(unknown)

Message text written by INTERNET:ssi_list@...
>If the two plantets were in a 1:1 resonance, or a 2:1 resonance,
then return trips would be hunky dory, but they're not, so if we
launch from Mars and after X days of transit, the cycler will reach
Earth orbit, but Earth will be somwhere else on its orbit.

Earth and Mars are on a 1.88:1 resonance (688/365) so the cycler has
to make 7 more trips without picking up or dropping any cargo before
it can intersect Earth on its orbit and Mars on its orbit again.
<

You can use gravity assists to alter the orbit at each pass at Earth and
Mars so the planets do not need to be in exact resonance.
Here is one source with some excerpts discussing this.

http://sci.newsfactor.com/perl/story/16392.html

Buzz Aldrin's Mars Vision: There and Back Again

By Brian McDonough
SCI:TECH
February 19, 2002 9:28AM

"Cyclers would take advantage of the gravitational forces of the sun, the
two planets and their moons for gravity assists. As a spacecraft nears a
planet, its flight path is bent, causing it to whip around the planet while
boosting its speed. This slingshot trajectory enables a spacecraft to
achieve the proper speed and heading.... ... Longuski told NewsFactor
that he and his students, who are handling the trajectory issues, have
looked at a variety of possible courses for the cyclers based on the
synodic period of just over two years, in which Mars and Earth essentially
line up. .....An initial plan that called for two craft to make the round
trip once per synodic period left the cyclers passing the planets so fast
that taxi vehicles would have a hard time making a rendezvous. They are now
looking at three and even four synodic periods per full orbit, requiring
three or four cyclers. "

LO