Yarkovsky effect

Why can an asteroid's own afternoon warmth shift its orbit more than any collision it has suffered?

The asteroid belt looks like a place where things happen by collision. Rocks hit rocks; orbits get knocked about; occasionally something is flung our way. For the sizes we care about most — the few-hundred-metre bodies that cross Earth's path — that picture is largely wrong.

What moves those orbits is heat: not the Sun pushing on them, but the asteroid's own warmth leaking back into space in the late afternoon. That sounds far too gentle to matter. A rock radiates a little infrared and drifts across the solar system as a result? Either the effect is bigger than intuition allows, or the intuition has the wrong quantity in mind.

Start with what sunlight already does. A photon carries momentum equal to its energy divided by c, so absorbing sunlight pushes an asteroid straight outward from the Sun. But that push is purely radial, and a radial force merely dilutes gravity: it resizes the orbit once and then stops mattering. To move an orbit secularly — to grow or shrink it year after year — you need a force with a component along the direction of travel. Where would one come from?

Look at the absorbed energy. It does not vanish; the surface warms, and warm surfaces radiate. Each departing infrared photon carries momentum too, so re-emission is itself a thrust, pointing away from wherever the surface is hottest. The question sharpens: where is the hottest point?

If rock had no thermal inertia, the answer would be the sub-solar point, dead noon, and the recoil would again be purely radial — nothing gained. But rock takes hours to warm and hours to cool, so on a rotating body the surface is hottest not at noon but in mid-afternoon, carried past the sub-solar point before it has finished heating up. The strongest thermal emission leaves the afternoon face, which is offset from the Sun-line, so its recoil has a transverse component. There is the missing force.

Which way does it point? Entirely on spin sense. For a prograde rotator the afternoon side trails, so the recoil pushes roughly along the direction of travel, adding orbital energy and expanding the orbit; reverse the spin and the orbit shrinks. That dependence is the mechanism's signature, and will serve as the test.

Now size the force. At 1 AU the solar constant is about 1361 W/m² (a measured value I am recalling). A body of radius 500 m presents πR² ≈ 7.85 x 10^5 m², intercepting about 1.07 x 10^9 W. If all of that left as photons in one direction the thrust would be P/c ≈ 3.6 N. It does not: most emission spreads over the whole surface and cancels. Call the surviving transverse fraction a few per cent, say 0.03, giving about 0.11 N. That fraction is the softest number here — it depends on thermal conductivity, spin rate and roughness, and is the one quantity I am estimating rather than deriving.

At a typical asteroid density near 2500 kg/m³, a 500 m sphere holds (4/3)πR³ ≈ 5.2 x 10^8 m³, so about 1.3 x 10^12 kg. The acceleration is 0.11 divided by that — roughly 8 x 10^-14 m/s². Absurdly small.

Except that orbits integrate. Specific orbital energy is -GM/2a, so dE/dt = (GM/2a²)(da/dt), while a transverse acceleration does work at rate a_T·v. Equate them, use GM = v²a, and the semi-major axis drifts at da/dt = 2 a a_T / v. With a = 1.5 x 10^11 m and v = 29.8 km/s that is about 8 x 10^-7 m/s — some 25 metres per year, and 250,000 km over ten million years. Radar ranging of near-Earth asteroids confirms drifts of this order; Bennu's, a body a few hundred metres across, is a few hundred metres per year — a recalled figure, and rather larger than my crude efficiency estimate gives.

Now the comparison the question demanded. Over a million years that acceleration supplies about 2.5 m/s of velocity change. To match it with one impact you would need M Δv / v_impact of mass — at 5 km/s, about 6.6 x 10^8 kg, a rock roughly 80 m across. An 80-metre body striking a 500-metre one is not a nudge but close to a disruption, and such events are far rarer than once per million years. The drizzle of afternoon photons wins because it never stops and never misses.

Three refinements hold this together.

First, this is not radiation pressure, and conflating them is the usual error. Sunlight pressure — the force shaping a comet's dust tail, explained elsewhere here — is incoming photons pushing radially. The Yarkovsky force is outgoing photons, and depends entirely on the thermal lag that makes them leave asymmetrically. Remove the lag and radiation pressure survives untouched while Yarkovsky vanishes.

Second, the acceleration scales as area over mass, that is as 1/R. A ten-metre boulder drifts fifty times faster than the body computed above; a fifty-kilometre asteroid barely moves. The effect is a size filter, sorting the small out of the belt while leaving the large where they formed.

Third, this is why the effect matters. The Kirkwood gaps, explained elsewhere here, are resonances that destabilise anything sitting in them — which raises the problem that they should have been swept clean billions of years ago and stayed clean. Yarkovsky drift is the resupply: it walks small bodies slowly across the belt until they fall into a resonance, which then does the violent part.

The refuting observation: because the drift direction is set by spin sense, radar-tracked near-Earth asteroids should show drift signs that correlate with independently measured rotation directions — and bodies delivered inward across a resonance should be retrograde-dominated. They are. If a survey found drift signs randomly distributed with respect to spin, the mechanism would be finished.

• How the same thermal recoil, acting on an irregular shape, spins asteroids up or down instead of moving them — the YORP effect.
• Why the seasonal variant, driven by obliquity rather than rotation, always shrinks an orbit no matter which way the body spins.

Every term the collection defines is gathered in the glossary.