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In the course of writing his junior paper, astrophysics major Tomer Yavetz ’14 developed a novel theoretical framework for why satellites stay in orbit around the Earth. Over the summer, Yavetz cowrote a paper with his adviser, Institute of Advanced Study astrophysicist Scott Tremaine, that was submitted in September to the American Journal of Physics.

Taking into account different effects that result from the fact that the Earth isn’t perfectly spherical, along with the effects of the moon and sun on satellite orbit, Yavetz’s paper provided an explanation for how satellites remain in orbit even with all these imperfections in the gravitational field.

“We just basically compiled all those together, and we tried to say why is it that when you add those all together you get satellites that stay up,” he explained.

Sukrit Ranjan, a Harvard graduate student studying astronomy who wrote a review of Yavetz’s paper in the daily scientific journal Astrobites, said that the paper made an original contribution to the literature on satellites.

"As far as I’m aware, this article is one of the first that really breaks down these perturbations and looks at them rigorously and analytically and says, 'Here’s a theoretical framework for why these satellites are stable,' " he said.

Tremaine said that he first came up with the idea for Yavetz’s JP while reflecting on extrasolar planets, his area of expertise, and how their orbits are often similar to those of satellites around Earth. Yavetz said that he found Tremaine’s idea the most interesting of the options available for his JP.

“Because there’s such a wide variety of configurations in extrasolar planets we know of and other planets and solar systems we know of, I began thinking about what the general properties of stability in satellite orbits are and how that plays out in the case of the Earth,” Tremaine said.

After Tremaine reviewed the JP and suggested theoretical additions, he and Yavetz cowrote the paper.

Yavetz’s JP differs from other publications in astrophysics in its use of manual calculations rather than the computational simulations that dominate the field, Yavetz said.

“It was a lot of pencil-and-paper calculations,” he explained. “I love these. I think these are the most intriguing and fun problems to work on.”

Ranjan said he was also excited by Yavetz’s reliance on manual calculations.“That was something really exciting to me because I thought the age for that kind of science had kind of passed,” he said.

The published paper could help astrophysicists understand what configurations of other planets and stars will be stable, Yavetz said.“It’s an interesting teaching problem. And it’s certainly an interesting thing to think about when we’re starting to imagine other worlds,” he noted. “We could easily imagine a world where the way things work out isn’t the way things work out here and you wouldn’t actually be able to have satellites.”

While the paper is novel in that it provides a theoretical understanding of what makes satellites stable, Tremaine said that it will not change the way satellites are actually launched into orbit.

“The paper doesn’t contain results in the sense that obviously the people who put satellites up —the engineers who design the best orbit for a satellite —understand, whether the satellite orbit is stable or not,” he said. “What we were trying to do was to provide a physical explanation for what properties of the earth’s gravitational field or what properties of gravitational fields in general make a difference between a stable and an unstable satellite orbit.”

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