Radial Velocity and Transit Method
K ∝ P^(-1/3), so doubling P scales K by 2^(-1/3)=0.7937, i.e. K would drop to about 79.4% of its original value, roughly 44.4 m/s instead of 55.9 m/s.
| Criterion | Points |
|---|---|
| Correct derivation of the scaling exponent | 6 |
| Correct numeric application | 5 |
| Correct interpretation | 4 |
Using the same numerical mass-function solve as Lecture 01's worked example with K=25.0 m/s, P=10.0 d, M*=1.11 Msun, e=0: Mp sin(i) ≈ 0.284 MJup.
| Criterion | Points |
|---|---|
| Correct mass-function setup | 6 |
| Correct numeric solve/units | 6 |
| Reasonable final value | 3 |
Method (a): delta=(Rp/Rstar)^2 = 1.295%. Method (b): density from mass/radius gives ρ=360 kg/m^3; using M and this density to recover R gives back the same Rp (since R was used to compute the density), so the two methods necessarily agree by construction -- the pedagogical point is recognizing this circularity rather than treating (b) as an independent check.
| Criterion | Points |
|---|---|
| Correct direct transit-depth calculation | 6 |
| Correct recognition of circularity in method (b) | 6 |
| Clear units/derivation | 3 |
T ∝ P^(1/3): at P=1.0 d versus the real 3.52 d, T scales by (1.0/3.525)^(1/3)=0.657, giving T≈2.08 h instead of 3.17 h -- a shorter transit is harder to schedule precisely but occurs more frequently (shorter period), a real trade-off in real observing proposals.
| Criterion | Points |
|---|---|
| Correct scaling exponent and application | 8 |
| Correct qualitative trade-off statement | 7 |
ρ = 360 kg/m^3 = 0.360 g/cm^3 -- lower than water (1.0 g/cm^3) and far below any solar-system planet in materials/ASTR350/data/, confirming its gas-giant, low-density interior rather than similarity to any specific solar-system body.
| Criterion | Points |
|---|---|
| Correct density calculation and unit conversion | 8 |
| Correct, well-justified comparison conclusion | 7 |
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 (AU/m, days/seconds, Jupiter/Earth mass-radius units), for comparative-magnitude statements given in the wrong direction, and for level-1/level-2/level-3 data-provenance conflation (e.g., presenting an illustrative Miller-Urey bar height as a precise measured yield) -- these are the most common sources of mistakes in this course.