Dear Nancy Ann,

Great question! To the best of my knowledge the density ratio is the quotient of two densities of the same quantity given in the same unit. An example is the powder density ratio, which is used in engineering to compare the (package) density of two powder layers, e.g. coated on top of lamp or display glass. Another example is the mass density ratio in chemistry of two different metals, e.g. Mercury Hg (13,59 g/cm3) and Aluminium Al (2,7 g/cm³), which is almost 5 to 1.

More relevant for astrophysics/cosmology is the "cosmological density parameter", which is the ratio of the average density of matter and energy in the Universe to the critical density (CD). CD is the density at which the Universe would stop expanding due to gravity solely after an infinite time.

All the best for you,

Thomas

Thomas Jüstel ,

Thanks so much for your reply to my RG question! Would it be possible to apply the very specific examples you enumerate to the rather broad and general astrophysical relationship which precipitated my question: our planet Earth is the densest rigid body orbiting the Sun, in Newtonian terms. It is my understanding that the Earth's density is five times greater than the density of the Sun. If this is correct, then might part of the explanationfor this five to one ratio involve chemistry on a microcosmic scale, on one hand, and, on the other hand, on a macrocosmic order of magnitude, the "cosmological density parameter" which you mention?

Dear Nancy Ann,

Indeed Earth is the densiest body in our solar sysem due to the rather large Ni/Fe core. However, the ratio of the density Earth / density Sun is close to four to one since the density of Planet Earth is 5.52 g/cm3 while the sun's density is 1.41 g/cm3. Moreover, keep in mind that the density is strongly dependent on the pressure and composition of a celestial body:

Earth Crust: 2.8 g/cm3

Earth Mantle: 4.5 g/cm3

Earth Core: 11.0 g/cm3

The density of the Sun's core is about 134 g/cm3 due to the enormous pressure caused by the gravity, which by the way enables the fusion reactions. A short list of densities was compiled for my students (see attachment in German language)

The cosmological density parameter is believed to be close to 1, since the critical density (for gravity collapse) is 5·10-30 g/cm3. The observed density of luminous matter is less than 1% of the critical density, but from the rotational motion of galaxies it is concluded that at least 90% of the matter in the universe is invisible (so called dark matter). Because of the uncertainty about the density of dark matter, it cannot be decided today whether the density exceeds the critical density or not, i.e. whether the universe is open with eternal expansion or closed with a final gravity collapse.

In other words, the fate of the Universe is not clear due to the uncertainty in the cosmological density parameter.

Thanks again for the great discussions you started!

Thomas

Dear Nancy Ann Watanabe

Thank you for this stimulating question. The formation of planets by accretion of dust and gas inside a protoplanetary disk remains an enigma although the process has been studied by generations of researchers from the original concepts proposed by Kant and Laplace. Today we know that the emergence of protoplanets is ubiquitous in the spinning discs of matter surrounding newly formed stars. Unfortunately, when we try to explain the formation of our planetary systems we encounter many obstacles due to the enormous range of scales involved. Even the most powerful computers are not sufficient to simulate the process requiring a better analytical model such as based on the generalized stochastic coagulation equation with a properly defined kernel.

Is there any significance in the average density ratios calculated for different bodies in the planetary system? My first guess is that the density ratio primarily suggests how far from the center of a solar system the planet formed; the object accreted in the inner hot part contains many more heavy elements than those originating outside the so called "snow line" of a protoplanetary disk.

PS.

For more information please consult the following paper:

Article Chemistry in Protoplanetary Disks