  The absolute magnitude and perihelion distributions of long-period comets are
derived, using data from the Lincoln Near-Earth Asteroid Research (LINEAR)
survey. The results are surprising in three ways. Firstly, the flux of comets
through the inner solar system is much lower than some previous estimates.
Secondly, the expected rise in comet numbers to larger perihelia is not seen.
Thirdly, the number of comets per unit absolute magnitude does not
significantly rise to fainter magnitudes. These results imply that the Oort
cloud contains many fewer comets than some previous estimates, that small
long-period comets collide with the Earth too infrequently to be a plausible
source of Tunguska-style impacts, and that some physical process must have
prevented small icy planetesmals from reaching the Oort cloud, or have rendered
them unobservable. A tight limit is placed on the space density of interstellar
comets, but the predicted space density is lower still. The number of
long-period comets that will be discovered by telescopes such as SkyMapper,
Pan-Starrs and LSST is predicted, and the optimum observing strategy discussed.
