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Suppose I am orbiting a rocky planet (density = 4.4 g/cm3) two-thirds the mass of Mars in the Habitable Zone of Gliese 251. This planet has a thin atmosphere, presumably from out-gassing, still has internal heating, has a weak magnetic field, but has no sign of tectonic activity. I need to mine precious and radioactive elements to replenish my ship. Gliese 251 only has about 8% of the metallicity of the sun. Can I assume that the planet (theoretically) would have about 8% of the elements (per volume of crustal material) as the Earth? Would lack of tectonic activity make them much harder to get to?

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No, it doesn't work like that. A rocky planet, to first order, will probably contain a similar mix of elements to the Earth.

The most likely reason that the star has a low metallicity is because it is old, and formed when the interstellar medium was less metal rich. But because rocky planets do not incorporate (much) hydrogen and helium, what you are really asking is how do the abundances of other elements scale to the iron abundance (which is often what is meant by metallicity)? The r-process events, such as type II supernovae that produce the heaviest radioactive elements (beyond lead), enrich the interstellar medium "promptly", because the progenitor lifetimes are short compared to the age of the Galaxy.

However, because a lot of the iron and nickel in the interstellar medium is not produced/disseminated by type II supernovae, but by type Ia supernovae with longer-lived, lower mass progenitors, then if anything I would expect a larger ratio of elements produced/disseminated by type II supernovae to iron/nickel. This will also be true of the "alpha" elements like Silicon, Oxygen and Magnesium.

The planet might be a bit short in those elements predominantly produced by the s-process in lower mass giant stars - so elements like carbon (!), nitrogen, barium, rubidium, strontium, zinc and many others may be scarce.

For a star of this age/metallicity I would expect these variations to be plus or minus a factor of two or so compared to the Earth.

Note, I am discussing bulk abundances. The accessibility of the material, where it is etc., is more of a speculative geology question, and I don't know the answer. A further complication is where exactly the planet forms compared with the condensation temperature of various elements and materials. The above discussion implicitly assumes that the planet forms in a protoplanetary disc material at a similar temperature and density to the conditions in which the Earth formed. However, a change in these conditions will alter the detailed compositional mix.

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