Astronomers and cosmologists have an astonishing array of distance indicators at their disposal. Here we will compare just three of them: comoving, angular diameter and lookback distances.
Comoving distance is the proper distance of a source in free, non-expanding space, determined by how long light takes to travel the distance today if space is not expanding (similar to radar distance in free space). It is called "D_now" in what follows.
Angular diameter distance is defined in terms of the object's actual size and the angular size of the object as viewed from Earth. It is approximated by the comoving distance divided by a function of the observed redshift of an object, giving the proper distance of the object when the light left it. It is called "D_then" in what follows.
Lookback distance is determined by how long light takes to travel the distance in an expanding space. It is mostly referred to as lookback time and not distance, but multiplying the time by the speed of light gives a distance. It is called "D_light" in what follows.
What follows is a set of equations and curves for the cosmic distances. If the text, equations and/or graphics below are not clear on your browser, click here for a more readable .pdf, where you can easily control the 'zoom' and/or magnification (provided that you have a pdf-reader on your system).
A more complete picture of cosmological equations and how to integrate them can be found in the eBook Relativity 4 Engineers.
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