Ruminating on the wobble of the Moon

Accurate predictions of the Moon’s position in space will be essential for lunar exploration and for establishing the Moon as a base for future space missions. However, the Moon’s rotation and orbit evolve in a very complex way on its journey around the Earth, and there is debate over how the many external and internal forces affect its motion. Researchers in Russia have published a new model in the journal Astronomy Reports that is independent of previous theories and reconsiders the Moon’s ‘wobble’ (also called a physical libration) from a fundamental perspective¹.

“To provide navigation support for planned space experiments in circumlunar space and on the lunar surface, a precise theory of physical libration with accuracy of a millisecond of arc is needed,” says Yury Nefedyev, from the Kazan Federal University research team. “Our goal is to achieve this accuracy by improving the models of the Moon, and the conditions of its motion.”

The Moon’s motion can deviate by up to 2 minutes of arc, which is equivalent to a kilometre or so on the lunar surface. Accuracy of one millisecond accounting for libration would provide location precision of a centimetre or better. However, although highly precise laser measurements from Earth can now track the Moon to within a few millimetres, the complexity of competing forces acting on and within the Moon have made it difficult to accurately reproduce and explain its motion.

“Our libration model considers indirect and direct perturbations from the planets, average tidal potential from the Earth, and up to the fourth order harmonic of ‘selenopotential’ - the effect of the Moon’s non-spherical shape and uneven internal mass distribution,” says Nefedyev.

The reaction of the Moon to gravitational perturbations from the Sun, Earth and planets depends on the internal structure of the Moon, which can be studied and theorized based on laser observations of libration.

“There are also free librations caused by spontaneous short-term processes that invoke additional oscillations determined by natural frequencies of the lunar body,” continues Nefedyev. “Laser observations have revealed dissipation of lunar rotation, which over geological time must have led to the extinction of free librations, yet they are still observed.”

The factors considered in the new model reduce the position inaccuracy by about two orders of magnitude, but further work is needed on the internal lunar structure and its effects.

“The important steps in such investigations are determining the Moon’s viscoelasticity and studying the parameters of the lunar core, such as size, flattening and chemical composition,” Nefedyev says.