= 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 $d=c\Delta t/2$, 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 $p$, $d\simeq b/p$, or $d$ in parsecs equals $1/p$ when $p$ is in arcseconds and $b$ 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> $L$ and observed bolometric flux $F$,
$$
\boxed{d_L=\sqrt{\frac{L}{4\pi F}},\qquad
m-M=5\log_{10}\left(\frac{d_L}{10\,\mathrm{pc}}\right)}
$$
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>.
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