sealPurdue News

August 2000

New method speeds planning of space missions

WEST LAFAYETTE, Ind. – Planning a mission to Jupiter, its moons and other destinations in the solar system has gotten quicker and easier, thanks to a Purdue University engineer.

James Longuski, a professor of aeronautics and astronautics, has developed a mathematical technique that takes hours or days instead of the usual months or even years to calculate the complex flight paths involved in planetary travel. The method has been applied to an upcoming mission to search for liquid water on the Jupiter moon Europa and will be discussed during a national conference in August. It has also been used to plan an escape route for the first human mission to Mars, in case of an Apollo 13 type of mishap that forces astronauts to abort their landing.

Spacecraft traveling to Jupiter, its moons and other bodies in the solar system can't simply make a beeline to those places because a direct path would require too much fuel and rocket power. Instead, the craft follow complex, roundabout routes called "tours" that take them past various planets and moons. Those bodies provide "gravity assists," commonly called "slingshot" trajectories, which enable the spacecraft to achieve the proper speed and heading.

A faster technique for mapping those trajectories is needed because space missions often require a series of several gravity assists from planetary bodies, precisely strung together in just the right way so that the spacecraft arrive properly at their final destinations. Engineers highly skilled in celestial mechanics may take months or even years to plan the complex tours, only to see their methodical calculations discarded because of launch delays that require entirely new tours to be calculated, possibly with little time to spare, Longuski says.

The new technique is different in two ways:

• It provides a graphical representation of the myriad possible paths that a spacecraft could take to a given destination. The graphing method could be likened to a map showing the numerous possible routes one could take to get to the same city.

• To compute details about each potential path, such as the travel time, distance and fuel consumption, Longuski used a software program called STOUR (pronounced Ess Tour), developed at NASA's Jet Propulsion Laboratory, where he worked in the 1980s. But Longuski and his students have now automated that program, making it work faster.

By looking at the graphs, engineers can quickly identify the routes that appear to be the best paths to a given destination; then STOUR is used to confirm whether those paths are, indeed, practical.

Longuski and his students have used the technique to design trajectories for the Europa Orbiter mission, scheduled tentatively for launch in 2006. Astronomers are excited at the prospect of possibly finding liquid water, and ultimately, perhaps some form of extraterrestrial life below Europa's frozen crust, Longuski says.

The Purdue engineers will discuss the new graphing method in several talks during the Astrodynamics Specialist Conference and Exhibit, from Aug. 14 to 17 in Denver. The conference is co-sponsored by the American Institute of Aeronautics and Astronautics and the American Astronomical Society.

Much to Longuski's surprise, the Purdue engineer has learned that the mathematical method he and his students devised for the graphical software was fundamentally not new at all. In the late 19th century, astronomer Francois Tisserand came up with the same mathematical formula to identify comets whose orbits had been perturbed by Jupiter. It was called Tisserand's criterion.

Longuski showed his theorem to an engineer colleague who visited Purdue last year.

"He looked at it and said, 'That's Tisserand's criterion,' " Longuski says. "We rediscovered it in a totally back-door way."

When the Europa spacecraft reaches Jupiter, which is about 483 million miles from Earth, a rocket will be fired to prevent it from sailing past the Jovian system and to place it into an orbit around the planet. At that point, the spacecraft will begin a complex series of orbits around Jupiter and three of its moons. Before it can be placed into the proper orbit around Europa, it will have to undergo various slingshot maneuvers that gradually adjust its approach speed to that moon. The trick is to approach Europa at just the right speed and distance to place the spacecraft in orbit around the moon using the least amount of rocket fuel. While the trip from Earth to Jupiter will take about three years, it will take about two additional years before the spacecraft is finally in its proper orbit around Europa. During that time it will be orbiting Jupiter and flying past Europa and the moons Ganymede and Callisto. It will make about a dozen such "flybys," each time coming close to a particular moon while completing an orbit around Jupiter in such a way that the probe's speed and position will be strategically adjusted.

"We play this sort of ballistic billiard game of gravity assists with the moons to pump down the energy of the orbit," Longuski says. "We can go to the computer and piece it together in an hour, doing something that a year ago you couldn't have done if you had six months."

STOUR automatically figures out the billions of possible ways the spacecraft could fly past the three moons and Jupiter, displaying graphs that show the orbital configurations that would result in the best final approach to Europa. The Purdue researchers are using the program to find the best combination of trajectories for the Europa spacecraft to follow after it arrives at Jupiter. The flyby tour will reduce the approach speed to Europa enough for engineers at Jet Propulsion Laboratory to begin maneuvers that will take the spacecraft out of orbit around Jupiter and into orbit around Europa.

Source: James Longuski, (765) 494-5139,

Writer: Emil Venere, (765) 494-4709,

Purdue News Service: (765) 494-2096;

NOTE TO JOURNALISTS:  A copy of papers related to this release are available from Emil Venere, (765) 494-4709,



A Graphical Method For Gravity-Assist Trajectory Design

Nathan J. Strange And James M. Longuski
School Of Aeronautics And Astronautics, Purdue University

We introduce a new analytical technique directly related to Tisserand's criterion, which permits us to quickly identify all viable gravity-assist sequences to a given destination from an energy standpoint. The method is best presented by a simple graphical technique. The graphical technique readily demonstrates that gravity assists via Venus, Earth and Jupiter are tremendously effective sequences. Estimates are made for the shortest flight times for a given launch energy to each planet. This graphical technique should provide mission designers with a potent tool for finding economical gravity-assist trajectories to many targets of high scientific interest in the solar system.

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