Student assignment · due date set by instructor
Submit complete derivations, units, assumptions, and a short physical interpretation. Include reproducible code for multi-step calculations and show intermediate values. Cite any external catalog or data product with its release/version. Collaboration on methods is allowed; submitted derivations and prose must be your own. Corrections and resubmissions with a change log are encouraged.
For a line at 1420.40575177 MHz measured 0.500 MHz lower, compute v_radio and the velocity width of a 10-kHz channel. State the validity regime.
Required: derivation, units, intermediate values, uncertainty/assumption, and an interpretation that identifies what the result does not prove.
For integrated brightness 120 K x 8 km/s, compute optically thin N_HI. If the optical depth is not small, state the direction of bias and what additional measurement is needed.
Required: derivation, units, intermediate values, uncertainty/assumption, and an interpretation that identifies what the result does not prove.
A Gaussian line has peak 80 K and FWHM 12 km/s. Derive its integrated area using the Gaussian area factor 1.0645 and calculate thin N_HI. Compare with a rectangular approximation peak x FWHM and quantify the fractional approximation gap.
Required: derivation, units, intermediate values, uncertainty/assumption, and an interpretation that identifies what the result does not prove.
OpenStax Astronomy 2e §§5.6 and 20.2, Chapter 20 Review Question 5, and Chapter 6 Thought Question 23 (the local exercise index identifies this as a Thought Question, not a Review Question). HI4PI Collaboration (2016), Table 1 and §3.1, provides the real survey response and optically-thin column relation.
The numbered anchors were checked against the local OpenStax Astronomy 2e extraction; exercise numbers/page breaks can vary by edition. Before assigning through an LMS, the instructor should spot-check each recommendation against the adopted print/PDF edition. Exact source scope and extraction notes are in ../reference-log.md. Do not present the synthetic teaching records as telescope observations.
Three problems, 100 points total. Submit a PDF or HTML report plus code/notebook where requested. Show figures with axes, units, captions, and data provenance.