Lab 02: Moment of Inertia and Radiogenic Heat Budget: Earth versus Mars

Apparatus and Setup

This is a data-analysis lab combining two independent real datasets: measured moment of inertia factors (from spacecraft tracking and precession) and measured/modeled surface heat flow, for Earth and Mars. Standard published values, not independently re-verified by live fetch this session (see ../reference-log.md).

Materials and Data

Procedure

1. Using the moment-of-inertia deviation-from-uniform method demonstrated in Lecture 03 (deviation from the uniform-sphere value 0.4), rank Earth, Mars, and the Moon from most to least core-concentrated, and state what this ranking implies about relative core size (as a fraction of planetary radius) for each body.
2. Compute the ratio of Earth's to Mars's mean surface heat flow, and compare it to the ratio of their radii cubed (a proxy for total volume, and hence for total radiogenic heat generation, if radiogenic element concentration per unit mass were identical).
3. Using the surface-to-volume cooling scaling argument from Lecture 04 (heat loss/generation ratio ∝ 1/R), predict qualitatively which planet should show a higher heat flow per unit surface area, and check whether your data are consistent with that prediction.
4. Using the radiogenic decay law from Lecture 04, compute what fraction of ⁴⁴K's original (4.5 Gyr ago) abundance remains today, and explain in one paragraph why this isotope was proportionally more important to a planet's heat budget in its early history than it is now.
5. Mars's moment of inertia factor (0.3644) is intermediate between Earth's (0.3307) and the Moon's (0.3931). State whether Mars's heat flow, given in the data table, is also intermediate between Earth's and the Moon's, and discuss in one paragraph whether core size and heat flow should necessarily track each other exactly.

Analysis and Uncertainty

Mars's heat flow value in this lab is a representative published geophysical estimate rather than a directly measured value, because InSight's HP³ heat-flow probe did not achieve its planned burial depth; students should treat this number as having larger uncertainty than Earth's or the Moon's directly measured heat flow values, and should state this explicitly in their analysis.

Deliverables

• A ranked comparison of core concentration (via C/MR²) for Earth, Mars, and the Moon.
• A computed heat-flow ratio and volume-ratio comparison for Earth and Mars.
• A radiogenic decay-law calculation for ⁴⁴K's remaining fraction after 4.5 Gyr.
• Written paragraphs addressing the surface-to-volume prediction and the core-size/heat-flow relationship.

Assessment Criteria

• Correct ranking and interpretation of moment-of-inertia deviations.
• Correct heat-flow ratio and volume-ratio arithmetic.
• Correct radiogenic decay-law calculation with the correct half-life and decay constant.
• Written analysis correctly distinguishes core size (a static structural property) from heat flow (a dynamic, time-dependent property) rather than conflating the two.

References and Provenance

• OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Section 9.1.
• Moment of inertia factors and heat-flow values: standard published geophysical values (Earth and Moon well established; Mars heat flow a representative modeled estimate given InSight's incomplete HP³ deployment), 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.