In conclusion, it was found that the mass-radius relationships can be used to approximate the chemical composition of various planets, which agrees with the theory by utilising the empirical methods in solving the Virial theorem. It was also found that by observing how the radius of a planet varies with mass, the dynamic processes at hand can be learned. Equation 6 shows how mass varies with radius, the heavier the body becomes, the smaller the radius as the gravitational pull will overcome the electrostatic repulsion of electrons. This effect is called the electron degeneracy pressure, and it arises due to the Pauli Exclusion Principle. Once a body reaches a certain limit, called the Chandrasekhar limit, in which a body approaches Black hole size and the radius will decrease with mass. This theory to stellar bodies within the solar system was applied and found that Equation 6 is not valid for stellar objects such as the sun because there are nuclear fusion reactions that take place within these objects that counteract gravitational pull. This effect is called the solar thermostat and it is due to degeneracy pressure.
The sun burns out hydrogen, then helium, then heavier elements until it dies. As it fuses heavier elements the radius gets larger, i.e. giants and supergiants are observed.
High mass stars larger than 8 masses of the sun end in supernova explosions, low mass stars less than 2 masses of the sun end up as white dwarfs. If the star is more massive this corresponds to longer fusion rate and larger radius 15.
Equation 6 also predicts that for a given mass a planet comprised of hydrogen will have a greater radius that one comprised of iron. This is due to the assumption stating that each electron occupies a spherical space within the planet. Higher mass elements increase the ratio of space occupied and this decreases the radius of the planet, therefore Increasing atomic number Z and mass number A the radius decreases (i.e. Hydrogen has A=1, Z=1 and Iron A=55, Z=26 which means iron is heavier in mass, therefore, smaller in radius).
Equation 8 was formulated to find an analytical approximation for the interior pressure of planets a function of depth. This equation was applied to known data about the Earth and found that the resultant interior pressure was very close to the observational data. It was also found that Equation 8 will not be accurate for soft materials. The calculation of the planet’s internal pressure is not accurate as the density is taken to be constant throughout the planet. It underestimates the pressure, therefore only for hard materials, the calculation of planet’s internal pressure is applicable. Because equation 8 was derived assuming that density remains constant throughout the planet, therefore is most accurate for hard materials.
Figures 9 and 14 are a valid indication as to the idea of what each planet is comprised of, although the equation used in part a makes a lot of assumptions thus systematic errors could arise. In addition, we cannot get an in-depth view of what each planet is comprised of as certain elements were used to represent different compounds such as oxygen represents rocks, gases and ices and silicon to represent rocks. For example, other compounds of molecules could be used as an indication instead of single elements to provide greater accuracy.