We present a deep optical survey of Uranus ’ Hill sphere for small satellites .
The Subaru 8-m telescope was used to survey about 3.5 square degrees with a 50 \% detection efficiency at limiting red magnitude m _ { R } = 26.1 mag .
This magnitude corresponds to objects that are about 7 km in radius ( assuming an albedo of 0.04 ) .
We detected ( without prior knowledge of their positions ) all previously known outer satellites and discovered two new irregular satellites ( S/2001 U2 and S/2003 U3 ) .
The two inner satellites Titania and Oberon were also detected .
One of the newly discovered satellites ( S/2003 U3 ) is the first known irregular prograde of the planet .
The population , size distribution and orbital parameters of Uranus ’ irregular satellites are remarkably similar to the irregular satellites of gas giant Jupiter .
Both have shallow size distributions ( power law indices q \sim 2 for radii > 7 km ) with no correlation between the sizes of the satellites and their orbital parameters .
However , unlike those of Jupiter , Uranus ’ irregular satellites do not appear to occupy tight distinct dynamical groups in semi-major axis versus inclination phase space .
Two groupings in semi-major axis versus eccentricity phase space appear to be statistically significant .