The term "core pressure" refers to the pressure within any mass anywhere within the structure of a planet or star.

This is a mathematical theory that manifestly works, and it is based upon Newton's laws of motion and planetary spin theory both of which are indisputable laws of nature.

Note: All the calculations are the sole copyright priority of Keith Dixon-Roche © 2017

Keith Dixon-Roche is also responsible for all the other web pages on this site related to planetary motions

A 'pdf' version of this paper can be found at: Planetary Spin - The Paper

A calculator is now available for Keith Dixon-Roche's core pressures

Core pressure may be calculated using a combination of Newton's laws of motion and spin theory.

The internal pressures and structure of a planet (or in fact any planetary body) may be calculated using core pressure and spin theory.

Isaac Newton's well-known formula can be modified to determine gravitational force (F) at the surface of a sphere thus:

F = G.m₁.m₂ / R²

where 'R' is the radius of the spherical pressure plane, 'm₁' is the mass of the substance inside the pressure plane (Fig 1) and 'm₂' is the mass of substance
outside the pressure plane.

Gravitational ...

... acceleration at 'R'; g = G.m₁/R²

... force on spherical surface at 'R'; F = m₂.g

... pressure at 'R'; p = F/A = G.m₁.m₂ / 4.π.R⁴

where A is the surface area of the pressure plane at 'R'

An active planetary body will comprise a number of layers each of varying density that can be accommodated using the polar moment of inertia for a thin shell of varying density:

J = 8.532041001 x mn x (ρ₂/ρ₁) / (r₁⁵/r₂³)

where 'mn' is the mass of the shell, ρ₂ is its density at its outer radius (r₂) and ρ₁ is its density at its inner radius (r₁)

We already know the polar moment of inertia (J) for any planetary body, which can be determined using spin theory.

All we need to do is calculate the 'best-fit' for each layer from the information we know. For example; the inner-core of the earth is said to be 13,000 kg/m³ and the density of the outer surface is seawater (slightly higher than this actually) but following calculator shows a compatible construction for the earth based upon such data (Fig 1).

Fig 1. Internal Pressure Model of the Earth as it is Today

The above calculation achieves virtually 1.0 for both factors; Fm and FJ (for mass and polar moment of inertia) and reveals the reason why the substructure of mountain ranges falls away from its continental mass; the density of the continental crust is higher than the upper mantle, and as such once melted will fall into the mantle.

An earth of constant density (5506.35 kg/m³) would have a polar moment of inertia of 9.68391E+37 kg.s² as shown in Fig 2 in which Fm & FJ are both equal to 1.0

There is one question to the above that needs answering:

It is claimed that the density of the earth's core is around 13,000 kg/m³ and it is also about 90% iron. However, we know that iron will not compress at the centre of the earth due to the force (coupling) ratio (φ) and insufficient pressure.

Therefore, either the density of the earth must be much closer to 7870 kg/m³ or it comprises less than 30% iron and more than 70% of very heavy metals.

Fig 2. Internal Pressure Model of an Earth With Constant Density

The earth comprises a number of layers similar to those shown in Fig 1 that match its behaviour according planetary spin theory; where J = 1.082125E+37 kg.s²

Given that Newton's laws of motion are known to be correct, and that planetary spin theory accords exactly with Newton's laws of motion as does the above Core Pressure, it is concluded that Fig 1 may be regarded as representative of the earth's construction

**Claim 1**: The pressure at the centre of the earth and probably any other planet (not star) is less than that required to generate Fissionable energy

**Claim 2**: The density of the earth's upper mantle is significantly less than the continental crust, but far hotter (upper mantle plumes) and sufficient to melt the substructure of mountains

**Claim 3**: The pressure at the centre of the earth's inner core is 1.35E+07 ≈bar

Refer to the following web pages for planetary properties that formed the basis for the above calculations:

Stars & Planets

Laws of Motion

Solar System Orbits

Planetary Spin

Dark Matter?

You will find further reading on this subject in reference publications^{(55, 60, 61, 62, 63 & 64)}