A few years ago, I was not thinking about asteroids at all. I was deep into contact mechanics and tire simulations. Rotating bodies? Sure. But rigid bodies on roads, not rocks tumbling through space.
Then I read something that stuck with me.
Asteroids do not spin nicely around their principal axes. They wobble. That wobble is called nutation. And over long time scales, that wobble dampens out. The asteroid ends up spinning neatly around its shortest or longest axis.
The question that bothered me: why?
In a vacuum, with no external torques, a rigid body should conserve angular momentum and energy. The wobble should never go away. But observations show it does. Something is draining energy from the wobble without draining angular momentum.
That is a beautiful physics puzzle.
The asteroid is not perfectly rigid. It is a rubble pile. Rocks, dust, voids. When it wobbles, internal stresses shift. Grains rub against each other. There is friction. Tiny bits of kinetic energy turn into heat.
That heat radiates away. Angular momentum stays conserved. But energy leaks.
This is nutational damping. And it explains why asteroids eventually settle into a pure spin state.
An ellipsoid with three unequal axes. Most asteroids approximate this shape. Credit: Wikimedia Commons
The asteroid is a triaxial rotor. Its moments of inertia about the three principal axes are all different. Call them A, B, C. Each is a different number.
When the spin axis does not align with a principal axis, the asteroid wobbles. That wobble has a frequency. And that frequency determines how fast internal friction can drain energy.
This problem has been studied since at least the 1960s. Early work by Burns and Safronov connected internal friction to asteroid spin states.
Later, researchers used energy dissipation rates to estimate how long damping takes. For a typical kilometer-sized asteroid, the damping time can be millions of years. Short compared to the age of the solar system. Long compared to a human lifetime.
The math involves:
The asteroid's shape (axis ratios)
Its material properties (Q factor, or quality factor, for internal friction)
The wobble amplitude
Q factor explanation on Wikipedia
The result is a differential equation for the wobble angle. It decays exponentially. The time constant is proportional to the asteroid's rigidity and inversely proportional to the wobble frequency.
Asteroid spin states affect:
Yarkovsky effect – how sunlight pushes asteroids over long timescales
Binary asteroid formation – many small asteroids have moons, and spin states influence their stability
Planetary defense – a tumbling asteroid is harder to deflect than a neatly spinning one
Spacecraft visits – knowing the spin state helps mission planners
The Yarkovsky effect on Wikipedia
I wrote a small matlab script to simulate nutational damping. Nothing fancy. Just:
A triaxial ellipsoid with given moments of inertia
An initial wobble angle
An empirical damping term proportional to wobble rate
The code is rough. But it worked. The wobble decayed exponentially, just like the theory said.
One-line description: – Simple Euler integration of wobble decay. Uses Burns 1973 damping model. Outputs time series of angular velocity components.
The simple model assumes uniform material properties. Real asteroids are not uniform. They have cracks. Large boulders. Voids. How does heterogenity affect damping?
Also, most models assume steady-state wobble. But asteroids experience impacts. Those impacts re-excite wobble. So the spin state is a competition between impact excitation and internal damping.
No one has a complete model yet. That is exciting. It means the problem is not solved. There is room to contribute.
Back in 2014, I wrote a half-page note about rotating rigid bodies. I was studying Euler's equations and thought: "What if internal friction matters?"
I did not pursue it then. I was busy with tires and contact mechanics. But the question stayed in my mental drawer.
Finding that note recently made me smile. The splinter was there all along. It just took years to come back to it.
[Link to 2014 note – rigid_rotor_notes.pdf]
One-line description: Handwritten notes from 2014. Euler equations, polhode plots, and a scribbled question about damping.
Implement a more realistic damping model using actual asteroid shape data from radar observations
Compare damping times for different asteroid families (C-type vs S-type, which have different material properties)
Write a short summary linking nutational damping to the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect
This is a side project. Not my main work. But it is exactly the kind of thing that belongs in a personal journal. Half-finished. Slowly growing. Not for publication. For the love of the puzzle.
Burns, J. A. (1973). "Where are the asteroids with large axial ratios?" – The paper that got me started
Efroimsky, M. (2001). "Relaxation of wobbling asteroids and comets" – More advanced damping theory
Sharma, I., et al. (2005). "Rubble-pile asteroids and internal friction" – Material properties focus
[Link to PDF – Burns_1973_asteroid_axial_ratios.pdf]
[Link to PDF – Efroimsky_2001_nutational_damping.pdf]
Moreover this work was done under Dr. Ishan Sharma - author of "Rubble-pile asteroids and internal friction"
This entry is a living document. I will add more as I learn. Last updated: June 11, 2026.