Human & Cosmic Size-Mass Diagrams |
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Size-mass diagram for humanly intuitable scales |
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Most objects can be placed somewhere on a diagram of this kind. Solid objects --
from sand grains, to people, to whales -- lie close to the diagonal line corresponding
to water density (1000 kg/m3; gradient 3 in this log-log plot), although
their non-spherical shape pulls the objects off the line a bit. Other densities are
illustrated by showing the location of a large room filled with air, water, or rock,
which weigh, in turn, 1, 1000, and 3000 tons (densities 1, 1000, 3000 kg m-3).
The limits of human intuitability span roughly our limits of visibility -- from a dust spec to the horizon. Amusingly, cosmic materials can be found at the extremes of our intuition: a volume of ISM as big as we can intuit weighs as little as we can intuit; and a spec of neutron star material as small as we can intuit weighs as much as we can intuit (a room full of rock).
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![]() The full size-sass diagram spanning nuclei to the Universe |
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In this second diagram, the axes span 50 (size) and 90 (mass) factors of ten.
The previous diagram occupies a small part (8 x 12 factors of ten) somewhere in the
middle, caught between the atomic and cosmic scales. The line of normal solid objects
reflects atomic density (roughly water density), although since atoms have roughly
the same size, they exhibit a fair range of density; while
hydrostatically supported objects (earth, jupiter, sun) can have somewhat different
densities depending on the degree of self-compression, and whether an internal
energy source provides additional pressure support.
When a star's energy production ceases, gravity acts on the core to create much denser white dwarfs and neutron stars. The latter fall on the nuclear density line, with of course extends down to single atomic nuclei (which, unlike atoms, fall along the line since nuclear matter is relatively incompressible).
Neutron stars lie close to the black hole region: a line of unit gradient
(3 km per solar mass) defines the Schwarzchild radius. As far as we know, there are
two mass ranges which astrophysical reality allows to form black holes -- core
collapse of stellar mass, and gradual buildup of roughly 1% galactic mass black holes.
Notice how the "density" of black holes decreases as mass increases: mass
At the low density extreme, cosmic closure density is 5 hydrogen atoms (equivalent) per cubic meter, with galaxies a few thousand times above this, and voids a few times below it. Notice that closure density meets the black hole line at the cosmic scale of the Hubble radius -- the universe has (marginally) closed space-time geometry which, on local scales, is essentially what defines black holes. |
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Animated power point slides of these two diagrams are to be found [here]. With successive clicks, the diagrams are built up roughly following the descriptions given here. Figures made for this course. | |