  We study the advantage of the co-existence of future ground and space based
gravitational wave detectors, in estimating the parameters of a binary
coalescence. Using the post-Newtonian waveform for the inspiral of non-spinning
neutron star-black hole pairs in circular orbits, we study how the estimates
for chirp mass, symmetric mass ratio, and time and phase at coalescence are
improved by combining the data from different space-ground detector pairs.
Since the gravitational waves produced by binary coalescence also provide a
suitable domain where we can study strong field gravity, we also study the
deviations from general relativity using the parameterized post-Einsteinian
framework. As an example, focusing on the Einstein telescope and DECIGO pair,
we demonstrate that there exists a sweet spot range of sensitivity in the
pre-DECIGO phase where the best enhancement due to the synergy effect can be
obtained for the estimates of the post-Newtonian waveform parameters as well as
the modification parameters to general relativity.
