Asteroid 3753 (1986 TO) is in a 1:1 mean motion resonance with Earth,
on a complex horseshoe-type orbit. Numerical experiments are performed
to determine its medium-term stability and the means by which it may
have entered its current orbit. Though 3753 moves primarily under the
influence of the Sun and Earth, the giant planets (and Jupiter especia
lly) play an important role by influencing, through torque-induced pre
cession, the position of the asteroid's nodes. Variations in the nodal
distance strongly affect the interaction of 3753 with Earth and may c
hange or destroy the horseshoe-like behavior currently seen. This prec
ession of the nodes provides a mechanism for placing minor planets int
o, or removing them from, a variety of horseshoe-type orbits. The chao
tic nature of this asteroid's orbit makes predictions difficult on tim
escales longer than its Lyapunov time (similar to 150 yr); therefore,
ensembles of particles on orbits near that of 3753 are considered. The
asteroid has a high probability of passing close to Venus and/or Mars
on 10(4) yr timescales, pointing to a dynamical age much shorter than
that of the solar system.