Parker Solar Probe and Remote-Sensing Geometry
At r=6 R_sun (closer than r_c=4.62 R_sun’s outer region, r/r_c=1.30), the predicted Parker-wind speed is v=181 km/s, versus 250 km/s at the real 9.86 R_sun perihelion -- the closer, hypothetical perihelion samples a *slower* wind, since it is closer to (or below) the critical point where the wind has not yet fully accelerated.
| Criterion | Points |
|---|---|
| Correct numerical solve at 6 R_sun | 8 |
| Correct slower-speed-closer-in conclusion | 7 |
Ten million independently measured, precisely determined mode frequencies constrain the interior sound-speed profile at many different depths and latitudes simultaneously (each mode's frequency depends on an integral of sound speed along its own distinct ray path), providing a hugely over-determined inversion problem -- vastly more constraining than a single inferred core temperature, which is only one number derived indirectly from overall energy-balance/neutrino arguments (Lecture 01).
| Criterion | Points |
|---|---|
| Correct qualitative explanation of over-determined inversion vs single-number inference | 10 |
Fraction unusable at 1.5 R_sun occulting radius = 0.250 (25.0%); at 2.0 R_sun, fraction = 0.333 (33.3%) -- a larger occulting disk *decreases* the coronagraph's useful observing fraction, from 75% to about 67% of the total field of view.
| Criterion | Points |
|---|---|
| Correct fraction arithmetic for both cases | 8 |
| Correct decreasing-usable-fraction conclusion | 7 |
Ratio = 191/29.8 = 6.4 -- PSP was moving about 6 times faster at its perihelion than Earth moves in its own orbit around the Sun.
| Criterion | Points |
|---|---|
| Correct ratio arithmetic | 15 |
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.