Extend this unit's hydrostatic scale-height tool to new temperatures and a hypothetical star, and connect the radiative-convective boundary to physical units.
Compute the scale height using the chromospheric top temperature (T=2e+04 K) and a mean molecular weight intermediate between the photospheric and coronal values, mu=1.0 (partially ionized chromospheric gas, a reasonable order-of-magnitude choice). Compare your result to the lab's photospheric and coronal scale heights and state where it falls between the two.
A hypothetical star has the Sun's mass but twice its radius. Compute this star's surface gravity and state whether its atmospheric scale height (at the same temperature and mu as the Sun's photosphere) would be larger or smaller than the Sun's own photospheric scale height, and by what factor.
Compute the ratio T_core/T_eff using the values in this unit's data table, and compute the same ratio using T_corona/T_eff instead. Compare the two ratios and explain, in one sentence, why the corona's temperature can exceed the photosphere's despite being much farther from the fusion-powered core.
Convert the radiative-convective boundary's fractional radius (r=0.71 R_sun) into physical units (km), and compute what fraction of the Sun's total volume lies inside this boundary (volume scales as r^3 for a sphere).
Submit a complete derivation with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without a visible derivation receives partial credit at most, and quoting a lecture number without adapting it to this problem's specific inputs receives no credit for that step.
OpenStax Astronomy 2e (local extracted reference copy: references/openstax-astronomy-2e-extracted.txt) covers the Sun in Chapter 15 ("The Sun: A Garden-Variety Star"): 15.1 The Structure and Composition of the Sun, 15.2 The Solar Cycle, and 15.3 Solar Activity above the Photosphere. Chapter 15’s section numbering was cross-checked directly against its own embedded figure numbering this session (Figures 15.1 through 15.24 all appear under their matching section headers with no offset), so this citation is verified against the local extracted text rather than extrapolated by analogy from a prior course. OpenStax’s treatment throughout Chapter 15 is descriptive and qualitative; nearly every quantitative derivation in this course (the hydrostatic solar-atmosphere/scale-height argument, the sunspot magnetic-pressure balance, the Parker solar-wind critical-point argument and its numerical transonic solution, flare free-energy budgets, the Chapman-Ferraro magnetopause standoff distance, and the Dessler-Parker-Sckopke ring-current/Dst relation) goes well beyond OpenStax Astronomy 2e’s introductory level; each lecture states explicitly where this course extends beyond the assigned reading.
materials/ASTR370/data/ where referenced above.