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Widdekind
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All rocky planetoids are born as balls of molten magma, and take millions of years to cool, crust over, & solidify. As a rule-of-thumb, a planetoid's Cooling Time (tcool) scales as its Surface Gravity (g):
For comparison, the Moon (probably) solidified something like ~2.5 billion years ago, about the time that Earth's Continents were forming, and atmospheric concentrations of Molecular Oxygen (O2) were at long last increasing*.
[tex]t_{cool} \approx \frac{Heat}{Dissipation Rate}[/tex]
[tex] \approx \frac{Mass}{Surface Area}[/tex]
[tex] \approx \frac{M}{R^{2}}[/tex]
[tex] \approx g_{surface}[/tex]
Now, Mars appears cold & dead, lacking a Dynamo-Driven (?) central magnetic field. But, there is evidence of relatively recent volcanic activity on Olympus Mons (w/in the last few million years*). Thus, Mars, whose Surface Gravity is roughly 0.4, seems to have lived roughly 4.0 billion years**.[tex] \approx \frac{Mass}{Surface Area}[/tex]
[tex] \approx \frac{M}{R^{2}}[/tex]
[tex] \approx g_{surface}[/tex]
* http://en.wikipedia.org/wiki/Olympus_Mons
** The Solar System, and the Earth, are around 4.5 billion years old.
This suggests the following Order-of-Magnitude estimate for planetoids' Cooling Times:** The Solar System, and the Earth, are around 4.5 billion years old.
tcool ~ g x 10 billion years
where g is measured in Earth Gravities (~9.81 m/s2). This yields the following estimates:
Code:
Planetoid g Cooling Time (Gy)
Mercury 0.376 4
Venus 0.949 9
Earth 1 10
Moon 0.17 2