  (Abridged) Out-of-the-ecliptic trajectories that are beneficial to space
observatories such as the Terrestrial Planet Finder and other potential mid-IR
missions are introduced. These novel trajectories result in significantly
reduced background noise from the zodiacal dust radiation and therefore allow a
reduction in telescope collecting area and hence cost. Two types of optimal
trajectories that are energetically feasible were derived using genetic
algorithms. These are highly inclined non-Keplerian heliocentric orbits. The
first optimal trajectory can use existing launch technology and the zodiacal
brightness for this trajectory is reduced by at least 50% for 60% of the
mission lifetime. The second optimal trajectory requires planned improvement in
launch technology but it renders a zodiacal cloud brightness reduction by at
least 70% for 82% of the mission lifetime. Heliocentric orbits at 5 AU have
been discussed because the zodiacal dust concentration is extremely low there
and the energy requirements to reach these trajectories are low if
gravitational assists can be used. Unfortunately such orbits are impractical
because of high cost, power source constraints (inability to use solar cells),
communication delays, and a long travel time before data return. Additionally,
the energy requirements to reach our low and high energy optimal trajectories
are respectively half as much and equivalent to a direct trip to 5AU with no
planetary gravitational assists.
