The mass fractions of the $10M_\oplus$ planet are
$$
\boxed{x_{\rm iron}=0.4,
\qquad x_{\rm silicate}=0.4,
\qquad x_{\rm H_2}=0.2}.
$$
On an <exoplanet bulk-composition ternary diagram> with iron, silicate, and hydrogen vertices, it lies in the interior on the line of equal iron and silicate fractions, one fifth of the way from the iron-silicate edge toward the hydrogen vertex.

Neglecting its atmosphere and minor volatile reservoirs, Earth lies on the iron-silicate edge at approximately
$$
\boxed{(x_{\rm iron},x_{\rm silicate},x_{\rm H_2})simeq(0.32,0.68,0)}.
$$

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 315 / 4 / d / Solution

A bulk-composition ternary diagram represents the mass fractions of three planetary components at a point whose barycentric coordinates sum to one.


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 Incoming links: Exoplanet bulk-composition ternary diagram