  It is important to know the accurate trajectory of a free fall object in
fluid (such as a spacecraft), whose motion might be chaotic in many cases.
However, it is impossible to accurately predict its chaotic trajectory in a
long enough duration by traditional numerical algorithms in double precision.
In this paper, we give the accurate predictions of the same problem by a new
strategy, namely the Clean Numerical Simulation (CNS). Without loss of
generality, a free fall disk in water is considered, whose motion is governed
by the Andersen-Pesavento-Wang model. We illustrate that convergent and
reliable trajectories of a chaotic free fall disk in a long enough interval of
time can be obtained by means of the CNS, but different traditional algorithms
in double precision give disparate trajectories. Besides, unlike the
traditional algorithms in double precision, the CNS can predict the accurate
posture of the free fall disk near the vicinity of the bifurcation point of
some physical parameters in a long duration. Therefore, the CNS can provide
reliable prediction of chaotic systems in a long enough interval of time.
