New work with an old equation may help scientists calculate the thickness of
ice covering the oceans on Jupiter’s moon Europa and ultimately provide
insight into planet formation.

Planetary bodies, such as the Earth and its moon, exert such gravitational
force on one another that tides occur, not just in the oceans, but also in
bodies of the planets themselves. The surfaces of planets actually rise and
fall slightly as they orbit one another.

The standard for calculating how the gravity of one celestial body affects
the shape of a second is an equation published in 1911 by A.E.H. Love. Sarah
Frey, a doctoral candidate at the University of Arizona in Tucson, decided
to see if she could figure out the thickness of ice on Europa by using
Love’s equation to calculate planetary tides.

"Love looked at two cases, which were very well behaved, very similar to
Earth’s values," she said.

However, Love didn’t have the power of modern computers at his disposal.

Working with Terry Hurford, a graduate student in UA’s department of
planetary sciences and Richard Greenberg, a professor of planetary sciences
at UA, Frey used computers to calculate what Love’s equations predicted for
various spheres that differed from one another in density, compressibility
and rigidity. The spheres serve as proxies for planets.

To their surprise, the researchers found that in specific cases, the
computer calculations suggested that the sphere would change shape
dramatically. Frey said these special circumstances, called singularities,
might ultimately reveal situations that would prevent the formation of

Greenberg said, "If a rocky planet was a little bit bigger than Earth or
Venus, it would be in the danger zone where the formula would predict a
substantial distortion in the planet’s shape. We’re wondering if in some way
this regulated the size of the planets."

Frey will discuss the team’s findings about Love’s equations,
"Characterization of instabilities in the tidal deformation of a planetary
body," on Wednesday, Jan. 7, at 10:30 a.m. at the Phoenix Civic Plaza at the
joint annual meeting of the American Mathematical Association and
Mathematical Association of America.