sealPurdue News

May 2001

Purdue engineer goes back to class
to put Einstein to the test

WEST LAFAYETTE, Ind. – An engineering professor who sat in on a physics course to pursue his lifelong dream of understanding the general theory of relativity, not only reached that goal but came up with a new way of testing Einstein's masterwork.

"For me, it all started as a dream to understand general relativity," said James Longuski, an aerospace engineer and professor of aeronautics and astronautics at Purdue University. "To actually make a contribution to general relativity was beyond my wildest dreams."

Longuski devised a new way of testing the theory by precisely measuring small changes in the position of a spacecraft as it passes near the sun. He developed a new mathematical formula for calculating precisely how much of the spacecraft's changing position would be due to general relativity. The formula makes it easier to test relativity by reducing pages of calculations into a single line of mathematical terms.

A scientific paper detailing the technique was published April 2 in Physical Review Letters, a journal published by the American Physical Society. Longuski wrote the paper with Ephraim Fischbach, a Purdue physics professor, and Daniel Scheeres, an assistant professor of aerospace engineering at the University of Michigan.

Fischbach said scientists are always looking for new ways of testing general relativity, which is a pillar of modern physics that is critical to learning how the universe evolved. Since the theory was published in 1915, numerous experiments have shown its predictions to be correct. However, even a small numerical deviation from the theory's predictions would be considered big news in physics, Fischbach said.

"General relativity is at the heart of understanding everything in cosmology – how the universe evolved – so it's very important that we continue to test it so that we can be sure that its predictions are correct," Fischbach said. "If one ever found a discrepancy, that would be a major contribution to science."

Longuski specializes in the effects of gravity on a spacecraft's trajectory, or its passage through space. The sun and planets in the solar system are used to help propel and guide spacecraft to their ultimate destinations. These bodies provide "gravity assists," commonly called "slingshot" trajectories, which enable spacecraft to achieve the proper speed and heading while minimizing fuel consumption.

Because general relativity can be tested by measuring how gravity bends the paths of moving particles or a beam of light, Longuski reasoned the theory could be tested by precisely measuring how the sun's gravity would affect a spacecraft's trajectory.

Einstein used general relativity in the early 20th century to solve a long-standing mystery about a tiny discrepancy in Mercury's orbit around the sun. Conventional Newtonian physics could not entirely account for the behavior of the planet's orbit. Astronomers had even resorted to postulating that an undiscovered planet, which they called Vulcan, must be located between Mercury and the sun, exerting additional gravitational forces on Mercury that affected its orbit.

Einstein precisely calculated Mercury's orbit using general relativity, providing critical evidence for the theory's validity and disproving competing theories, such as the existence of Vulcan.

Longuski's technique represents a more controlled method for measuring the same effect seen in Mercury's orbit.

"The trouble with observing Mercury is that it is given to us by nature and we can't tinker with it," Fischbach said. "Instead of observing a planet, we would use a spacecraft and measure its motion to get the equivalent information, but under more controlled circumstances, in a way that you get a more precise test."

Longuski, a seasoned engineer and educator who has written more than 100 research papers, derived his new formula not as a teacher but as a student. His lifelong desire to learn about general relativity prompted him to sit in on a course taught by Fischbach in 1997.

As part of the course, Fischbach requires his students to write a research paper by the end of the semester.

Longuski, who decided to write a paper showing how to test general relativity using a spacecraft's trajectory as it whipped past the sun, credits his findings to a "cross pollination" of ideas from diverse areas of research: physics and astronautics.

"This demonstrates the value of learning, even for people who are already established experts in their given fields," Longuski said.

When Longuski showed Fischbach his formula, the physics professor realized that no one had thought of it before. By itself, the new formula probably would have been worthy of publication in a scientific journal. But it would be far better to create a realistic experiment using the formula to test general relativity.

Longuski learned about a mission proposed in 1994 by scientists at the California Institute of Technology and the Jet Propulsion Laboratory. That mission, as conceived by Caltech space physicist Richard Mewaldt and his colleagues at JPL, would use the sun's gravity as a slingshot to catapult a spacecraft out of the solar system. The craft would be sent close to the sun, and its rocket would be fired at just the right moment to make for maximum use of the sun's gravity.

Although the Small Interstellar Probe mission was designed to study the characteristics of space outside the solar system, the spacecraft's trajectory around the sun could be used to test general relativity. By precisely tracking the spacecraft's position at its closest approach to the sun, a point in the orbit called its perihelion, researchers could test general relativity.

Furthermore, Scheeres determined no additional hardware would be needed to track the spacecraft. A network of NASA antennas known as the Deep Space Network, which uses radio waves to communicate with spacecraft, could be used for the experiment.

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

Ephraim Fischbach, (765) 494-5506,

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

Purdue News Service: (765) 494-2096;

NOTE TO JOURNALISTS: A copy of the research paper referred to in this news release is available from Emil Venere, (765) 494-4709,


Deflection of Spacecraft Trajectories
as a New Test of General Relativity

James M. Longuski, Ephraim Fischbach, and Daniel J. Scheeres

We derive a simple formula which gives the general relativistic deflection of a spacecraft, idealized as a point mass, for all values of the asymptotic speed V(infinity) (0 < V(infinity) < 1). Using this formula we suggest a new test of general relativity (GR) which can be carried out during a proposed interstellar mission that involves a close pass of the sun. We show that, with foreseeable improvements in spacecraft tracking sensitivity, the deflection of a spacecraft's trajectory in the gravitational field of the sun could provide a new test of GR.

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