This image from NASA’s Mars Reconnaissance Orbiter shows small ripples, about 10 meters apart, located in Her Desher Vallis. (Source: NASA)

One Woman’s Math Could Help NASA Put People on Mars

(Bloomberg Businessweek) -- Kathleen Howell never aspired to walk on the moon. When she watched the first lunar landing as a teenager in 1969, she was more intrigued by the looping route that brought the Apollo 11 astronauts from Earth to the Sea of Tranquility and back. Orbits became her life’s passion. In 1982 she wrote a doctoral thesis on orbits in “multibody regimes” that earned her a Ph.D. from Stanford. She soon received a Presidential Young Investigator Award.

Howell’s world-leading expertise in unconventional orbits is in fresh demand. NASA has decided that a ­near-rectilinear halo orbit (NRHO)—a specialty of hers—would be an ideal place to put the Lunar Orbital Platform-Gateway, a planned way station for future human flights to the moon and eventually Mars. Mission planners have already brought her in for advice.

Unlike an ordinary flat orbit, an NRHO can be slightly warped. Also, it stands on end, almost perpendicular to an ordinary orbit—hence “near rectilinear.” The plan is for the Gateway’s circuits to pass tight over the moon’s north pole at high speed and more slowly below the south pole, because of the greater distance from the moon. Imagine moving your hand in circles, as if washing a window, while you walk forward. Except you’re making hand circles around the moon while walking around Earth.

Although an NRHO appears to be an ordinary circuit of the moon, it’s actually part of a family of orbits centered on an empty point called L2, or Lagrange Point 2, about 45,000 miles beyond the far side of the moon, where the gravitational forces of Earth and the moon are in balance with the centrifugal forces on the spacecraft.

Contrary to what you were taught in school, it’s quite possible to orbit around nothing, as long as that nothing is a Lagrange point, says Howell, now a chaired professor at Purdue University, which calls itself “the cradle of astronauts.” “It is elegant and very rich,” she says. “All the forces come together to produce an unexpected path through space.” She likens the competing gravitational fields that influence a spacecraft in an NRHO to the effects of a tricky green on a golf ball. Space scientists need to work with those contours like a skilled putter. “I need to build the nuances of the green into my mathematics, to take advantage of the green,” Howell says.

One Woman’s Math Could Help NASA Put People on Mars

Her work builds on an 18th century discovery. In 1760 the Swiss mathematician Leonhard Euler theorized that for any pair of orbiting bodies, there are three points in space where gravitational and centrifugal forces precisely balance. In 1772 his protégé Joseph-Louis Lagrange found two more such spots. He apparently won naming rights: All five are now known as Lagrange points, or sometimes as libration points. For a space station or a satellite, a Lagrange point is like a mooring in a safe harbor. An object parked at one of these sweet spots can remain in lockstep with the smaller body as it orbits the larger one. Observation satellites have been positioned near Lagrange points, and sci-fi writers have imagined colonies stationed at them.

Howell’s doctoral thesis explored a family of orbits around Lagrange points, called halo orbits because from Earth they appear to form a halo around the moon. A satellite or spacecraft in a halo orbit can be constantly in Earth’s sight and can therefore maintain communication between astronauts on the far side of the moon and control rooms back home. Each circuit around the moon is slightly different, like a spinning plate wobbling on a tabletop.

The few people who knew anything about halo orbits in the early 1980s perceived them as interesting but erratic. Howell found a subset that was more stable. In simulations, she tipped her orbit upward, dragging it so it would be more vertical and less “bent,” and also pulled it nearer to the moon. When the orbit got close to the moon, it became “meta­stable.” That meant it could stay on course with minimal use of thrusters—extending its useful life and saving NASA and other would-be spacefarers money. “If I run out of propellant, I’m done,” she says.

President Trump has proposed spending $500 million in fiscal 2019 and $2.7 billion over the next five years for the Gateway. Its first module, a “space tug,” is slated to be put into orbit in 2022, with American astronauts returning to lunar orbit a year later. The orbital math the Gateway will use is complex, because it must account not just for Earth and the moon, but the pull of the sun and even Jupiter. Howell’s computer simulations offer a close approximation of the craft’s path; perfect prediction is in principle impossible. “You can’t include everything in the universe in your calculation,” she says, “but we do amazingly well for what we don’t know.”


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