Why Can't Asteroids Spin Faster Than Two Hours?
― They Are Heaps of Rubble Held Together Only by Gravity
Measure how an asteroid's brightness changes through a telescope, and you can tell how fast it spins. Do this for thousands of asteroids and a strange "wall" appears. No asteroid bigger than a few hundred metres spins faster than about 2.2 hours per turn. The reason lies inside them.
You climb onto a playground merry-go-round and ask someone to spin it fast. Your body is pulled outward, and you have to grip the rail hard to avoid being thrown off.
In 2018, the Hayabusa2 probe reached the asteroid Ryugu. The pictures showed a shape like an abacus bead, with a bulge running right round the equator. The surface was covered in rocks, big and small.
What would happen if an asteroid had no rail and spun fast? That bead shape may be the answer, written in the asteroid's own body.
There are only two reasons they can't spin faster
On anything that spins, a force pushes outward (centrifugal force). Double the spin speed and this force becomes four times as strong. An asteroid's gravity is very weak, so it is quickly overtaken.
Many of the larger asteroids are not solid rock. They are "rubble piles": rocks shattered in collisions, then gathered by gravity alone. With no glue and no rail, once centrifugal force beats gravity, the surface stones fly off.
Put these two together and something odd follows. The speed limit does not depend on an asteroid's size. It depends only on how tightly packed the inside is (its density). Let's take it step by step.
Where does the tug-of-war between gravity and centrifugal force end?
Suppose a single pebble sits on an asteroid's equator. Gravity pulls it toward the centre, and the spin's centrifugal force pushes it outward. This tug-of-war decides whether the pebble stays or flies off.
Use the slider in Figure 1 to change the time for one turn. For an asteroid about twice as dense as water, centrifugal force beats gravity once the time drops below about 2.3 hours. That is the limit.
The key point is that making the asteroid bigger does not change the limit. A bigger asteroid has stronger gravity. But the circle the equatorial pebble travels is also bigger, so centrifugal force grows by the same proportion. The two cancel out, and the limiting time depends only on density.
Has this "wall" really been found?
Around 2000, researchers in the Czech Republic and the United States lined up asteroids with measured spin rates by size. They found that almost every asteroid with a diameter of more than a few hundred metres turned more slowly than about 2.2 hours per turn (Figure 2).
This time matches the limit worked out for a rubble pile well. It became strong evidence that most asteroids are not solid rock. Later, Itokawa, which Hayabusa visited, was also confirmed to be a jumble of rubble.
Now look at the left side of Figure 2. Some asteroids smaller than a few tens of metres spin in a few minutes, and sometimes in under a minute. Small asteroids are often single solid rocks, so they are thought to hold their shape through the strength of the rock itself.
What happens to an asteroid that spins too fast?
An asteroid's spin does not stay the same forever. When its sunlit surface warms up and gives off heat, the tiny recoil changes the spin bit by bit. Depending on its shape, an asteroid can spin up over millions of years.
Near the limit, stones and sand on the equator first slide slowly toward it and pile up there. One theory says the abacus-bead shapes of Ryugu and Bennu formed this way, back when they spun faster. Go further, and flung-off pieces may gather into a small "moon".
In 2019, the US probe OSIRIS-REx repeatedly photographed pebbles leaping off the surface of the asteroid Bennu. Bennu turns once in about 4.3 hours, and observations show its spin is gradually speeding up.
Using Earth's average density, the limit comes out at about 1 hour 24 minutes. Earth turns once in 24 hours, so there is plenty of margin. Earth holds its shape through the strength of its rock, so whether it would really fall apart is a separate question.
Summary
Larger asteroids are heaps of rubble gathered by gravity alone. If they spin fast, centrifugal force beats their weak gravity and surface stones fly off. This limit does not depend on size, only on density, and for a density twice that of water it is about 2.3 hours. The "2.2-hour wall" found by telescope was a clue that told us, from the outside, what asteroids are made of inside.
An asteroid's "speed limit" is the best
proof that its inside is a heap of rubble.
Why planets and moons are round is explained in "Why is the Earth round?", and how something can keep falling while going round is explained in "Why doesn't the Moon fall down to Earth?".
- Put a paper plate on a cake turntable (or a swivel chair), and place a few grains of rice near the centre and a few near the edge.
- Start turning slowly, then gradually speed up. Check that the grains at the edge fly off first.
- Now turn at about half the speed at which they began to fly. The grains should stay put.
On a paper plate, the force holding the rice (friction) is the same everywhere, so grains at the edge fly off more easily. On an asteroid, gravity is also stronger toward the outside, so the limit arrives at the same speed whatever the size. When you spin it, make sure no people or objects are nearby.
For those who want to know more ― terms, formulas and links to textbooksEach section is labelled with its level, from middle-school science to university courses
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school physics
- High school+Advanced high-school material, or textbook sidebars
- UniversitySpecialist university subjects (planetary science, celestial mechanics) not taught in high school
- ResearchTopics even universities do not teach as settled; researchers are studying them now
Middle schoolTerms: this phenomenon has names
- Rotation period: the time a body takes to turn once. For asteroids, it is found from how the brightness changes periodically (the light curve).
- Rubble-pile body: a body formed when pieces of shattered rock gather under gravity. This is the proper name for a "heap of rubble".
- Spin barrier (the spin wall): the observed boundary that asteroids larger than a few hundred metres across almost never spin faster than about 2.2 hours per turn.
Middle schoolHigh schoolChecking with a formula: how many hours is the limit for a rubble pile?
For a spherical asteroid, we find the rotation period at which gravity and centrifugal force exactly balance at the equator. If the period is shorter than this, equatorial stones leave the surface.
| In symbols | P ＝ √( 3π ÷ ( G × ρ ) ) |
| In words | Limiting period = square root of (3 × pi) ÷ (gravitational constant × density) |
| Where it comes from | The balance between gravity (universal gravitation) and centrifugal force on a stone at the equator. The radius R cancels out on both sides, so only density remains. |
| Symbol | Meaning and unit |
|---|---|
| P | Limiting rotation period (seconds) |
| G | Gravitational constant (6.67 × 10⁻¹¹ m³/(kg・s²)) |
| ρ | Average density of the whole asteroid (kg/m³) |
| π | Pi (about 3.14) |
| Gravitational constant G | 6.67 × 10⁻¹¹ m³/(kg・s²) |
| Average density of a rocky asteroid (gaps included) | About 2000 kg/m³ (twice water) |
| Average density of Ryugu | Taken to be about 1190 kg/m³ |
| Actual rotation period of Ryugu | About 7.63 hours |
| 3 × pi | 3 × 3.14 ＝ 9.42 |
| The number part of G × ρ (leave 10⁻¹¹ until the end) | 6.67 × 2000 ＝ 13340 |
| So G × ρ is about 1.334 × 10⁻⁷. Divide 9.42 by this | 9.42 ÷ 1.334 ≒ 7.06 |
| The result is 7.06 × 10⁷ (s²). Take the square root | About 8400 seconds |
| Convert seconds to hours | 8400 ÷ 3600 ≒ 2.33 |
| The number part of G × ρ for Ryugu's density | 6.67 × 1190 ≒ 7937 |
| So G × ρ is about 0.794 × 10⁻⁷. Divide 9.42 by this | 9.42 ÷ 0.794 ≒ 11.9 |
| Square root of 11.9 × 10⁷ (s²) | About 10900 seconds |
| Ryugu's limiting period (hours) | 10900 ÷ 3600 ≒ 3.03 |
| Limiting period ÷ actual period | 3.03 ÷ 7.63 ≒ 0.397 |
| Centrifugal force ÷ gravity is the square of that | 0.397 × 0.397 ≒ 0.158 |
For twice the density of water, the limit is about 2.3 hours, which matches the observed "2.2-hour wall" well. Ryugu is porous and has a low density, so its limit is longer, at about 3 hours. At its present spin of about 7.6 hours, centrifugal force at the equator is only about 16% of gravity. One theory says the abacus-bead shape formed when it spun once every 3.5 hours or so, a speed very close to the limit.
High schoolHigh school+Why size makes no difference
High schoolA sphere of radius R has a mass of density × 4/3 × π × R³. The gravitational acceleration at the equator is G × mass ÷ R², so it is proportional to R. Meanwhile the centripetal acceleration at the equator, for angular velocity ω, is ω² × R, which is also proportional to R. Since both are proportional to R, the balance condition ω² ＝ 4/3 × π × G × ρ has no R left in it.
High school+This period is the same as the period of a satellite skimming the surface. The period of a circular orbit just above Earth's surface is about 84 minutes, which matches the value from the same formula with Earth's density. The "spin limit" can be put another way: it is the speed at which a stone on the equator starts to orbit just above the ground.
UniversityThe shape of a body with no strength, and sunlight that changes its spin
Real asteroids are not perfect spheres. They also have friction between rocks (the internal friction angle) and a weak binding (cohesion) from van der Waals forces between fine grains. Stability analyses that include these apply the Mohr–Coulomb failure condition from soil mechanics to celestial bodies. The main cause of spin-up or spin-down is thought to be the YORP effect (Yarkovsky–O'Keefe–Radzievskii–Paddack effect), produced by the recoil of heat radiated from the surface.
📖 Derivations and further reading: Rubble-pile body (Wikipedia, in Japanese) ／ YORP effect (Wikipedia, in Japanese)
ResearchWhat is still not clear
- Large asteroids that spin faster than the wall. A few asteroids about 1 km across have been found spinning faster than 2.2 hours. Whether their cohesion is stronger than expected, or they are solid rock, is still debated.
- When the abacus-bead shape formed. It is not settled whether the shapes of Ryugu and Bennu came from fast spin, or from the way they first gathered together.
- How Bennu throws out stones. Spin speed alone does not explain it. Rocks cracking from temperature changes and impacts by tiny meteoroids are also candidates.
So what this article says is also "an explanation as far as we know now". As analysis of samples brought back by probes goes on, our understanding of what asteroids are made of may change further.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Science: the solar system and celestial bodies; the action of forces | Size and shape of asteroids, gravity |
| High school | Physics: uniform circular motion, universal gravitation | Balance of centrifugal force and gravity; the limiting-period formula |
| High school+ | Physics: periods of artificial satellites | A surface-skimming orbit and the spin limit being the same |
| University | Planetary science, celestial mechanics, soil mechanics | Rubble-pile bodies, the Mohr–Coulomb condition, the YORP effect |
| Research | Asteroid exploration, light-curve observation | Large asteroids faster than the wall; particle ejection from Bennu |
| ― | Links to daily life | The feeling of being pulled outward on a merry-go-round; news about Hayabusa and Hayabusa2 |
- Pravec, P. & Harris, A. W. (2000) Fast and Slow Rotation of Asteroids. Icarus 148, 12–20.
- Watanabe, S. et al. (2019) Hayabusa2 arrives at the carbonaceous asteroid 162173 Ryugu — A spinning top-shaped rubble pile. Science 364, 268–272.
- Fujiwara, A. et al. (2006) The Rubble-Pile Asteroid Itokawa as Observed by Hayabusa. Science 312, 1330–1334.
- Lauretta, D. S. et al. (2019) Episodes of particle ejection from the surface of the active asteroid (101955) Bennu. Science 366, eaay3544.
- Ryugu (asteroid) (Wikipedia, in Japanese; リュウグウ (小惑星)（ウィキペディア）)
- National Institute of Standards and Technology (NIST), Fundamental Physical Constants (recommended value and uncertainty of the gravitational constant)
* This article is a general-audience science explainer. The figures given are rough guides to help you understand how things work. Asteroid densities and rotation periods vary from one observation to another, and may be revised as research advances.