The Earth is not a perfect sphere. This makes very precise modelling of our planet’s gravitational field rather tricky. To simplify the maths, scientists can consider a so-called Brillouin sphere: the smallest planet-centred sphere that completely encloses the mass composing the planet. In the case of the Earth, the Brillouin sphere touches the Earth at a single point—the top of Mount Chimborazo in Ecuador. The gravitational field outside the sphere can be accurately simulated by combining a series of simple equations called a spherical harmonic expansion.

But does this still hold true for the field inside the Brillouin sphere, which by definition includes the planet’s surface? Scientists from Ohio State University and the University of Connecticut say “no”. The team presented an analytical and numerical study that demonstrates clearly how and why the spherical harmonic expansion leads to prediction errors.

However, all is not lost. Their ultra-accurate simulations of the gravity field offer guidance toward a new mathematical foundation of gravity modelling. An upgraded simulator, which accounts for density variations within planets, will allow rigorous testing of proposed alternative ways to represent the gravity field beneath the Brillouin sphere.