1. Calibration calculation
I_cal = (18500 − 2046.0) / 1.02 = 16454.0 / 1.02 = 16131.4 ADU.
| Criterion | Points |
|---|---|
| Setup and units | 5 |
| Calculation | 5 |
| Interpretation | 5 |
Worked Solutions
2. Airmass and extinction
z = 90° − 25° = 65°. X = 1/cos(65°) = 2.37. Δm = 0.15 × 2.37 = 0.35 mag.
| Criterion | Points |
|---|---|
| Setup and units | 5 |
| Calculation | 5 |
| Interpretation | 5 |
3. Uncertainty budget
σ_total = √(1.71² + 1.32²) = √(2.92 + 1.7424) = 2.16 ADU. The two terms are comparable (within about 30% of each other), so neither cleanly dominates; this indicates the calibration-floor noise on this camera comes from a mix of read noise (captured by the bias master) and residual dark-frame noise (captured by the matched-exposure dark master), not from one overwhelming source.
| Criterion | Points |
|---|---|
| Quadrature method | 8 |
| Correct comparable-terms reasoning | 7 |
4. Observing-plan critique
Noise term = 9 × (450 + 5 + 64) = 4671. SNR = 700/√(700+4671) = 9.55. This is still a secure detection (SNR > 5), but substantially degraded from the dark-sky assumption, and the student’s plan should have stated the actual sky brightness rather than assuming a dark-sky value.
| Criterion | Points |
|---|---|
| Correct SNR | 8 |
| Correct critique of the plan | 7 |
Grading Notes
Award full marks for correct method, units, and a numeric result consistent with the arithmetic shown (allow reasonable rounding). Common partial-credit errors: omitting units, failing to combine uncertainties in quadrature, or overstating the confidence of a marginal (SNR 3–5) result.