One of the neat things about the visit to Urth is the way that the visitors give us a different, objective view of Nessus and the dying Old Sun. They give new figures on the ruinification of Nessus, the size, timeframe, and all that--they really are our stand-ins, doing exactly what we Wolfe readers would do if given the chance.
And when they notice how bloated the Old Sun is, we get the inference of another piece of the Lune's orbit puzzle (in fact, it might be the main reason why Lune is so much closer to Urth than the Moon is to Earth): it has to be, in order to fully eclipse the bloated Old Sun!
=mantis=
*This is WHORL, for discussion of Gene Wolfe's Book of the Long Sun.