  We describe how long-term solar system orbit integration could be implemented
on a parallel computer. The interesting feature of our algorithm is that each
processor is assigned not to a planet or a pair of planets but to a
time-interval. Thus, the 1st week, 2nd week,..., 1000th week of an orbit are
computed concurrently. The problem of matching the input to the (n+1)-st
processor with the output of the n-th processor can be solved efficiently by an
iterative procedure. Our work is related to the so-called waveform relaxation
methods in the computational mathematics literature, but is specialized to the
Hamiltonian and nearly integrable nature of solar system orbits. Simulations on
serial machines suggest that, for the reasonable accuracy requirement of 1" per
century, our preliminary parallel algorithm running on a 1000-processor machine
would be about 50 times faster than the fastest available serial algorithm, and
we have suggestions for further improvements in speed.
