Online Calculator: Core Pressure

Keith Dixon-Roche's core pressure theory
Keith Dixon-Roche's Core Pressure Theory

{Keith Dixon-Roche © 08/11/17}
Keith Dixon-Roche has given us the theory of core-pressure within any mass. This calculator uses this theory to determine its internal structure based upon its delta value (Δ).
Isaac Newton's gravitational constant 'G' and Keith Dixon-Roche's spin theory have together enabled us to determine the internal pressure and structural density of planetary bodies based upon their mass, delta value and polar moment of inertia.

Isaac Newton's force law may be used alone to calculate the internal pressure anywhere within a solid body of homogeneous matter. But it is a little more complicated to calculate the internal pressure of a non-homogeneous body, such as a planet or star.

The Calculator

You enter the density and outside radius of each layer (maximum of seven) until the mass and polar moment of inertia match those of the celestial body (see online calculator for spin); factors Fm and FJ must both equal '1' for ultimate structural accuracy.
You may calculate the "Known Body Properties" (below) using our online spin calculator and copy and paste the appropriate values into the text boxes below.
The default input data is approximate for the earth.
Press 'F5' to reset the calculator.

Constants:
G: m³ / kg.s²

Layer Properties:
The following is a list of input data for each layer (1 to 7), you modify these values for each new calculation.
Bear in mind that the densities you enter (ρ₁ to ρ₇) for each layer are assumed to be homogeneous or average values.
Note: The downloadable version of this calculator (below), calculates 'J' & 'm' using variable densities between adjacent radii.
For homogeneous matter of non-variable density, simply input identical densities in at least two layers, the radii of which includes that for which you need the internal pressure.

ρ₁: kg r₁: m
ρ₂: kg r₂: m
ρ₃: kg r₃: m
ρ₄: kg r₄: m
ρ₅: kg r₅: m
ρ₆: kg r₆: m
ρ₇: kg r₇: m

Known Body Properties:
The following information is used to calculate factors; 'Fm' & 'FJ' (below) and are only needed for bodies of non-homogeneous matter of variable density such as stars and planets.
It may be ignored for homogeneous matter of non-variable density.

J: kg m: kg


Calculation

The following is a list of the internal pressures (p₁ to p₇) at each radius.



Internal Pressures:
m₁: kg J₁: kg.m² p₁: N/m²
m₂: kg J₂: kg.m² p₂: N/m²
m₃: kg J₃: kg.m² p₃: N/m²
m₄: kg J₄: kg.m² p₄: N/m²
m₅: kg J₅: kg.m² p₅: N/m²
m₆: kg J₆: kg.m² p₆: N/m²
m₇: kg J₇: kg.m² p₇: N/m²

  J: kg.m²      FJ: (should be '1.000')
m: kg Fm: (should be '1.000')

Notes

1) The above default "Layer Properties" (for the earth) have been set deliberately incorrect (neither 'FJ' or 'Fm' are equal to '1') to give you (the user) the opportunity to correct them.
Accurate figures for the "Layer Properties" can be found for the earth on our web page for the theory of core-pressure Fig 1; but bear in mind that the densities in Fig 1 apply only at the radii concerned. The intermediate densities vary between radii.

Downloadable Version

A full (more accurate), downloadable version of this calculator is available from this website at; Core Pressure.
Note: greater accuracy is achieved in the downloadable version of this calculator because it calculates 'J' & 'm' using variable densities across each layer