Solution

ID: past-exam-of-the-general-relativity-and-cosmology-course-of-the-university-of-oxford/2018/3/a/solution

The cosmic distance ladder starts by calibrating a physical baseline. Radar echoes from planets or spacecraft give a round-trip light time and hence a distance , after accounting for orbital motion and propagation delays. Combining this with orbital geometry fixes the Earth-Sun orbital scale; directly timing a reflected pulse from the solar surface is not required.
That baseline supplies annual stellar parallax: for small parallax angle , , or in parsecs equals when is in arcseconds and is one astronomical unit. Nearby parallax distances calibrate stellar absolute magnitudes. Main-sequence fitting extends the scale to star clusters, and the calibrated Cepheid period-luminosity relation gives luminosities for Cepheids visible in nearby galaxies.
Cepheid-host galaxies then calibrate Type Ia supernovae. After light-curve and colour standardization, their high luminosities permit distances to much more remote galaxies. For a source of calibrated luminosity and observed bolometric flux ,
with consistent bandpass definitions and corrections. Interstellar extinction, composition, stellar-population differences and calibration uncertainty must be propagated through the steps. Redshift can subsequently provide a distance within a fitted cosmological model; using it alone cannot independently calibrate the Hubble constant.

New to topics? Read the docs here!