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I know the title sounds odd. You might be thinking "Doesn't Mercury have the highest uncompressed density of any terrestrial planet? Much higher than a planet its size normally should have?" Here's the thing, though: Iron has an uncompressed density of $7.874\ \mathrm{g/cm^3}$ and silicon has an uncompressed density of $2.329\ \mathrm{g/cm^3}$. I know the distinction for planet composition is usually metals-silicates, not iron-silicon, but iron and silicon comprise the vast majority of those two categories.

Mercury is said to be 70% metals 30% silicates with an uncompressed density of $5.4\ \mathrm{g/cm^3}$.1 However, if you run the numbers, 70 % iron and 30 % silicon gives you an uncompressed density of $6.21\ \mathrm{g/cm^3}$, or over $0.8\ \mathrm{g/cm^3}$ higher. My question is, why is Mercury's actual density lower than my proposed figure? I know that there are other materials in Mercury, like nickel, sulfur, etc., but can these things really make up the difference?


1Wikipedia and NASA

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    $\begingroup$ Interesting! Most silicates are even denser than silicon, quartz is only slightly lower, so I guess one will have to dig in to the proposed composition details. $\endgroup$ – uhoh Feb 18 at 6:22
  • $\begingroup$ Pressure is countered by high temperature. $\endgroup$ – Mithoron Feb 18 at 19:24
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The actual density depends on the mineralogy, we don't have a crystalline iron core and silicon crust. You do have a lot of oxygen available, too when you look at the overall elementary abundance. So the abundant materials are Fayalite (${\rm Fe_2SiO_4}$), Olivine (${\rm (Fe,Mg)_2SiO_4}$), Fosterite (${\rm Mg_2SiO_4}$) etc. which make up most of the crust. These have a bulk density between ${\rm 3g/cm^3}$ and ${\rm 4.5g/cm^3}$ at normal pressure and of course a somewhat higher density under pressure.

In the core we are talking about some iron nickel sulfide alloys which have a density of less than pure iron, too (typically ${\rm FeS}$ is around ${\rm 4.8g/cm^3}$ at norm pressure). So conversely knowing the total mass from celestial mechanics and satellite date, the volume from imaging and the surface composition from spectroscopy we can actually make density estimates on the core's composition (with some further guesstimates on the equations of state on the alloys in question).

Add to these figures that we will have in the interior some high-pressure phases which have somewhat higher density, the estimated mean density of ${\rm 5.4g/cm^3}$ seems to fit quite well.

Also mind, whether a source talks about weight% (thus referencing the weight contribution of single elements. One iron atom weighs nearly 4x as much as one oxygen and twice that of magnesium) or whether the source talks about number fractions (thus counting actual atoms, disregarding weight). For one single molecule of Olivine we have ${\rm Fe:Mg:Si:O}$ in the weight ratio 56:24:28:64 while we have the number ratio of 1:1:1:4.

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    $\begingroup$ @B--rian thanks for the ping but everything seems OK: all my typo fixes are still intact: astronomy.stackexchange.com/posts/41518/revisions $\endgroup$ – Glorfindel Feb 18 at 13:47
  • $\begingroup$ @Glorfindel Yeah. I just felt like with nice typesetting, things are easier to read. $\endgroup$ – B--rian Feb 18 at 13:48
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    $\begingroup$ @B--rian ... we're doing exactly what's mentioned in the Help Center, collaborative editing. High five! :) $\endgroup$ – Glorfindel Feb 18 at 13:50

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