Apparatus and Setup
This is a data-analysis lab using real, spacecraft-measured parameters for the
two most massive main-belt asteroids, Ceres and Vesta, both characterized in detail by NASA's Dawn mission
(2011-2018; standard published values, not independently re-verified by live fetch this session -- see
../reference-log.md). No telescope time is required; the lab tests Lecture 02's frost-line and
condensation-sequence prediction directly against two real bodies straddling the frost line.
Materials and Data
| Body | Mass (kg) | Radius (km) | Semimajor axis (AU) |
|---|---|---|---|
| Ceres | 9.393e+20 | 469.7 | 2.7675 |
| Vesta | 2.590e+20 | 262.7 | 2.3615 |
Procedure
- Compute the mean density of Ceres and Vesta from their measured mass and radius, using the identical density formula from Lecture 01 (ρ = M/(4/3πR³)).
- Using Lecture 02's frost-line estimate (∼2.8 AU from the equilibrium-temperature calculation, or your own recomputation of it), state whether each asteroid's semimajor axis places it inside, at, or beyond the frost line.
- Compare the two computed densities to the terrestrial-planet and icy-body density ranges established in Lecture 01's table (terrestrial planets: ∼3900-5510 kg/m³; icy satellites are typically 1000-2000 kg/m³) and state whether the condensation-sequence prediction (bodies closer to the frost line should be less dense/more ice-rich) is supported.
- Ceres shows direct spectroscopic and gravity evidence (Dawn mission) for a partially differentiated interior with a hydrated, ice-and-salt-rich mantle, while Vesta shows a basaltic crust and an iron core (confirmed by its HED meteorite family, directly linked to Vesta by spectroscopy). Explain in one paragraph how this differentiation evidence is or is not consistent with your density comparison.
- Estimate the uncertainty in each computed density given a plausible ±2% uncertainty in each body's measured radius (recall from Lecture 01 that density depends on R⁻³, so a small radius uncertainty is tripled in the resulting density uncertainty), and state whether this uncertainty could account for any part of the density difference found in step 3.
Analysis and Uncertainty
Because ρ ∝ R⁻³, the fractional uncertainty in a body's computed density is approximately three times its fractional radius uncertainty (for a fixed, precisely known mass); Dawn's radar and imaging-derived radii for Ceres and Vesta are precise to well under 1%, so this uncertainty is small compared to the roughly 60% density difference between the two bodies, meaning the observed density contrast is a real physical result, not a measurement artifact.
Deliverables
- Computed densities for Ceres and Vesta, with full unit conversions shown.
- A frost-line comparison stating each body's position relative to the ∼2.8 AU frost line from Lecture 02.
- A written paragraph connecting the density comparison to each body's independently known differentiation and meteorite-family evidence.
- An uncertainty propagation estimate and a judgment of whether it could explain the observed density contrast.
Assessment Criteria
- Correct density calculation for both bodies with correct units.
- Correct identification of each body's position relative to the frost line.
- Written paragraph correctly connects density and differentiation evidence rather than treating them as unrelated facts.
- Uncertainty propagation correctly applies the tripled fractional-uncertainty scaling for density versus radius.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Section 7.2 and Section 15.3 (asteroids).
- Ceres and Vesta mass, radius, and orbital parameters: standard published Dawn mission values (Russell et al. 2012, 2016, Science), not independently re-verified by live fetch this session; see
materials/ASTR320/reference-log.md. - Generated by
materials/ASTR320/src/generate_astr320_labs_psets.py.