  Aims. Based on measurements by the Ulysses spacecraft and high-resolution
modelling of the motion of interstellar dust (ISD) through the heliosphere we
predict the ISD flow in the inner planetary system and on to the Earth. This is
the third paper in a series of three about the flow and filtering of the ISD.
  Methods. Micrometer- and sub-micrometer-sized dust particles are subject to
solar gravity and radiation pressure as well as to interactions with the
interplanetary magnetic field that result in a complex size-dependent flow
pattern of ISD in the planetary system. With high-resolution dynamical
modelling we study the time-resolved flux and mass distribution of ISD and the
requirements for detection of ISD near the Earth.
  Results. Along the Earth orbit the density, speed, and flow direction of ISD
depend strongly on the Earth's position and the size of the interstellar
grains. A broad maximum of the ISD flux (2x10^{-4}/m^2/s of particles with
radii >~0.3\mu m) occurs in March when the Earth moves against the ISD flow.
During this time period the relative speed with respect to the Earth is highest
(~60 km/s), whereas in September when the Earth moves with the ISD flow, both
the flux and the speed are lowest (<~10 km/s). The mean ISD mass flow on to the
Earth is ~100 kg/year with the highest flux of ~3.5kg/day occurring for about 2
weeks close to the end of the year when the Earth passes near the narrow
gravitational focus region downstream from the Sun. The phase of the 22-year
solar wind cycle has a strong effect on the number density and flow of
sub-micrometer-sized ISD particles. During the years of maximum electromagnetic
focussing (year 2031 +/- 3) there is a chance that ISD particles with sizes
even below 0.1\mu m can reach the Earth.
  Conclusions. We demonstrate that ISD can be effectively detected, analysed,
and collected by space probes at 1 AU distance from the Sun.
