  Gravitational-wave observations by the Laser Interferometer
Gravitational-Wave Observatory (LIGO) and Virgo have provided us a new tool to
explore the Universe on all scales from nuclear physics to the cosmos and have
the massive potential to further impact fundamental physics, astrophysics, and
cosmology for decades to come. In this paper we have studied the science
capabilities of a network of LIGO detectors when they reach their best possible
sensitivity, called A#, given the infrastructure in which they exist and a new
generation of observatories that are factor of 10 to 100 times more sensitive
(depending on the frequency), in particular a pair of L-shaped Cosmic Explorer
observatories (one 40 km and one 20 km arm length) in the US and the triangular
Einstein Telescope with 10 km arms in Europe. The presence of one or two A#
observatories in a network containing two or one next generation observatories,
respectively, will provide good localization capabilities for facilitating
multimessenger astronomy and precision measurement of the Hubble parameter. Two
Cosmic Explorer observatories are indispensable for achieving precise
localization of binary neutron star events, facilitating detection of
electromagnetic counterparts and transforming multimessenger astronomy. Their
combined operation is even more important in the detection and localization of
high-redshift sources, such as binary neutron stars, beyond the star-formation
peak, and primordial black hole mergers, which may occur roughly 100 million
years after the Big Bang. The addition of the Einstein Telescope to a network
of two Cosmic Explorer observatories is critical for accomplishing all the
identified science metrics. For most metrics the triple network of next
generation terrestrial observatories are a factor 100 better than what can be
accomplished by a network of three A# observatories.
