1. A faster CME's naive transit time
t(2x speed) = 13.23 hr, exactly half the real event's naive transit time (26.5 hr) -- confirming t ∝ 1/v at fixed distance.
| Criterion | Points |
|---|---|
| Correct arithmetic | 8 |
| Correct factor-of-2 confirmation | 7 |
Worked Solutions
2. Parker wind speed at Mercury's orbit
r/r_c(Mercury)=18.14. Solving gives u=3.352, v=482 km/s -- slower than the 1 AU speed (559 km/s), since the wind continues to accelerate outward beyond the critical point (r/r_c(Mercury) is smaller than r/r_c(1 AU), and the transonic solution's speed increases monotonically with r beyond r_c).
| Criterion | Points |
|---|---|
| Correct r/r_c computation for Mercury | 5 |
| Correct numerical solve and speed | 5 |
| Correct slower-at-Mercury conclusion with reasoning | 5 |
3. Sensitivity to coronal temperature
At T=1.0e6 K, c_s=117 km/s (lower than the 144 km/s used in the lab), and r_c=6.93 R_sun -- since r_c ∝ 1/c_s^2, a cooler corona has a *larger* critical radius, moving the transonic point farther from the Sun.
| Criterion | Points |
|---|---|
| Correct cooler sound speed | 7 |
| Correct larger-critical-radius conclusion | 8 |
4. Drag-model sensitivity
A longer time constant (25 hr vs 15 hr) means the CME approaches the ambient wind speed more slowly, so it remains closer to its initial fast speed for longer -- predicting a *shorter* transit time than the 15-hour-time-constant model, not a longer one, since the CME spends more of its transit moving faster.
| Criterion | Points |
|---|---|
| Correct qualitative direction (slower relaxation -> shorter transit) | 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 (Gauss vs Tesla, nT vs T, km/s vs m/s, hours vs seconds), for comparative-magnitude statements given in the wrong direction, and for level-1/level-2/level-3 data-provenance conflation (e.g., presenting the order-of-magnitude flare free-energy estimate as a precise measurement, or presenting a Carrington-Dst estimate as a directly measured historical value) -- these are the most common sources of mistakes in this course.