  The Galactic massive black hole (MBH), with a mass of Mbh=3.6\times10^6 Solar
masses, is the closest known MBH, at a distance of only 8 kpc. The proximity of
this MBH makes it possible to observe gravitational waves from stars with
periapse in the observational frequency window of the Laser Interferometer
Space Antenna (LISA). This is possible even if the orbit of the star is very
eccentric, so that the orbital frequency is many orders of magnitude below the
LISA frequency window, as suggested by Rubbo et al. (2006). Here we give an
analytical estimate of the detection rate of such gravitational wave bursts.
The burst rate is critically sensitive to the inner cut-off of the stellar
density profile. Our model accounts for mass-segregation and for the physics
determining the inner radius of the cusp, such as stellar collisions, energy
dissipation by gravitational wave emission, and consequences of the finite
number of stars. We find that stellar black holes have a burst rate of the
order of 1 per year, while the rate is of order 0.1 per year for main sequence
stars and white dwarfs. These analytical estimates are supported by a series of
Monte Carlo samplings of the expected distribution of stars around the Galactic
MBH, which yield the full probability distribution for the rates. We estimate
that no burst will be observable from the Virgo cluster.
