The NY Times article Cassini’s Final Mission: Obliteration says that the Cassini spacecraft will end it's more than a decade long exploration of the Saturn system by raising the inclination of its orbit around the planet to about 64°, then orbiting between the rings and the planet 22 times before entering Saturn's atmosphere.
To protect Titan and other potentially life-bearing places, Cassini’s final mission calls for its obliteration. Researchers have dubbed the spacecraft’s swan song the “Cassini Grand Finale” because it includes an ambitious maneuver: 22 loops through the gap between Saturn’s surface and its innermost rings.
Before launching Cassini, NASA drew up plans to dispose of it in Saturn’s upper atmosphere, but they only developed its elaborate end-of-mission maneuver in the past couple of years. Once they found that some of Saturn’s moons may be potentially habitable to life, keeping the probe clear of them as it ran out of fuel became crucial.
Before Cassini can thread the needle through the planet’s gap, it must first reach the proper angle in its orbit. That means climbing to an inclination of approximately 64 degrees. The problem is that Cassini doesn’t have the power to propel itself to that position.
“Each of the six (Titan flybys) will raise the tilt of the orbit a little bit,” said Dr. Spilker, “until we get the right orbit to go in between the rings and the planet.”
...Linda Spilker (is) the Cassini project scientist at NASA’s Jet Propulsion Laboratory in Pasadena, Calif.
After reading the NASA news item Cassini Heads for 'Higher Ground' at Saturn, I still don't understand:
Why must Cassini reach an orbital inclination of about 64° before "threading the needle" between Saturn and its rings? (why not 40°, 50°, 60°...)