Problem set for Unit 5.
Using your Kepler-derived Sirius AB total mass from Problem Set 04 (3.079 M⊙) and the independently measured mass ratio M_B/M_A = 0.4935, split the total mass into individual masses for Sirius A and Sirius B.
Europa (M = 4.7998e+22 kg, R = 1.5608e+06 m) orbits Jupiter (mean density 1326 kg/m³) at a semimajor axis of 671100 km. Compute Europa's mean density, then its rigid-body Roche limit around Jupiter, and state whether Europa is safely outside its own Roche limit.
Compute Europa's own surface gravity (g = GM_Europa/R_Europa²) and the differential tidal acceleration across Europa due to Jupiter, and express the tidal acceleration as a percentage of Europa's own surface gravity. Compare your result (as a ratio) to Io's tidal-acceleration-to-surface-gravity percentage from Lecture 10/Lab 05, and state which moon experiences the stronger relative tidal stress and why (consider both distance and radius).
Europa, like Io, is held in a slightly eccentric orbit by the same Laplace orbital resonance (with Io and Ganymede). Europa is thought to have a subsurface liquid water ocean, plausibly maintained partly by tidal heating. Using your Problem 3 comparison to Io, explain qualitatively why Europa's tidal heating is expected to be significant but weaker than Io's, consistent with Europa showing an icy (not volcanically resurfaced) surface.
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 reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 18.4-18.5 and Chapter 3.6.
materials/ASTR310/data/ where referenced above.