Apparatus and Setup
This is a data-analysis lab using the Sun's standard-model core conditions (standard published values, flagged for spot-check in ../reference-log.md) together with the equation-of-state and opacity formalism of Lecture 02 and the hydrostatic-equilibrium estimate carried forward from ASTR 310, Lecture 05. No telescope time is required.
Materials and Data
| Quantity | Value |
|---|---|
| Sun mass, radius | 1.989e+30 kg, 6.957e+08 m |
| Standard solar-model core density (published) | 1.50e+05 kg/m³ |
| Standard solar-model core temperature (published) | 1.570e+07 K |
| Standard solar-model central pressure (published) | 2.477e+16 Pa |
Procedure
- Compute the uniform-density hydrostatic central-pressure estimate P_c ≈ (3/8π)GM²/R⁴ and compare it (percent difference) to the published standard-solar-model value.
- Compute the electron-scattering opacity κ_es = σ_T(1+X)/(2m_p) for X = 0.70, and the schematic Kramers-law opacity κ_Kramers at the published core density and temperature, and compare the two.
- Compute the radiation-to-gas pressure ratio P_rad/P_gas at the published core density and temperature (using μ = 0.62 for fully ionized solar composition), and state whether radiation pressure is negligible, comparable to, or dominant over gas pressure in the Sun's core.
- Using the equation of state P = ρkT/(μm_p) + (1/3)aT⁴, compute the total pressure implied by the published core density and temperature, and compare it (percent difference) to the published central pressure used in step 1.
Analysis and Uncertainty
The uniform-density hydrostatic estimate in step 1 ignores the Sun's true, centrally concentrated density profile; state whether the direction of the discrepancy you find (over- or under-estimate) is consistent with the same discrepancy direction found for the same calculation in ASTR 310, Lab 03.
Deliverables
- Completed central-pressure, opacity, and pressure-ratio calculations with full unit conversions shown.
- Written comparison of the equation-of-state pressure (step 4) to the published central pressure.
- Written discussion of the hydrostatic-estimate discrepancy direction, cross-checked against ASTR 310.
Assessment Criteria
- Correct unit conversions and arithmetic in all four steps.
- Correct qualitative and quantitative classification of the radiation-to-gas pressure ratio.
- Valid cross-check against the ASTR 310 Lab 03 precedent for the hydrostatic-estimate discrepancy direction.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 16.1-16.2.
- Standard solar-model core density, temperature, and central pressure: standard published values, not independently re-verified this session; see
materials/ASTR330/reference-log.md. - Generated by
materials/ASTR330/src/generate_astr330_content.py.