Your Jewelry and the Mysterious Tilt of the Moon

Title: Collisionless encounters and the origin of the lunar inclination

Authors: Kaveh Pahlevan & Alessandro Morbidelli

First Author’s Institution: Laboratoire Lagrange, Université Côte d’Azur, Observatoire de la Côte d’Azur, France

Status: Published in Nature, open access


‘I don’t pay much attention to this topic…’, said Professor Z with much dismay as I expressed to him my fondness for this paper a few weeks ago.

‘Then perhaps I should write an astrobite about it’, I thought to myself.

Whether it was expected or coincidental, we know not, but the formation of the Moon is definitely good news for all life residing on our planet. While it’s comforting to gaze at it through the window on most nights, the true understanding of the Moon’s formation remains elusive to its admirers.

With most satellites in our Solar System having inclinations of less than 2˚ relative to the equatorial plane of their primaries, our Moon is unique in that it lies in an orbit with an inclination of 5˚ (~10˚ at the time of formation) relative to the equatorial plane of the Earth. The prevailing scenario of the Moon’s formation, referred to as the Giant Impact Hypothesis, does not reproduce this anomalous orbital inclination, baffling scientists for a long time.

The Giant Impact Hypothesis posits that the Moon formed out of a compact disk of Earth-orbiting debris that arise from the collision of the still-forming Earth with a planet-sized body named Theia. Numerical simulations and theoretical models pertaining to this picture predict that in the inner regions of the disk, the Earth’s gravity pulls the debris apart, thus preventing them from coming together. However, in the outer regions, the debris rapidly coalesce to form the Moon, which then coexists with the inner disk material for some time. Since the Moon results out of “sticky” collisions, consequent energy dissipation is expected to smooth out all relative motions of the colliding debris, leaving the Moon in a nearly coplanar orbit (within ~0.5˚ of the Earth’s equatorial plane). The actual inclination of the Moon’s orbit is about 10x this value today, whereas the model predicts a current inclination of no more than 1˚, leading scientists into what’s called the “lunar inclination problem” – one of the last remaining unresolved kinks in the Impact Hypothesis.

Over the past few years, researchers have approached this challenge in a number of ways. For example, the interaction of the Moon with ripples produced in the inner disk due to its own gravity, or a repeated periodic pull from the sun, can both yank the Moon into a high inclination orbit. However, these scenarios are complex and necessitate a special set of impact conditions to reproduce the observed effect. The authors of today’s paper, on the other hand, propose a model where the moon starts in a post-impact equatorial orbit and naturally evolves into the configuration that we observe today (see Fig. 1).


Figure 1. (Figure 1 from Canup, R. (2015) Nature, 527(7579), 455-456; not to scale) a. The formation of the Moon in the equatorial plane of the Earth. b. The expansion of Moon’s orbit and collisionless encounter with a large inner Solar System body. c. The cumulative effect of many such encounters have inclined the orbital plane of the Moon relative to the Earth.

Realizing that there were collisions both before and after the formation of the moon (like collisions between the Earth-Moon system and other large bodies from the inner Solar System), the authors conduct a large suite of numerical simulations to study their effects. Specifically, they investigate whether the latter collisions and “close call” encounters associated with them could have a role to play in amplifying the Moon’s orbital inclination. Starting out right after the Moon’s formation in the Earth’s equatorial plane, the authors study the effect of a population of Moon-sized flyby objects on the early lunar orbit for tens of millions of years until this population is depleted via accretion either onto the planets or the Sun. As it turns out, these flying bodies undergo many misses before they actually collide with the Earth, randomly tugging at the moon and altering its orbit just enough each time to cumulatively impart an inclination of 5˚. In fact, due to the late nature of events, this inclination decays only slightly with the expansion of  the lunar orbit over time (see Fig. 2).


Figure 2. (Figure 1 in the original paper) Results from a sample simulation of the early lunar orbit, subject to several close encounters that eventually led to the collision of Earth with two bodies with 1/3rd the present mass of the Moon. The general increase in inclination (on y-axis) with time can be clearly noted.

As a further matter of interest, the prerequisite of this model – the collision of inner Solar System bodies with the early Earth – is compellingly consistent with models of a collision-deposited Earth’s “late veneer”, that explains the anomalous presence of precious metals such as gold and platinum on the Earth’s surface. These metals, on account of being siderophiles or “iron-loving”, would otherwise only be found alongside iron in the Earth’s core. Better yet, the relative amount of these metals received by the surface of the Moon in this late collision model well-matches chemical observations.

We see that a characteristic description of the Moon’s formation is a crucial piece in the puzzle of our Solar System’s formation as a whole, and has the potential to shed light on several yet-unresolved riddles. But for now, it might suffice for us to find solace in knowing that a bunch of mini-planets gave our Moon its tilt and our Earth its gold. In their absence, the Moon would be coplanar and the Earthlings would be witnessing a beautiful solar eclipse every month – except, in the absence of the beautiful jewelry they now adorn themselves with, of course.

About Bhawna Motwani

Astronomy grad student doing computational research in galaxy formation and evolution in New York City. In my leisure time, I like to go Latin dancing, enjoy live theatre/music, and take on cultural and culinary pursuits.

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    • Thank you for the arXiv link, Navneeth.
      And thank you to Bhawna for an interesting astrobite.

      • Glad you liked it, Marguerite!



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