Lesson 2 of 6 · density and composition
Use density without inventing an interior
10 minute lesson · 3 checks along the way
Your goal for this lessonCalculate bulk density and distinguish a constrained mixture from a unique composition or surface description.
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Mass and radius describe the whole planet
is total mass divided by total volume. For a spherical planet, volume depends on the cube of radius. Combining a with a transit radius therefore provides a valuable physical constraint, but it averages over every layer. An iron-rich center, rocky mantle, water-rich region, and extended gas envelope can contribute very different amounts to the mass and to the observed radius.
The radius measured in a transit also corresponds to where the planet becomes opaque in the observing band. For a planet with a thick atmosphere, that is not necessarily a solid surface. Temperature, pressure, atmospheric , and internal compression affect the relationship between mass, radius, and material. A catalog number alone cannot tell a reader where a spacecraft could land or what a surface would look like.
Check 1 of 3
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Work through a decision
Worked comparison: respect the radius cube
Take two fictional spherical planets with masses of eight Earth masses. Planet A has twice Earth’s radius; planet B has three times Earth’s radius. Their densities relative to Earth are 8 divided by 2 cubed, or one, and 8 divided by 3 cubed, or about 0.296. Using 5.5 grams per cubic centimeter only as a rounded Earth reference, the averages are about 5.5 and 1.63.
Equal mass did not produce equal density because planet B occupies 27 Earth volumes while A occupies eight. Neither answer identifies an exact mixture. Even A’s Earth-like average does not establish Earth’s composition: pressure changes how materials pack, and different layers can compensate. If an inferred radius increases by ten percent at fixed mass, the inferred density is multiplied by 1 divided by 1.1 cubed, about 0.751.
Equal mass can occupy unequal volumes
Original schematic for the lesson’s fictional spherical planets. Disk radii use one common scale, while the labeled three-dimensional volumes grow as radius cubed. Uniform fill is a drawing convention and does not claim uniform internal density or a particular composition.
Open full-size diagram in a new tab: Equal mass can occupy unequal volumesSeveral interiors can fit one measurement
Interior models predict radii for specified masses, temperatures, and compositions. Comparing those curves with a measured uncertainty region can rule out some models while leaving several viable. A low-density may occupy a large volume while contributing little mass. Conversely, a dense can offset a lighter outer layer. This is a degeneracy: different internal arrangements can lead to similar measurements at the telescope.
The Spitzer Space Telescope helped measure repeated transits in the compact TRAPPIST-1 system. A 2021 analysis combined timing and photometric information to constrain its seven planets’ masses and radii. Several compositional explanations remained possible, including changes in iron content or additional lighter material. That dated analysis illustrates inference from a shared system; it is not a photograph of interiors or a final inventory of oceans.
The Spitzer Space Telescope, then called SIRTF, made this 100-second IRAC engineering observation on September 1, 2003 before reaching its final operating temperature and focus. Assigned display colors make infrared sources visible. This field is an instrument test, not a resolved view of the TRAPPIST-1 planets discussed in the reading.
Look closely
Why would a sharper-looking point in this field still not supply a planet’s bulk density? What two physical quantities are missing?
See what to notice
The image does not measure a resolved planetary volume or its dynamical mass. Bulk density requires mass and radius with their inference assumptions; the appearance of a stellar point cannot replace either quantity.
Check 2 of 3
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Choose observations that discriminate
Atmospheric spectra can add information about accessible gases, while stellar abundances supply context for the material available during formation. Neither automatically determines the deep interior. The atmosphere may evolve through escape, chemistry, and exchange with underlying layers, and a star’s elemental ratios need not map directly onto each planet’s layer fractions. Useful constraints must be combined with a model that states which connections it assumes.
When comparing two composition claims, inspect whether their mass-radius ranges overlap, whether they use the same temperature assumptions, and whether correlated stellar errors were included. Ask which additional observation would separate the remaining models. A precise density is valuable even when the interior stays ambiguous: it narrows the possibilities and identifies the next measurement instead of turning a familiar numerical average into an unsupported terrestrial landscape.
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Put it together
Your lesson progress
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Go to the source
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