Help for a Model for examining gravity from the surface of the Earth to the center.

It is called MODELBS which stands for Model Below Surface or modelling gravity, temperature and pressure in the various layers of the Earth.
The model is still a bit raw and can be improved.

click here to return to the home page.

click here for more on temperature and pressure.

This modelling program will attempt to examine the way Newton forces act on a small standard 1kg object and the changes as the small object is taken at intervals toward the center of a large object.
It uses gravity as the main force and includes Mass in Front and Mass Behind.
It takes into account the density of the various layers of the Earth.
An assumption was that gravity at the center is zero due to an object being pulled equally in all directions and this is a basis to prove the model.
The properties of Earth - such as Radius, Average Density, Layers, Density and Temperature are taken as fixed constants based on the best empirical knowledge from other sources. Much data and images are borrowed from the internet and I wish to acknowlege the original authors and not take credit work already done.

My Maxim is this:
We as humans need to study the Earth first. It is our immediate source of best knowledge. From empirical and inferred knowledge of the Earth, we can exptrapolate findings to suns and planets beyond.
So a study of the Earth is the best starting place before going beyond. There is so much we still do not know about the Earth.

It seems the best data we have for the interior of the Earth are siesmic waves and mainly p waves and s waves which give a clue to the density of inner layers. So Seismic waves indicate a liquid Outer Core and a solid Inner Core. Some new data indicates temperatures can exceed 6,000c and above the previous 4,000c. So I am using the newer data.

In this model, I introduce extra layers to try and examine density, temperature in more detail. So here are the layers of the Earth with properties as a table. They are called Shells rather than layers and the idea of a shell is like onion rings or onion shells. The interior structure of the Earth is layered in spherical shells, like an onion. The VeryCore in the model is small and is the center of the Earth which was a target of the model and an unfinished analysis. The densities have been taken from other sources and further guestimated and adjusted because the average density of each layer has to add to the average density of the Earth (5514 kg/m^3). This provides a mathematical check to see that the volume mass and densities of each layer make sense. The model does this but behind the scenes. The first surface layer is an invention to try and build the mass of water at the surface into the model. It does not make much difference to the overall model.

Shell # Shell Name Depth to bottom of shell m Density kg/m^3 Temperature C
1 Surface 2000 1000 20
2 Crust 33000 2600 870
3 UpperMantle 700000 3300 1627
4 MiddleMantle 1700000 5000 2727
5 LowerMantle 2850000 5700 4000
6 OuterCore 5155000 10000 6000
7 InnerCore 6370700 12600 6000
8 VeryCore 6371000 13000 6000

The following table shows infered values in the model for volume and mass for each shell.

Shell # Shell Name Shell Volume m^3 Shell Mass kg
1 Surface 1.0198E+18 1.0197956E+21
2 Crust 1.5725E+19 4.0885767E+22
3 UpperMantle 3.0251E+20 9.9827387E+23
4 MiddleMantle 1.6853121E+24 1.6853121E+24
5 LowerMantle 2.4405E+20 1.3910603E+24
6 OuterCore 1.7535E+18 1.7531487E+24
7 InnerCore 7.5316E+18 9.4898617E+22
8 VeryCore 1.13098E+8 1.4702654E+12

There are a few interesting things to glean from the model and things that need further exploration.

Firstly, the assumption is that Newton forces of gravity decrease as a small object it taken conceptually to the center of the large mass (Earth).

For gravity considerations, pressure is caused by weight and weight is caused by gravity. For example, any heavy object is virtually weightless in deep space. So a mass does not have a weight unless there is gravity. It seems to follow that as a small object is taken conceptually, beneath the surface of the Earth, then weight and pressure should decrease because gravity decreases.

It seems intuitive that pressure increases toward the center but it may be so. We tend to see the center of mass as being the center but when examines gravity forces toward the center it decreases.

Take this example. Take a boiled egg and cut the top off. If the egg is round you get two sperical caps. Put the std 1kg small object in the center of the cut and put the top back on. One gets mass in front (larger) and mass behind. This is the basis for calculating gravity forces and it gets complex in the calculation detail. The center of mass of the larger sperical shell is not the center of the Earth but somewhere past it. Once the small object gets to the center of the Earth, the mass in front and mass behind become equal and hence zero gravity force.

At this stage, Pressure in the model seems too high and is a work in progress.

click here for more on temperature and pressure.

For the student of science, and we are all students, questions have to be asked as to the nature of the center of the Earth.

The following is a reproduction of another earlier model of the interior of the Earth and credits are given to the author.

Modeling the core of the Earth must rest upon even more indirect evidence. We observe that the metallic meteorites have cores of iron and nickel, and this correlates with other evidence that suggests that the Earth's core is similarly composed of iron and nickel. Modeling the density of the center of the Earth yields densities of about 14 times that of water, which could be obtainable by compressing iron and nickel, but not surface type rocks. An iron core also gives us a circulating electrical conductor, which could provide the necessary mechanism for creating the Earth's magnetic field.

The following table of density and depth data was taken from a USGS publication by Eugene C. Roberson entitled The Interior of the Earth. (

Data on the Earth's Interior
Thickness (km) Density (g/cm3) Types of rock found
Top Bottom
Crust 30 2.2 Silicic rocks
2.9 Andesite, basalt at base
Upper mantle 720 3.4 Peridotite, eclogite, olivine, spinel, garnet, pyroxene
4.4 Perovskite, oxides
Lower mantle 2,171 4.4 Magnesium and silicon oxides
Outer core 2,259 9.9 Iron + oxygen, sulfur, nickel alloy
Inner core 1,221 12.8 Iron + oxygen, sulfur, nickel alloy
Total thickness 6,401
Robertson gives credit for most of the data to Anderson, Don L., Theory of the Earth: Boston, Blackwell Publications, 1989.

We are told that solids do not compress much. So densities of 13,000 kg/m^3 are not explained by rocks compressing. It could be explained by a concentration of heavier elements such as gold and lead.