Problem set for lecture unit 7.
A photometric measurement has a Poisson term of 8.0 mmag, a flat-field residual of 4.0 mmag, and an extinction-correction residual of 6.0 mmag. Compute the total RSS error budget and identify the dominant term.
Using the collecting-area (D²) scaling, estimate how much longer an exposure with an 8.1 m telescope (Gemini-class) would need to reach the same SNR as a 300 s exposure with the 10 m Keck aperture, in the background-limited regime.
A science case requires resolving a 30 milliarcsecond angular separation at K band. Using Keck's AO-corrected diffraction-limited FWHM (46.7 mas, Lecture 11), determine whether this requirement is achievable with Keck's AO system at the representative Strehl ratio used throughout this course, and justify your answer.
Write a short (4-6 sentence) technical justification paragraph, in the style of Lecture 14's capstone framework, that combines your Problem 1 error budget and Problem 3 resolution check into a single coherent argument for or against a specific proposed Keck AO observation.
Submit a complete derivation with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without a visible derivation receives partial credit at most, and quoting a lecture number without adapting it to this problem's specific inputs receives no credit for that step.
OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 6 (astronomical instruments), descriptive only; this course exceeds that introductory treatment throughout.
materials/ASTR340/data/ where referenced above.