A planet is detected via transit photometry, and astronomers measure a precise planet radius from the dip in starlight. A student says 'Now we know what the planet is made of.' An astronomer disagrees. Why?
ATransit photometry cannot reliably measure radius — only radial velocity can determine planetary size
BRadius alone cannot determine composition because a rocky super-Earth and a puffy mini-Neptune can have identical radii but very different masses and densities
CPlanetary composition can only be inferred from atmospheric spectroscopy, not from radius measurements
DThe transit radius is the planet's atmospheric radius, not its solid surface radius, making all composition inferences invalid
Knowing radius alone is insufficient because density — the key discriminator of composition — requires both mass and volume. A rocky super-Earth and a water-rich mini-Neptune or a gas-dominated sub-Neptune can occupy the same radius while differing by a factor of 3–10 in mass. Only by combining transit-derived radius with mass from radial velocity or transit timing can you compute mean density and constrain composition. This is why mass determination is called the 'essential second measurement' — a radius without a mass is an incomplete characterization.
Question 2 Multiple Choice
Radial velocity measurements of a host star yield 'M sin i' rather than the planet's true mass. Under what condition does this ambiguity resolve?
AWhen the planet's orbital period exceeds one Earth year
BWhen the host star's spectral type is precisely determined by spectroscopy
CWhen the planet also transits, confirming a nearly edge-on orbit so sin i ≈ 1 and the true mass is recovered
DWhen at least three complete orbital cycles have been observed
Radial velocity measures the star's reflex motion along our line of sight. If the orbital plane is tilted at angle i to our line of sight, we only see the component v sin i of the star's true velocity amplitude. This gives M sin i — always a lower bound on the planet's mass. If the planet transits, the geometry is constrained: the planet must pass directly across the star's disk, requiring a nearly edge-on orbit (i close to 90°). When sin i ≈ 1, the measured M sin i equals the true mass to good approximation. Combining transit geometry with radial velocity is how most exoplanet masses are precisely determined.
Question 3 True / False
A planet with a mean density below 1.5 g/cm³ almost certainly has a thick hydrogen-helium atmosphere, because such a low density cannot be achieved by rock or water alone.
TTrue
FFalse
Answer: True
Rock has density ~3–8 g/cm³ depending on composition; water ice is ~1 g/cm³. A planet composed predominantly of these materials will have a mean density well above 1.5 g/cm³ for any realistic mass. Hydrogen and helium are the only abundant materials with sufficiently low density to bring a planet's mean density below ~1.5 g/cm³ — they must form a significant fraction of the planet's mass. This is why density is such a powerful compositional diagnostic: very low density is nearly unambiguous evidence for a gas-dominated envelope.
Question 4 True / False
Radial velocity measurements give you the planet's full, true mass in most cases, as long as the spectral data is precise enough.
TTrue
FFalse
Answer: False
Radial velocity yields M sin i — the planet's mass multiplied by the sine of the orbital inclination. Since inclination is generally unknown from radial velocity data alone, you get a minimum mass, not the true mass. If the orbit is face-on (i = 0°), you would detect no Doppler shift at all despite the planet's gravity. Inclination can only be independently constrained by other observations — most usefully, a transit detection, which requires i close to 90°. Without inclination information, radial velocity gives a lower bound on mass, and the true mass could be significantly larger.
Question 5 Short Answer
Why is knowing both a planet's mass and its radius more scientifically valuable than knowing either alone? What additional quantity does the combination enable, and why does that quantity matter?
Think about your answer, then reveal below.
Model answer: Mass and radius together give you mean density (density = mass / volume). Density is the single most powerful constraint on planetary composition available from indirect observation. A rocky, Earth-like planet has density ~5–6 g/cm³; a gas giant like Jupiter has density ~1.3 g/cm³; a water-dominated world might be ~2–3 g/cm³. Without density, a measured radius of 2 Earth radii is ambiguous — it could be a dense rocky super-Earth or a low-density sub-Neptune with a thick gas envelope. Without density, a measured mass of 10 Earth masses could be a rocky object or one with substantial water. The combination breaks this degeneracy and allows planets to be placed on a mass-density diagram that physically distinguishes composition classes.
This is the central payoff of combining multiple measurement techniques. Transit photometry and radial velocity individually produce incomplete characterizations; together, they unlock composition constraints that transform a 'detected planet' into a 'characterized world.' This is why astronomers invest heavily in follow-up mass measurements for every transiting planet candidate — the radius alone, however precisely measured, cannot tell you what you actually want to know about the planet's nature.