Scope: Lectures 01-02. Four questions; submit derivations and code/output where requested.
State units and model assumptions. Keep unrounded values in code and round only in your final communication. Revisions and resubmissions are encouraged.
Question 1
A spectral line has rest wavelength 500.0 nm and is observed at 510.0 nm. Calculate z and state what additional assumption is required before treating cz as a recession speed.
Work to show: equations, units, assumptions, and a reproducible computation where requested.
Question 2
Using the course fiducial H0, calculate c/H0 in Mpc and the Hubble time in Gyr. Explain why the Hubble time is not automatically the age of the Universe.
Work to show: equations, units, assumptions, and a reproducible computation where requested.
Question 3
Starting from the distance-modulus definition, derive the low-z approximation mu=5 log10(cz/H0)+25 when D_L is expressed in Mpc. State where the approximation fails.
Work to show: equations, units, assumptions, and a reproducible computation where requested.
Question 4
A nearby galaxy has a 300 km/s peculiar velocity. At what redshift is cz equal to 300 km/s? Explain why this sets a practical scale for peculiar-velocity importance.
Work to show: equations, units, assumptions, and a reproducible computation where requested.