What is a hyperbolic rendezvous?

I am reading this paper about cyclers between Saturn and some of it's moons. In the beginning is discusses the Earth-Mars cycler as "suffering" from the "risky requirement to perform hyperbolic rendezvous." So, what is a hyperbolic rendezvous? Does it mean that the orbiting vehicle must enter a body's SOI at a high-speed hyperbolic trajectory? Is it the speed which makes it risky?

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What you're missing is another, related paper :) Here's the Guidance Strategy for Hyperbolic Rendezvous, Landau & Longuski (PDF). Since you're already studying it, I think this would be a good opportunity for a self-answer. ;) –  TildalWave May 7 at 14:31
Ah, the source! Good thinking. Let's see if I can figure it out before someone else. –  Stu May 7 at 14:31

The sentence reads "Earth-Mars cycler applications generally suffer from long repeat periods, infrequent launch opportunities, and the risky requirement to perform hyperbolic rendezvous"

The bolded portions are important parts of that sentence.

If a rendezvous is botched during planetary fly by, there won't be another opportunity until next fly by. The taxi is now on a heliocentric orbit that won't fly by a cycler or planet for years. Passengers aboard are as good as dead.

The Saturnian moon cyclers also fly by the moons at hyperbolic trajectories with regard to the moons. But trip times and launch opportunities are on the order of days or weeks instead of years.

Here is a perhaps an over-simplified pic of two possible Mars cyclers:

As you can see fly bys are infrequent for both VISIT 2 and Aldrin Cyclers, though Aldrin flies by both earth and Mars more often. But the Aldrin Cycler has much bigger Vinfinity (also known as hyperbolic excess velocity). The Vinfinity vectors are colored red in the illustration above. You can see the Aldrin Cycler Vinfinity at Mars fly by is quite large, around 10 km/s

The Aldrin cycler also needs its line of apsides rotated about 50 degrees each synodic period. Buzz Aldrin hopes to accomplish that with earth's gravity instead of propellent.

Here's a spreadsheet that shows synodic period and trip times between moons of Saturn as well as moons of Jupiter. If you play with it you can see the tempo for travel between gas giant moons is a lot quicker than travel between planets.

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Thanks, this is great. I also really enjoyed your blog post. –  Stu May 7 at 19:47
Is this basically how Hohmann transfers use the least amount of energy? Because the Vinf is much lower, you need less energy to enter the Martian orbit? –  Stu May 7 at 23:24
See how both the cycler orbits are tangent (just touching) to earth's orbit? Only speed change is needed. For example two cars 30 and 33 mph in the same lane bump, difference is 3 mph. But if they hit while traveling different directions, difference is higher –  HopDavid May 7 at 23:28
A Hohmann orbit would be tangent to Earth orbit as well as Mars orbit. The VISIT 2 is nearly Hohmann, slight direction change adds to delta V. Aldrin cycler is decidedly un Hohmann. The big direction change hikes Vinfinity quite a bit. –  HopDavid May 7 at 23:29

Coming from one of the sources, a hyperbolic trajectory rendezvous is dangerous because if the rendezvous doesn't do as planned, the cycler taxi will escape the body's gravitational pull and venture out into space.

From the paper: "Apollo missions included a similar risk when the lunar module docked with the command/service module in lunar orbit. If this rendezvous failed, two of the three astronauts would not make it home."

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As an aside, that source document uses $3\sigma$ as a "gold standard". That's where the space industry is now, but it's actually a "tarnished bronze with chipped gold paint standard" rather than a gold standard. Think of what would happen if three out of every thousand airplane flights ended with one or more fatalities. There would be no airline industry with a $3\sigma$ success standard. The airline industry is pushing six nines, 99.9999% success. Many nines of reliability will be the reality by the time cyclers become reality, and that will drastically impact design. –  David Hammen May 7 at 16:20