Please answer all parts (a), (b) and (c) of the question. For reference, the textbook used is Barbara Ryden's Introduction to Cosmology.

(a) Uncertainties on observed distances to astronomical objects are typically of order 5% (or more). At what redshift is it necessary to start paying attention to whether your distance indicator measures luminosity distance (standard candle) or angular diameter distance (standard ruler)? More precisely, compute (approximately) the redshift at which the difference between these two measures corresponds to a 5% difference. Do this for a cosmology With 9m); 2 0.3, QM] : 0, and 9A,!) : 0.7, and H0 : 2.23 X 1018 s'1 using the Taylor series approach (i.e. using the go approach discussed in class and in the textbook). (b) Galaxies have typical peculiar velocities of order 500 km/s (i.e. they are moving at these velocities relative to an observer locally at rest in the expanding spacetime). If we assume the same cosmology as above, at what distance do we need to go to (i.e. what is the minimum distance d of an astronomical object) in order that galaxy peculiar velocities introduce errors of less than 5% in the measured distance? (c) On this distance scale, do we need to worry about whether the measured distance is a lumi nosity distance or an angular diameter distance? Justify your