The solar system has existed for billions of years — but is it stable or can planets veer off course? That is one of many questions posed by the field of celestial mechanics and explored by mathematicians like Brigham Young University math professor, Tiancheng Ouyang.
Ouyang studies the movement of a group of interacting celestial bodies like planets and stars. Using a differential equation, Ouyang can solve what is known as the n-body problem and predict planetary motions in the past and the future.
“We’re using mathematics to discover,” Ouyang said. Equations involving just two planetary bodies are simple, but become more difficult with three or more celestial objects, he said — and the problems get even more complex when they involve a third dimension.
Because of the difficulty of a 3D problem, scientists are still not certain whether the solar system is stable, Ouyang said.
“Our solar system is very close to 2D,” he said, “but it’s not exactly flat, so under the assumption it’s flat, someone could prove our solar system is stable. But if you consider [it as three dimensional] then nobody knows if our solar system is stable or unstable.”
Ouyang and his colleagues developed a numerical simulation that shows the ways bodies of different mass will interact with one another. Tiny spheres spin around his computer screen, the stable systems moving along intricate orbits and the unstable systems careening out of control.
“We try to find the right position and the right velocity to make the points run the orbit that [we] designed,” Ouyang said. “The difficult part is getting the initial position and the initial velocity.”
The n-body problem has many uses outside celestial mechanics, Ouyang said. “If you want to launch a satellite, what kind of initial position and initial velocity will let this satellite go into orbit?” he said. “This has a big application in that field.”
Whether it is using the n-body problem to launch satellites, determine the Space Shuttle’s orbit or unlock the mysteries of the Solar System or the universe, celestial mechanics allows Ouyang and his colleagues to continue using math to discover.