gi (field density) to 1 m ∗ s∗∗-2
     (acceleration) -- a striking convenience! Again, we will go in parallel:
     electric field units and gravitational field units.

                  C and gi  (coulomb and gilotti)
                  A and in  (ampere and intensity)

              gi = m ∗ s∗∗-2
              in = gi ⁄ s = m ∗ s∗∗-3

              μ = kg ∗ m ∗ s∗∗-2 ∗ in∗∗-2
                 = kg ∗ m ∗ s∗∗-2 ∗ m∗∗-2 ∗ s∗∗6
                 = kg ∗ m∗∗-1 ∗ s∗∗4
                 = kg ∗ s∗∗4 ⁄ m     (gravitational permeability unit)

              γ = kg∗∗-1 ∗ m∗∗-3 ∗ in∗∗2 ∗ s∗∗4
                 = kg∗∗-1 ∗ m∗∗-3 ∗ m∗∗2 ∗ s∗∗-6 ∗ s∗∗4
                 = kg∗∗-1 ∗ m∗∗-1 ∗ s∗∗-2  (gravitational permittivity unit)

          Use the equation (3) to verify the constants units

               C = 1 ⁄ √μ ∗ γ
               μ ∗ γ = kg ∗ m∗∗-1 ∗ s∗∗4 ∗ kg∗∗-1 ∗ m∗∗-1 ∗ s∗∗-2
                       = m∗∗-2 ∗ s∗∗2
               C = 1 ⁄ √m∗∗-2 ∗ s∗∗2
                  = m ⁄ s   (meters per second -- unit of the speed of light)

           The gravity constant stands.

            The GS theory is, obviously, in the realm of spherical geometry, even if
     its spheres are rarely perfect. Gravity is a spherical force field with
     influence both inside and outside the mass. At the present moment we will
     focus our attention on the external part of the field (outside the surface
     of the mass).

            Two new and essential variables in the theory are density and intensity
     of gravity. Density is the "amount of gravity" in the cubic meter of
     gravitational force field (gi = in ∗ s) and intensity is how much of gravity
     "substance"  circulates through a cubic meter of the field per second
     (in = gi / s).

            The nature of gravitational force field can be defined for a stationary point-particle with the unit of density from zero at the gravitational limit to maximum at the surface of a mass.                     

          This allows the gravitational field to be dependent on the source
     distribution alone.

            Applying the Coulomb's law to our point-particle

                    g = (1  ⁄  4 ∗ π ∗ γ) ∗ (gi  ⁄  r∗∗2) ∗ ř

                where:  gi  -  gravity density at the point
                             r   -  distance from the particle with gravity density gi to
                                          the g-field evaluation point
                              ř  -  unit vector pointing from the particle with gravity
                                          density gi to the g-field evaluation point
                              γ  -  gravity constant

            The total g-field due to the total  n of point-particles is the superposition
     of the contribution of each individual point-particle

                          n           n
                    g = ∑ gᵢ   = ∑ (1  ⁄  4 ∗ π ∗ γ) ∗ (gi  ⁄  rᵢ ∗∗2) ∗ řᵢ  
                         i=1        i=1

            Well, let's make it even simpler. The total strength of a g-field can be
     computed by summing up the densities of its spheres. We will take the
     Earth as an example.

            One cubic meter of the gravitational force field is the main unit. Its
     gravitational density depends on gravitational acceleration at the point
     (quantitatively, gravitational density equals acceleration). Gravitational
     density is zero at the Earth's gravitational limit and maximum at the
     surface of the Earth.

            Arbitrarily, we assign the gradient for spheres to be one meter (at this
     point, the real gradient is not important). This gradient is the depth of
     density for a sphere. We can now compute the total density for each
     sphere between the gravitational limit and the surface at one meter
     intervals, then sum up the spheres
                           rᵥ
                    g = ∑ giᵢ ∗ 4 ∗ π ∗ rᵢ ∗∗2
                          i=rᵤ

                    where  rᵤ  -  radius of the outermost sphere
                                rᵥ  -  radius of the surface sphere
                                giᵢ -  density of one cubic meter of the given sphere
                                rᵢ   -  given radius

            Why is it important to know the total strength of the gravitational force
     field of a mass? Because it contributes to the gravitational force field  of the
     larger "mother" mass, extends and strengthens it. An example? The Earth
     and the moon. We add both masses together and compute the gravity
     limit for the sum using one very simple equation

                    R = km

                    where  m  -  mass in kg
                                 k  -  galactic gravitational constant in m/kg

             And that brings us to the center of our theory.

             When we published this website, we received a certain number of
     responses both positive and negative, about fifty-fifty. One of the
     questions thrown at us was how did we derive the galactic gravitational
     constant to compute gravity limits. Here is how.

              We had to define the task, adopt some assumptions, and create a
     working model. What was the task? To find the galactic gravitational
     constant for computing gravity limits. Assumptions? The assumption
     that gravitational limits exist and they depend on the mass only. The
     model? The model of the solar system. What is the algorithm for k? It is 
     a program (too extensive and complex to be included here) which 
     constructs a model of the Solar system, then attempts to fit its 
     workings with the proven parameters. The best fit coefficient is the 
     answer.

              To the best of our knowledge, there is no interaction between
     our sun and the closest twin star Alpha Centauri 4.37 light years, or
     about 41.5 trillion kilometers away.

              In order to simplify computations, we did not include any of the
     moons in the solar system or its belts (we did include Pluto though,
     it was a planet then). Thus, our model was only an approximation of
     the system, that is why we call the constant k theoretical.

              The gravity limit of the solar system had to be somewhere
     between the sun and Alpha Centauri. Also, it had to fit within the solar
     system, in other words, the model of the system had to function
     flawlessly. Cray's answer was

                    k = 1.54 ∗ 10∗∗-14 m/kg  (meters of distance per kg of mass)

              We had to verify the newly created constant. Cray created an
     equation for computing Mercury's unaccounted perihelion advance
     based on the new k constant. And we had a perfect fit, better than the
     conventional one (see the MATH page). The Mercury's perihelion
     advance was precisely as observed. Then we used the galactic equation
     to compute the perihelion advance for the other planets, and it worked.




                          (   ...  in the process of development )



 
The Gravity Spheres theory opens up a wide field of exploration in many sciences.
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