Just how small a force are we talking about? Chesney estimates that when the asteroid is nearest the sun, the force on 1999 RQ36 would be roughly half an ounce - the weight of three grapes, compared to a rock that weighs millions of tons.
It takes years before any noticeable orbital changes can be measured, but in this case, his colleague, Michael Nolan of the Arecibo Observatory, provided a dozen years' worth of data.
Chesney combined that data with similar data from the Goldstone Solar System Radar observatory, figuring in the gravitational effects of the sun, moon, planets and other asteroids.
It turns out that the orbit of 1999 RQ36 has deviated from the predictions of the mathematical model by about 100 miles in the last 12 years. The only explanation for this would be the Yarkovsky effect.
Based on this, Chesley and his colleagues were able to determine any particularly close approaches to Earth that the asteroid would make. Its closest approach should occur in 2135, when it will pass within 220,000 miles of Earth - closer than the moon, which orbits at 240,000 miles from Earth. Chesley insists, however, that the odds of an actual collision with Earth in the 22nd century remain about one in a few thousand.
Josh Emery of the University of Tennessee, Knoxville, also contributed to the project, by using NASA's Spitzer Space Telescope back in 2007 to study the asteroid's thermal emissions, from which he could derive its temperature.
Once the orbit, size, thermal characteristics and Yarkovsky effect were taken into consideration, the rest was relatively easy: Chesney basically solved for "x" and calculated the asteroid's bulk density. The verdict: 1999 RQ36 measures half a kilometer across and weighs around 60 million metric tons, similar to the density of water. Chesley thinks this means it's likely the asteroid is "a very porous jumble of rocks and dust."
I guess we'll know more when OSIRIS-REx returns from its mission with a sample of 1999 RQ36, although that will take about 10 years. It is scheduled to launch n 2016 and won't reach the asteroid intil 2019, with a slated return to Earth in 2023.
Images: (top) Series of radar images of asteroid 1999 RQ36, obtained by NASA's Deep Space Network antenna in Goldstone, Calif. on Sept 23, 1999. Credit: NASA/JPL-Caltech. (bottom) Illustration of the Yarkovsky effect. Credit: NASA/OSIRIS-REx.