1. Unit conversion
P = 0.102424063 days × 86400 s/day = 8.849439e+03 s. a = 832000 km × 1000 m/km = 8.320000e+08 m.
| Criterion | Points |
|---|---|
| Correct period conversion | 8 |
| Correct semimajor-axis conversion | 7 |
Worked Solutions
2. Total mass from Kepler’s third law
(m1+m2) = 4π²a³/(GP²) = 2.1871 M⊙.
| Criterion | Points |
|---|---|
| Correct formula rearrangement | 8 |
| Correct arithmetic and final mass | 12 |
3. Cross-check
Percent agreement = |2.187 − 2.182| / 2.182 × 100% = 0.24%.
| Criterion | Points |
|---|---|
| Correct percent-agreement arithmetic | 8 |
| Correct comparison value used | 7 |
4. Synthesis
A strong answer notes that the orbital (Keplerian) total-mass determination depends only on the measured period and semimajor axis and Newtonian/relativistic gravity, while the individually measured neutron-star and white-dwarf masses depend on entirely different physics (pulsar timing, Shapiro delay, and white-dwarf spectroscopy); their close agreement is therefore not a coincidence but strong, largely independent confirmation of both methods, exactly analogous to ASTR 310 Lecture 14's radiative-versus-dynamical cross-check for Alpha Centauri AB.
| Criterion | Points |
|---|---|
| Correct identification of the two independent methods | 10 |
| Correct analogy to the ASTR 310 precedent | 10 |
Grading Notes
Award full marks for correct method, units, and a numeric result consistent with the arithmetic shown (allow reasonable rounding). Verify that the student re-derives the number for this problem's specific inputs rather than quoting a lecture example without adaptation. Watch specifically for unit-conversion errors (km/AU/m, years/seconds, kg/M⊙) and for comparative-magnitude statements stated in the wrong direction (e.g., "X times greater" versus "a small fraction of") -- these are the most common sources of order-of-magnitude mistakes in this course.