In 1980, he noticed a small discrepancy between the Doppler shifts he expected to receive based on his algorithm and the actual, measured shifts of the radio signals coming from the spacecraft. Their expected and actual motions weren't quite matching up. As they moved outward against the gravitational pull of the sun and planets, the spacecraft were, of course, slowing down. But the problem was they were slowing down too much. Each year, both of the spacecraft were a few hundred miles farther behind where they should have been on their respective paths, according to the algorithm. That isn't much in the context of space travel, to be sure, but it isn't trivial either. The constant, extra acceleration amounted to 8.74 x 10-10 m/s2 directed toward the sun– a factor ten billion times smaller than the acceleration due to gravity, but still, undeniably, there.