Aldrin's cycling stations stay in synch with Earth and Mars by using gravity assists. They take about six months to reach Mars, travel out through the main asteroid belt for about a year and swing by Mars again for a six month trip back to Earth. As Dr. Robert Zubrin suggested in "The Case for Mars" mag-sails could also be used to adjust the orbits of cyclers. I like a combination of mag-sails with solar sails affixed to the mag-sail staying lines. This will give cyclers plenty of ability to adjust their orbits and encounter planets at the right speed and distance to take advantage of gravity assists. A computer program shows that a solar orbit with a perihelion of 150 million km. and an aphelion of 350 million km. will have a period of 2 and 1/7 years like Aldrin's cyclers. The cycler will fly by Earth at 5.45 kps faster than Earth orbital velocity around the Sun. Since (hyperbolic excess speed squared)=(burnout speed squared)-(escape velocity squared) the taxis will have to reach 12.276 kps but they will already be moving in LEO at 7.8 kps so they must speed up by 4.476 kps to reach the speeding cycler. If the taxis must travel 200,000 km to reach the cyclers they will take roughly 10 hours based on the simple estimate 200,000 km/5.45 kps. That figure may be arguable but we get a rough idea of the time needed to rendesvouz.
High Mars Encounter Speeds
My program also indicates that Mars encounter delta V will be about 6.3 to 7.3 kps. The average of that is 6.8 kps. If the taxi retros by 5 kps and uses up all its fuel (4.476+5=9.476. It has enough for 9.54 kps) it will slow down to 1.8 kps but be sped up by maritan gravity by Mars Vesc or 5 kps for a total of 6.8 kps. It will have a hyperbolic excess speed of 4.6 kps at distance and escape into space. It will have to aerobrake by 3.3 kps to enter low Mars orbit at 3.5 kps ( 6.8-3.3=3.5 kps). The taxi I have envisioned can reach 9.54 kps so there isn't much cushion. If the taxi fails to reach the cycler on its way out from Earth it should have enough delta V capacity to "fall back" into an orbit from which it can be rescued by using the rocket power it would have used to retro at Mars.
Aerobraking Solution
It looks like the LANTR taxi beats the NTR+water powered taxi and aerobraking is needed. We will need to develop space cyrogen production, storage and transfer technology. It seems that's impossible to avoid. Machines on the cycler will reliquefy taxi propellant boil off since LH2 refrigeration requires heavy and power draining equipment that might not be applicable to the taxis without a large mass penalty. Aerobraking radically changes the design of the taxis. The sleek ET based vehicles will still be good for fast interlunar flight.
Other Orbits
We must wonder about other cycling station orbits. Some can be based on Hohmanns taking 260 days each way but travel by these will be years apart unless the cycling stations can change their orbits with sails. At least planet encounter speeds will be lower by these orbits. Some cycler orbits might swing down by Venus, pick up a gravity assist to redirect the cycler's course and ride up to Mars. The orbital mechanics of cycling stations can become very complex. Future engineers and mathematicians have lots of work to do. Hopefully, young space scientists will find these pages inspiring.
