  Slow-moving particles capable of interacting solely with gravity might be
detected on Earth as a result of the gravitational lensing induced focusing
action of the Sun. The deflection experienced by these particles are inversely
proportional to the square of their velocities and as a result their focal
lengths will be shorter. We investigate the velocity dispersion of these
slow-moving particles, originating from distant point-like sources, for
imposing upper and lower bounds on the velocities of such particles in order
for them to be focused onto Earth. We find that fluxes of such slow-moving and
non-interacting particles must have speeds between ~0.01 and ~0.14 times the
speed of light, $c$. Particles with speeds less than ~0.01 c will undergo way
too much deflection to be focused, although such individual particles could be
detected. At the caustics, the magnification factor could be as high as ~10E+6.
  We impose lensing constraints on the mass of these particles in order for
them to be detected with large flux enhancements to be greater than E-9 eV. An
approximate mass density profile for Jupiter is used to constrain particle
velocities for lensing by Jupiter. We show that Jupiter could potentially focus
particles with speeds as low as ~0.001c, which the Sun cannot. As a special
case, the perfect alignment of the planet Jupiter with the Sun is also
considered.
