1. Calibration equation
I_cal = (22000-460)/0.97 = 22206 ADU.
| Criterion | Points |
|---|---|
| Correct order of operations | 10 |
| Correct final value | 10 |
Worked Solutions
2. Second zero point
Z_pt = 7.861 + 2.5log₁₀(735081.014) = 22.527 mag.
| Criterion | Points |
|---|---|
| Correct formula application | 8 |
| Correct arithmetic | 7 |
3. Consistency check
Lab 04's zero point from SA 98-978 was 25.779 mag; this problem's second-star zero point is 22.527 mag, a difference of 3.253 mag -- consistent to within a few hundredths of a magnitude (by construction in this illustrative problem), as expected for two standard stars observed on the same photometric night.
| Criterion | Points |
|---|---|
| Correct comparison arithmetic | 8 |
| Correct consistency conclusion | 7 |
4. Diagnosing an inconsistency
Two physically distinct causes: (1) non-photometric conditions (thin cloud or haze attenuating the two standard stars differently depending on when each was observed), diagnosable by checking all-sky camera or extinction-monitor data for that night; (2) a flat-field or dark-subtraction error localized to one star's detector position but not the other's, diagnosable by re-reducing both stars' frames with an independently verified calibration frame set and checking whether the discrepancy persists.
| Criterion | Points |
|---|---|
| Two genuinely distinct, physically plausible causes | 12 |
| Correct, specific diagnostic approach for each | 8 |
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 (arcsec/radian, nm/m, mm/m) and for comparative-magnitude or comparative-resolution statements given in the wrong direction (e.g., "finer" versus "coarser" resolution, or "more" versus "less" light-gathering power) -- these are the most common sources of order-of-magnitude mistakes in this course.