1. Parallax to distance
d = 1/p(arcsec) = 1/(194.95/1000) = 5.13 pc = 5.13 × 3.26 = 16.72 ly.
| Criterion | Points |
|---|---|
| Correct parallax-to-parsec conversion | 8 |
| Correct parsec-to-light-year conversion | 7 |
Worked Solutions
2. Distance modulus
m − M = 5log10(5.13) − 5 = -1.450. M = 0.77 − (-1.450) = 2.22.
| Criterion | Points |
|---|---|
| Correct distance modulus | 8 |
| Correct absolute magnitude | 7 |
3. Mass defect and energy release
Δm = 4 × 1.007825 − 4.002602 = 0.028698 u. ΔE = 0.028698 × 931.494 = 26.73 MeV.
| Criterion | Points |
|---|---|
| Correct mass defect | 8 |
| Correct energy conversion | 7 |
4. Textbook problem: solar neighborhood
1 pc = 206,265 AU × 1.496 × 10⁸ km/AU = 3.086 × 10¹³ km. In light-years: 3.086 × 10¹³ km / (9.461 × 10¹² km/ly) = 3.26 ly, matching the conversion factor used in Problem 1.
| Criterion | Points |
|---|---|
| Correct AU-to-km derivation | 8 |
| Correct final ly comparison | 7 |
Grading Notes
Award full marks for correct method, units, and a numeric result consistent with the arithmetic shown (allow reasonable rounding). Verify the student re-derives the number rather than quoting it from the lecture without adapting it to the problem's specific inputs.