Anyone who has taken a freshman physics class has used Newton's Second Law — that the force acting on an object is equal to its mass times its acceleration — on countless agonizing problem sets.

Although most physicists believe Newton's law applies for all ranges of accelerations, only recently did scientists show that F=m*a holds true for extremely low accelerations.

"What we did is take a PHYS 121 experiment and do it to very high precision," said Chris Spitzer, a physics graduate student who participated in the experiment.

The researchers used a torsion pendulum, a mass tethered to a thin wire that rotates rather than swings.The wire was rotated very slowly; the tension generated in the wire caused a tiny acceleration. A small mirror attached to the mass reflected light from a laser into a tracking device. As the mass rotated, the extremely sensitive tracking device recorded the position of the reflected laser beam, Spitzer said.

The researchers found that F=m*a held for accelerations as low as 5*10-14 m/s2, a value about 1,000 times smaller than the previous measurement, according to an article in the April 13 issue of Physical Review Letters.

"If something had been accelerating at that rate for the entire history of the universe, it would still be going very slowly," Spitzer said.

The results may have implications for two physics quandaries.

The first is called "The Pioneer Anomaly" and deals with the Pioneer satellites that are leaving our solar system, physics professor Blayne Heckel said

"People track the distance of the pioneer satellite from us, it sends radio signals back and we can track where it is and figure out what speed it is traveling at," Heckel said. "It is not where you would expect it to be if the only thing acting on it was the gravity from the sun. It is going a little bit faster."

This discrepancy between the theoretically predicted and measured velocity also shows up when astronomers measure the speed of stars at the fringes of galaxies, said Brian Woodahl, a professor of physics at the Purdue campus of Indiana University and an author on the paper. Stars on the periphery of galaxies experience extremely low accelerations and are moving faster than expected from just gravitational forces and Newton's law alone, he added.

"Both of these issues hint at the possibility that Newton's Second Law may not be correct — out in deep space, far away from stars and planets — when the acceleration is very small," Woodahl said.

Physicists have tried to explain these discrepancies by claiming Newton's law breaks down at very low accelerations, but most scientists remain skeptical of such theories, Heckel said.

"People claim the satellites don't have quite the right acceleration," he said. "But there are so many other possible explanations that are much more plausible."

The new measurement puts more constraints on any theories that claim Newton's law breaks down, said Ephraim Fischbach, a professor at Purdue University and an author on the paper.

"We now know that F=m*a is valid in a laboratory down to very small accelerations," Fischbach said. "This means that the anomalies cannot be routinely 'blamed' on a failure of this law."

While the new measurement hints at Newton's law being solid — at least above the quantum scale — the experimental results cannot be directly applied to outer space, Spitzer said.

"The rotation in the torsion pendulum was caused by electromagnetic forces between the wire and the mass," Spitzer said.

In outer space, however, gravitational force causes acceleration in distant stars and satellites. In light of this, researchers plan to repeat the same experiment, this time causing rotation by using a gravitational source, Fischbach said.

Being stuck in Earth's gravitational field also limits how relevant these experiments are to celestial bodies experiencing very weak gravity, Spitzer said.

"It would be great if we could convince NASA to fund this same experiment but have it performed out in space — outside the influence of Earth's own gravity," Woodahl said. "Then we could say for certain that Newton's Second Law holds at small accelerations at all locations."

Reach columnist Tia Ghose at news@thedaily.washington.edu.