  Doppler tracking of interplanetary spacecraft provides the only method
presently available for broad-band searches of low frequency gravitational
waves. The instruments have a peak sensitivity around the reciprocal of the
round-trip light-time T of the radio link connecting the Earth to the
space-probe and therefore are particularly suitable to search for coalescing
binaries containing massive black holes in galactic nuclei. A number of Doppler
experiments -- the most recent involving the probes ULYSSES, GALILEO and MARS
OBSERVER -- have been carried out so far; moreover, in 2002-2004 the CASSINI
spacecraft will perform three 40 days data acquisition runs with expected
sensitivity about twenty times better than that achieved so far. Central aims
of this paper are: (i) to explore, as a function of the relevant instrumental
and astrophysical parameters, the Doppler output produced by in-spiral signals
-- sinusoids of increasing frequency and amplitude (the so-called chirp); (ii)
to identify the most important parameter regions where to concentrate intense
and dedicated data analysis; (iii) to analyze the all-sky and all-frequency
sensitivity of the CASSINI's experiments, with particular emphasis on possible
astrophysical targets, such as our Galactic Centre and the Virgo Cluster.
