@Pythagorean,
Astronomers use Cepheid variable stars (Standard Candles) to assess size and distance. Using the same idea of a candle light dimming due to distance they can work out both the brightness size and distance of objects near its vicinity
There are whole Cepheid Galaxies like great light houses shining in the cosmos
Standard Candles
The term standard candle applies to celestial objects with well-defined absolute magnitudes which are assumed to not vary with age or distance. Type I and II Cepheids and
RR Lyraes are all examples. All Cepheids with a certain period are assumed to have the same absolute magnitude.
Measuring the apparent magnitude of a Cepheid then allows us to determine its distance using the period-luminosity relationship. If two Cepheids have the same period but is fainter than the other it must be further away. RR Lyraes similarly can be used as standard candles although as their intrinsic luminosity is lower than Classical Cepheids they cannot be detected at the great distances of Cepheids.
Type Ia supernovae may be approximated to standard candles as their absolute magnitude reaches about -19 at maximum brightness. Given their extreme luminosity they can be used to probe much further out into the Universe than Cepheids. Two recent projects, the
Supernova Cosmology Project and the
High-Z SN Search have both observed dozens of supernovae in distant galaxies to try and determine H and the geometry of the Universe.
Both teams independently arrived at the the conclusion that not only is our Universe expanding but it is actually accelerating, a result that the prestigious American magazine
Science announced was the research advance of 1998.