  Recent exoplanet surveys have predicted a very large population of planetary
systems in our galaxy, more than one planet per star on the average, perhaps
totalling about two hundred billion. These surveys, based on electro-magnetic
observations, are limited to a very small neighbourhood of the solar system and
the estimations rely on the observations of only a few thousand planets. On the
other hand, orbital motions of planets around stars are expected to emit
gravitational waves (GW), which could provide information about the planets not
accessible to electro-magnetic astronomy. The cumulative effect of the planets,
with periods ranging from few hours to several years, is expected to create a
stochastic GW background (SGWB). We compute the characteristic GW strain of
this background based on the observed distribution of planet parameters. We
also show that the integrated extragalactic background is comparable or less
than the galactic background at different frequencies. Our estimate shows that
the net background is significantly below the sensitivities of the proposed GW
experiments in different frequency bands. However, we notice that the peak of
the spectrum, at around $10^{-5}$Hz, is not too far below the proposed space
based GW missions. A future space based mission may be able to observe or
tightly constrain this signal, which will possibly be the only way to probe the
galactic population of exoplanets as a whole.
