Suppose that the Jovian planets have the same overall...

Suppose that the Jovian planets have the same overall composition as the Sun. a. From Table $33.1,0.14 \%$ of a Jovian planet's mass would be iron. What fraction of their mass would be silicates, assuming that oxygen atoms combined with silicon in the ratio $3-t 0-1 ?$ b. What would be the mass of rock (silicates) and iron in Jupiter compared to Earth's mass? c. What would be the mass of rock and iron in Uranus compared to the Earth's mass? What terrestrial planet's mass is this closest to?

Suppose that the Jovian planets have the same overall composition as the Sun.
a. From Table $33.1,0.14 \%$ of a Jovian planet's mass would be iron. What fraction of their mass would be silicates, assuming that oxygen atoms combined with silicon in the ratio $3-t 0-1 ?$
b. What would be the mass of rock (silicates) and iron in Jupiter compared to Earth's mass?
c. What would be the mass of rock and iron in Uranus compared to the Earth's mass? What terrestrial planet's mass is this closest to?

Key Concepts

Solar Composition

This concept refers to the relative abundances of elements found in the Sun, which are used as a baseline for understanding the overall composition of other astronomical objects such as planets. In the problem, the assumption that the Jovian planets share the same composition as the Sun means that the elemental mass fractions (for instance, for iron and other elements) can be directly compared to solar values, providing insight into the planets’ bulk makeup.

Mass Fraction Calculation

Mass fraction is the ratio of the mass of a given component to the total mass of a system. Here, the mass fraction of iron is given as 0.14%, and similar calculations are used to infer the fraction of silicates. This concept is crucial for quantitatively determining the contribution of different elements or compounds to the overall mass of a planetary body.

Stoichiometry in Silicate Formation

This concept involves the quantitative relationship between reactants in chemical compounds, particularly the ratio of oxygen to silicon atoms in silicates given as 3:1 in the problem. Stoichiometry allows one to calculate the mass contribution of a silicate compound based on the elemental abundances, taking into account the atomic mass and the fixed ratios in which the atoms combine.

Comparative Planetary Analysis

This concept pertains to comparing the properties and compositions of different planets by using a common reference—in this case, Earth’s mass. By estimating the mass of rock (silicates) and iron in planets like Jupiter and Uranus and then expressing these quantities relative to Earth’s mass, one can draw conclusions about the differences in planetary structure and composition among terrestrial and Jovian bodies.

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