ASTR 101 Problem Set 03 Solutions

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Worked Solutions and Rubric Notes

1. Frequency from Wavelength

650 nm = 6.50e-7 m, so nu = 3.00e8 / 6.50e-7 = 4.62e14 Hz. 450 nm = 4.50e-7 m, so nu = 6.67e14 Hz. Blue light has higher frequency.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

2. Doppler Shift of H-alpha

Delta lambda = 1.7 nm. Fractional shift = 1.7/656.3 = 0.00259. v = 0.00259c = 777 km/s using c = 3.00e5 km/s. The line is redshifted, so the motion is away along the line of sight.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

3. Collecting Area

Diameter ratio is 2.0/0.20 = 10. Area scales as D^2, so area ratio is 100. It improves photon collection and ability to detect faint objects. It does not automatically fix atmospheric seeing, poor tracking, detector noise, or bad calibration.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

4. Resolution Limit

For the same wavelength, theta scales as 1/D. The 1.0 m telescope has 10 times smaller diffraction limit than the 0.10 m telescope. Ground-based images may be limited by atmospheric seeing, optics, focus, tracking, and detector sampling.

Rubric: Award credit for setup, physical reasoning, units, calculation or evidence, and interpretation. Distinguish arithmetic slips from conceptual errors.

Textbook Problem Rationale

OpenStax Astronomy 2e, Astronomical Instruments exercises, Review Question 1, extracted index line 8320: components of a modern astronomical instrument.
OpenStax Astronomy 2e, Astronomical Instruments exercises, Review Question 4, extracted index line 8326: why larger telescope apertures are better.
OpenStax Astronomy 2e, Astronomical Instruments exercises, Figuring for Yourself 28, extracted index line 8390: pupil diameter and light gathering.
OpenStax Astronomy 2e, Astronomical Instruments exercises, Figuring for Yourself 30, extracted index line 8394: Keck telescope light gathering compared with an amateur telescope.

Use these recommendations for additional practice or adaptation. Confirm numbering against the final adopted edition before assigning.