When it comes to voyages of discovery, NASA's venerable Cassini mission is about as good as it gets.
In six years of cruising around the planet Saturn and its neighborhood, the Cassini spacecraft has discovered two new Saturn rings, a bunch of new moons and a whole new class of moonlets. It encountered liquid lakes on the moon Titan, water ice and a particle plume on the moon Enceladus, ridges and ripples on the rings, and cyclones at Saturn's poles. Cassini also released a European space probe that landed on Titan. And Cassini has sent back enough data to produce more than 1,400 scientific papers -- at last count.
But besides the science, Cassini is state of the art in the arcane discipline of orbital mechanics -- how to get from one place to another in space to fulfill a mission's science requirements without running out of fuel. The plans are for Cassini to keep working for seven more years, but it currently has only 22 percent of the maneuvering propellant it had when it started.
Figuring out how to more than double the duration of the mission with less than a quarter of the fuel is hard. Cassini's orbital mechanics present an astonishingly complex exercise in Keplerian physics and geometry. The enormous array of science objectives and targets -- moons, rings, Saturn itself -- makes it one of the most complex missions ever flown.
Brent Buffington, a Cassini mission designer at NASA's Jet Propulsion Laboratory, compared the task to plotting a seven-year road trip around the United States for more than 200 scientists, all with different interests and all wanting to see different things. "Now add the fact that you have a finite amount of time to design this road trip and need to adhere to the laws of physics, speed limits, the limited capabilities of the bus" and the bus driver, he said. "Oh, and the targets they want to see are moving."
Cassini arrived at Saturn in 2004 for a four-year mission, but it was so successful that NASA gave it a two-year extension, to September 2010. Then, in February, NASA extended it a second time for what it calls the Solstice mission, lasting until Saturn's northern hemisphere summer in 2017. If all goes as planned, on Sept. 15, 2017, Cassini will die a warrior's death, diving inside the rings for 22 spectacular orbits on the fringes of Saturn's atmosphere before plunging into the planet.
Cassini made it to its first, two-year extension in part because the science was simply too good to pass up. But another reason was that it performed so well and remained so healthy that it was left with enough unused propellant to enable it to maneuver through 64 additional orbits, after having already completed 75 in its first four years.
Figuring out how to organize the Solstice mission took two years. Scientists presented wish lists of places they wanted to visit and things they wanted to see. The tour designers showed them a plan and told them what was possible and what was not. Then both sides did it again.
"The competition was fierce, but collegial," said Jonathan I. Lunine, a Cassini scientist and a professor of planetary science and physics at the University of Rome Tor Vergata.
Still, there were trade-offs. Nobody got everything, but everybody got a good many things. "We try to satisfy as many people as possible," said Cassini's mission planning engineer, John C. Smith of the Jet Propulsion Laboratory, who, with Mr. Buffington, is responsible for designing the tour. "We have to kill at least two and sometimes three birds with one stone."
One of the fundamental tools for adjusting the trajectory of a large manufactured object in space -- the essence of orbital mechanics -- is the gravity assist. As a spacecraft approaches a planet or moon, gravity grips it and flings it in a different direction. In the 1970s and '80s, NASA used the gravity assist technique to enable the tiny Voyager 2 to complete its "grand tour" of the outer planets of the solar system. Voyager 2 employed four gravity assists. The Cassini Solstice mission alone will require 56.
The popular analogy for the gravity assist is "slingshot," but that term makes today's orbit designers grit their teeth. "It's a lot more sophisticated than that," said David Seal, Cassini's mission planning supervisor. "We can do a lot of things to get pretty much any trajectory we want."
A better analogy, he said, is two ice skaters in a hockey rink: a little girl and her father. The little girl is Cassini, small and fast; Dad is slow but strong. When the little girl reaches Dad at the red line, they clasp hands and Dad rotates. He can fling his daughter farther down the ice toward the far goal, toss her at right angles into the boards, send her back where she came from or let her go off at an angle.
In Cassini's case, Dad, aptly perhaps, is Titan, Saturn's largest moon. Bigger than the planet Mercury, it is the only thing in the Saturn system, besides Saturn, with enough gravity to make radical changes in the spacecraft's trajectory every time it flies by.
"Without Titan," Mr. Seal said, "we would go into one orbit around Saturn and be stuck there." Thus Titan, in the argot of orbital mechanics, is Cassini's "tour engine."
The basic geometry of the Saturn system is not difficult to understand. Like Earth, the polar axes of both Saturn and Titan run from north to south and are canted slightly, which gives both the planet and its largest moon "seasons." A Saturn year lasts almost 30 Earth years. Cassini arrived at Saturn in the southern summer and will finish 13 years later in the northern summer. Being able to observe the change of seasons for half a Saturn year was the dominant principle in designing the Solstice mission.
The rings of Saturn and the vast majority of its moons, including Titan, are spread out on a roughly horizontal plane from the planet's equator. Cassini needs to fly two kinds of orbits of Saturn to get the science it wants. Equatorial orbits put the spacecraft on the same plane as the moons and the rings. Using this type of orbit -- always elliptical -- Cassini can get great views of Saturn and is able to cross the orbits of several of Saturn's icy moons for close observations and imagery.
Equatorial orbits, however, make it impossible to see the rings, which appear as a knife edge in the middle of the planet. For ring observations, inclined orbits are a must. The spacecraft has orbited Saturn at latitudes as high as 74.7 degrees, enabling the spacecraft to look down -- or up -- at the rings, and also to observe the poles.
Throughout Cassini's lifetime the tour designers must keep a close watch on the amount of fuel that it has for navigation. This is measured as a change in spacecraft velocity in meters per second and is known in aerospace parlance as delta-V. For example, if scientists want a closer approach to the moon Enceladus, the designers might tell them the delta-V cost is 10 meters per second, and scientists and engineers will decide whether the science is worth the expenditure.
When Cassini began, the spacecraft had 742 meters per second delta-V available, and for the initial four-year prime mission" and extended two-year Equinox mission, "the cost of doing business was about 100 meters per second per year, maybe a little more," Mr. Seal said.
That has left 158 meters per second delta-V for the next seven years. What makes the Solstice mission doable is that designers can trade time for fuel -- it may cost less delta-V to reach a target if the spacecraft takes longer to get there. They also use ingenuity to achieve mission objectives at lower fuel cost. And each flyby of Titan adds as much as 840 meters per second of delta-V, which is the energy used for major alterations in Cassini's trajectory.
For purposes of planning, the Cassini scientists were divided into five "disciplines": those concerned with Saturn; with Titan; with the rings; with the icy satellites; and with the magnetosphere. Leaders of the groups, beginning in early 2008, huddled with the designers every few months to examine orbits and argue their respective causes.
"We decided the theme of the Solstice mission was 'seasonality,' " said Dr. Lunine, co-chairman of the Titan and icy satellites disciplines. "Not just the ringed planet itself, but also Titan." With a seasonal weather cycle, "it was very important to see what happened to Titan when summer moved from the southern hemisphere summer to northern hemisphere."
There was a lot of competition among the disciplines, and not just over target selection: "If you're interested in the magnetosphere, you collect data over long periods of time," while "Titan is short bursts," Dr. Lunine said. "And within the Titan group, you have radar versus spectroscopy." The icy satellites group wanted a visit to a small moon, he added, "but it didn't connect with seasonality, and we lost."
The first time Mr. Smith and Mr. Buffington met with the discipline teams, they offered three possible tours. The next time, they offered two, and, in January 2009, the scientists picked one of them. Last July, after six months of tweaking by Mr. Smith and Mr. Buffington, the final "reference trajectory" was delivered. It now includes 56 passes over Titan, 155 orbits of Saturn in different inclinations, 12 flybys of Enceladus, 5 flybys of other large moons -- and final destruction.
"It's not like any problem set you get in college, because you have so many factors pulling in different directions," Mr. Seal said. "The best way to measure it is to look at how much better the next iteration is than the previous one" until "you're only making slight improvements." Then you stop.
This article originally appeared in The New York Times .