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Massive astronomical objects are frequently encircled by groups of smaller objects that revolve around them, like the planets around the Sun.

For example, supermassive black holes are orbited by swarms of stars, which are themselves orbited by enormous amounts of rock, ice, and other space debris. Due to gravitational forces, these huge volumes of material form into flat, round disks.

These disks, made up of countless individual particles orbiting en masse, can range from the size of our Solar System to many light-years across.

Astrophysical disks of material generally do not retain simple circular shapes throughout their lifetimes. Instead, over millions of years, they slowly evolve to exhibit large-scale distortions, bending and warping like ripples on a pond.

Exactly how these warps emerge and propagate has long puzzled astronomers, and even computer simulations have not offered a definitive answer, as the process is both complex and prohibitively expensive to model directly.

Caltech planetary scientist Konstantin Batygin turned to an approximation scheme called perturbation theory to formulate a simple mathematical representation of disk evolution. This approximation, often used by astronomers, is based upon equations developed by mathematicians Joseph-Louis Lagrange and Pierre-Simon Laplace.

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Category: Science