1. Differential magnitude
Δm = −2.5×log10(0.945/0.998) = −2.5×log10(0.9469) = 0.0592 mag.
| Criterion | Points |
|---|---|
| Correct ratio | 5 |
| Correct Δm | 10 |
Worked Solutions
2. Dip depth
Depth = 0.0592 − 0.0054 = 0.0538 mag ≈ 54 millimagnitudes.
| Criterion | Points |
|---|---|
| Correct baseline subtraction | 8 |
| Correct depth | 7 |
3. Plate scale
Plate scale = 16.8/20.4 = 0.824 arcsec/pixel.
| Criterion | Points |
|---|---|
| Correct setup | 5 |
| Correct value | 10 |
4. Rate of motion
Rate = 16.8 arcsec / 12 min = 1.40 arcsec/min. This is far faster than a typical main-belt asteroid (well under 1 arcsec/min near opposition), so it is more consistent with a fast-moving near-Earth object.
| Criterion | Points |
|---|---|
| Correct rate | 8 |
| Correct classification with justification | 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.