How are redshift, temperature, distance and time related?
Briefly

How are redshift, temperature, distance and time related?
"But that's only because our planet, our Solar System, our galaxy, and even our Local Group are all gravitationally bound together. The space that separates two points within these structures is not expanding, but if we look to the broader Universe and to all galaxies more than about 5 million light-years away, the expansion of the Universe begins to matter. We have a few different parameters we can use to describe any distant object, including redshift,"
"Let's start with the easiest thing to measure: redshift. When you measure a distant object, what you're actually measuring is its light, or the photons (or, equivalently, light waves) emitted from that source that are now arriving at your eyes. When we have atoms, molecules, or ions in a laboratory setting, we can see that there are three types of light signals that can emerge from them."
Nearby objects within gravitationally bound systems produce light whose arrival time equals their distance in years, exhibit a cosmological redshift of zero, and share the present 2.725 K background temperature. Beyond roughly 5 million light-years the expansion of space changes photon wavelengths and separates distance measures, so redshift, cosmic temperature, comoving distance, and lookback time no longer correspond directly. Redshift is the most direct observable because it measures how much photon wavelengths have stretched during transit. Spectral measurements include continuum thermal emission and discrete line emission from atoms, molecules, or ions, which together reveal temperature, composition, and motion.
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