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 will be published Monday
(4/2) 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 ñ 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

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.


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.


James Longuski, (765) 494-5139, longuski@ecn.purdue.edu

Ephraim Fischbach, (765) 494-5506, ephraim@physics.purdue.edu


Emil Venere, (765) 494-4709, venere@purdue.edu

Purdue News Service:

(765) 494-2096; purduenews@uns.purdue.edu