Gravity field differential equations

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New Gravity field differential equations are suggesting to discuss at the Forum.
These equations complete Maxwell Equations for Electromagnetic field and make them symmetric.
So, Gravity field intensity "g" has dimension of acceleration, it is a vector value.

curl g = 0 , this is first equation
div g = -4*pi*G*(ro) -G/(2*c2)*(E2 + H2) - g2/(2*c2)
this is second equation.
G is Newton constant, (ro) is density of substance, E and H are the electromagnetic field intensity, c -speed of light, c2, g2, E2, H2 are (c Squared) and etc. pi=3.1415927
From these equations we find the Gravity field density as:

W = - g2/(8*pi*G)

It is unexpected, that gravity constant G is in a denominator in this expression.

These equations are suggesting to discuss.

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  • #2

Part 1. It is possible to complete Maxwell Equations for Electromagnetic field with differential equations for gravitational field:

curl g = 0

div g = - 4πG( ρ + p/c2) – G/(2 c2)( E2 + H2) - g2/(2 c2)

The first equation reflects the fact, that gravity waves are still not found in the nature. The second equation describes sources of gravity field: these are usual substance with density ρ, electromagnetic field with intensity Е and Н , and also gravitational field with
intensity g , (g - has dimension of acceleration), p – is pressure. G - is the Newton constant,
c - speed of light. π = 3.1415927

Part 2. Gravity field energy density .
From these equations we find expression for Gravity field energy density :

W = - g2/(8πG)

It is unexpected, that gravity constant G is in a denominator in this expression. So for gravitational field at a surface of the Earth for g = 9.81 m/sec2 , we find : W ~ - 10E11 Joul/m3 .
The “-“ sign in this expression shows, that Gravity field energy density is negative as well, as appropriate Gravity interaction energy.

Part 3. Newton law improved
It is not difficult to result the formula for the Newton law improved, taking into account that gravity field is also a source of gravitation:

g = - GM/ (R2( 1 – GM/(2 c2)(1 - (1/Ro – 1/R)))

M - mass of a body, Ro - radius of a body.
At large distance, according to this , gravity field results larger, compare to it traditional value.
In our opinion this formula can explain, for example, why the space vehicle " Pioneer - 10 ", NASA, that is outside the Solar system now, is slowed down faster, than it follows from calculations. “” journal writes in this occasion: "Movement of the “Pioneer 10 " in space is interested for the scientists, as it was found , that it is impossible to explain its observed slowering by only one gravitational attraction of Solar system. It can serve as the certificate of existence of force, still unknown to science, or is connected to some properties of the space vehicle.”
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  • #3
Correction to Last expression for Newton low improved:

g = - GM/ (R2( 1 – GM/(2 c2)(1/Ro – 1/R))