Dr. Marian Gidea

Researchers at the Katz School of Science and Health have developed a mathematical model for analyzing the motion and gravity of a family of Trojan asteroids orbiting Jupiter.

Their paper, “Hill Four-Body Problem with Oblate Bodies: An Application to the Sun-Jupiter-Hektor-Skamandrios System,” was published in the Journal of Nonlinear Science in July.

“This is a mathematical model to accurately describe the dynamics of a space probe flying by an oblate asteroid, taking into account the gravity exerted by the sun and Jupiter, which are slightly oblate as well,” said Dr. Marian Gidea, a co-author of the paper and chair of mathematics at the Katz School.

He and Ph.D. student Wai-Ting Lam, another co-author, joined an international team of researchers to understand how a space probe would behave on approach to a series of asteroids, including Hektor, the largest Jupiter Trojan at 250 miles long that has its own moonlet, Skamandrios.

“We found several possible orbits that can be used by a space probe to observe the asteroid, or for landing on the asteroid,” he said.

Asteroids are typically small rocky planets left over from the formation of the solar system. There are several distinct families of asteroids in the solar system. Jupiter has the most discovered Trojans—more than 6,000 as of 2014. Asteroids not only hold clues to the formation of the solar system, they are rich in minerals that are ripe for commercial exploitation.

“Besides interest from the aspect of planetary dynamics, another motivation to study the motion of a Trojan asteroid comes from astrodynamics,” said Dr. Gidea. “NASA is preparing the first mission, Lucy, to Jupiter’s Trojans in October 2021.”

Dr. Gidea said their mathematical model is novel because it assumes that the asteroids are flat, or oblate, at their poles. The shape of the asteroid determines its gravitational field, which is factored into the design of the space probe’s orbit.

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