Yarkovsky Effect

A rotating rock is a slow, biased rocket

Every body warmer than its surroundings radiates infrared photons. Each photon carries momentum p = E/c, and each emission gives the body a tiny kick in the opposite direction. For a spherical body radiating isotropically into space, those kicks cancel out and there is no net force. For a real asteroid, they do not cancel. The reason is not its irregular shape — although that matters too, via the related YORP torque — but a much subtler effect: thermal inertia. The sunlit surface does not radiate the heat it absorbs instantly. It absorbs energy on the dayside, conducts a little of it into the regolith, and continues to radiate after sundown. As the asteroid rotates, this lag shifts the hottest local-time away from noon toward mid-afternoon — typically 20° to 45° of rotation past the subsolar point for typical regolith thermal conductivity.

Photon emission rises steeply with temperature: a black body radiates as σT⁴, so a surface 10% hotter emits 46% more thermal infrared. The hotter afternoon side therefore emits noticeably more IR photons than the cooler morning side, and the recoil pushes the asteroid sideways — not toward or away from the Sun, but tangent to its orbit. That tangential thrust either adds to or subtracts from the orbital velocity, slowly raising or lowering the orbital energy and the semi-major axis with it. This is the Yarkovsky effect.

Diurnal versus seasonal components

The full Yarkovsky force decomposes naturally into two parts that respond to different parts of the heat cycle.

• Diurnal Yarkovsky. Driven by the day-to-night temperature variation as the body rotates. The phase lag between the absorbed and emitted flux maxima depends on the thermal parameter Θ = (ωτ_eq)^(1/2), where ω is the spin rate and τ_eq is a thermal relaxation timescale. The diurnal term scales inversely with spin rate and is the dominant component for typical main-belt and near-Earth asteroids in the 1 m – 10 km size range. Its sign depends on the spin sense relative to the orbit. Prograde rotators drift outward — their semi-major axis a increases. Retrograde rotators drift inward.
• Seasonal Yarkovsky. Driven by the seasonal heat cycle when the spin axis lies in or near the orbital plane (obliquity near 90°). One pole bakes through perihelion-season summer and continues radiating into the next "season," producing a net along-track force averaged over an orbit. The seasonal term always shrinks a, regardless of spin sense.

For most observed asteroids the two terms partly compete. The dominant component depends on size (which sets the relative weight of conduction versus radiation), obliquity (which projects the diurnal-versus-seasonal balance), spin rate, and rotation pole orientation. The full vector force has a complicated geometric form; only the orbit-averaged, along-track component matters for long-term semi-major-axis drift.

Why it matters most for 1 m – 10 km bodies

The Yarkovsky thrust acts on the cross-section A ∝ R² of an asteroid but accelerates a mass M ∝ R³. The acceleration therefore scales as A/M ∝ 1/R — small bodies feel a much larger Yarkovsky deceleration in absolute terms than big ones. At the smallest end (sub-metre dust), radiation pressure and Poynting-Robertson drag take over and the diurnal Yarkovsky component vanishes because thermal inertia is too small to sustain a day-night contrast. At the largest end (tens of kilometres) the effect drops below the noise of mutual gravitational perturbations and collisional effects. The sweet spot — where Yarkovsky dominates orbit evolution — is the 1 m to ~10 km regime, exactly the population that supplies the Earth-crossing near-Earth objects we worry about.

Yarkovsky, Öpik, and a half-century in the drawer

The effect was first described by Ivan Osipovich Yarkovsky, a Polish civil engineer working in Russia around 1900-1901. Yarkovsky published the idea in a privately printed pamphlet in Bryansk in 1901, in a Russian-language tract on the dynamics of ether and asteroids that combined a correct insight (asteroids feel a thrust from anisotropic thermal re-radiation) with several theories now considered unsupported. The pamphlet was almost entirely forgotten. Half a century later, Estonian astronomer Ernst Öpik resurrected the idea in 1951 when working at the Armagh Observatory: he was puzzling over how main-belt meteoroids reach Earth-crossing orbits in less than a few hundred million years despite the apparent absence of strong perturbations, and he remembered (or independently rederived; the historical record is murky) Yarkovsky's argument that thermal recoil could supply the missing slow drift. Öpik's 1951 paper named the effect for Yarkovsky and re-introduced it to the celestial-mechanics community, but it remained a curiosity until much later.

The effect went mainstream in the 1990s when David Vokrouhlický, William Bottke and collaborators reformulated the diurnal and seasonal terms in modern form and showed it could quantitatively explain a string of observations: the orbital distribution of meteorites, the size-frequency slope of NEAs, the depletion of Kirkwood gaps, and the spreading of asteroid families across the main belt with age. Direct measurement on a real asteroid finally followed in 2003.

Direct measurements: from Golevka to Bennu

The Yarkovsky drift on any single asteroid is tiny — metres to kilometres per year — but it accumulates linearly with time, while gravitational position errors only grow as t^(3/2) at worst. Given enough decades of high-precision astrometry, plus the leverage of radar ranging at multiple apparitions, the effect can be measured directly.

Target	Year	Method	Measured drift (da/dt)	Spin sense
6489 Golevka	2003	Goldstone-Arecibo radar + optical	≈ −6 × 10⁻⁴ AU / Myr	Retrograde
1862 Apollo	2007	Long-baseline optical astrometry	~ −3 × 10⁻⁴ AU / Myr	Retrograde
101955 Bennu	2014, refined 2021	Radar + OSIRIS-REx tracking	−19.0 m / yr ≈ −284 m / Gyr (a-shift)	Retrograde
(99942) Apophis	2020	Radar + Subaru optical	−197 m / yr in a	Retrograde
(152563) 1992 BF	2008	Multi-decade optical	−10 × 10⁻⁴ AU / Myr	Retrograde

Bennu is the cleanest case. OSIRIS-REx orbited the asteroid for more than two years (2018-2021), and continuous radio tracking with the Deep Space Network constrained the spacecraft state — and hence Bennu's centre-of-mass state — to centimetre precision. Combined with pre-encounter radar and optical, the orbital state is now known to absurd accuracy, including the Yarkovsky transverse acceleration. The 284 m / Gyr semi-major-axis drift (about 19 m / yr) is small enough that no one could have anticipated extracting it from ground-based astronomy alone a generation ago; today it is the headline non-gravitational parameter in Bennu's ephemeris.

Yarkovsky and NEO impact prediction

For decade-to-millennium-scale impact predictions, a Yarkovsky transverse acceleration term must be carried in the orbit integrator. The reason is geometric: a small along-track acceleration accumulates into an in-track position error proportional to t², and over a century or two that position uncertainty grows from kilometres to thousands of kilometres — comparable to or larger than the size of a gravitational keyhole.

A keyhole is a narrow region in the b-plane of an Earth flyby such that passage through it produces a resonant return impact at a specific later epoch. For Bennu, the next deep encounter is in September 2135; Bennu will pass roughly 1.5 lunar distances from Earth. The 2135 encounter shuffles Bennu onto a slightly different orbit, and several centimetre-wide keyholes (in projected b-plane coordinates) lead to potential impacts between 2175 and 2199. The cumulative 2026 estimate of total impact probability over that window is 1 in 1750, with the dominant single date being September 2182 at ~1 in 2700. Subtract Yarkovsky from the model and Bennu's projected 2135 b-plane position shifts by tens of thousands of kilometres — completely missing every keyhole. The impact-probability calculation is therefore a Yarkovsky calculation.

Apophis is the other touchstone. Its 2029 Earth flyby at ~31 000 km altitude — closer than geostationary orbit — was once feared to lead to a 2036 impact. Radar measurements in 2021, combined with a refined Yarkovsky drift, ruled out impacts for at least the next century. The all-clear for Apophis is, again, a Yarkovsky calculation.

Depleting the Kirkwood gaps

Daniel Kirkwood noticed in 1866 that the distribution of main-belt asteroids has prominent gaps at heliocentric distances corresponding to mean-motion resonances with Jupiter: 3:1 at 2.50 AU, 5:2 at 2.82 AU, 7:3 at 2.96 AU, 2:1 at 3.27 AU. Inside a resonance, an asteroid's eccentricity is pumped up rapidly — on a timescale of 10⁵ to 10⁷ years — until its orbit crosses Mars or even Earth, at which point planetary scattering ejects it from the belt. The gaps are evolutionary holes.

But here is the puzzle: collisional grinding within the main belt is constantly producing new fragments adjacent to those resonances. Without something to refill the gaps, they should be partly populated by collisional fragments younger than the eccentricity-pumping clock. They are not. The reason is Yarkovsky drift: any fragment small enough to feel a measurable thrust will slowly migrate in semi-major axis. Fragments born just outside a resonance drift across it; once inside, the resonance scoops them out. The continuous supply of small bodies near the gaps is therefore continuously drained. The same drift also explains the long-recognised observation that asteroid families — clusters of fragments from a single disruption event — spread in semi-major axis over their age, the spread scaling roughly as √(age) modulated by the inverse-radius dependence of the Yarkovsky drift. From the present-day extent of a family in (a, H) space, one can read off the age of the parent collision.

YORP — the spin-rate cousin

The Yarkovsky effect is the net force from anisotropic thermal re-emission. The same anisotropy on an irregularly shaped body also produces a net torque: the Yarkovsky-O'Keefe-Radzievskii-Paddack effect, universally abbreviated YORP. YORP changes an asteroid's spin rate and obliquity on timescales of 10⁵ to 10⁸ years. Several outcomes are observed.

• YORP spin-up to rotational fission. A rubble-pile asteroid spun above the centrifugal limit (~2.2-hour rotation period) sheds mass from its equator, often forming a binary. The contact-binary asteroid (66391) Moshup with its satellite, and many ~30% of small NEAs that are in fact binaries, are explained this way.
• YORP obliquity asymptotes. The torque tends to drive obliquities toward 0° or 180° on long timescales, with consequences for the diurnal Yarkovsky drift sense (obliquity 0° → max prograde outward drift; obliquity 180° → max retrograde inward drift).
• YORP-Yarkovsky coupling. Because YORP changes obliquity, it modulates the Yarkovsky thrust. The two effects must be modelled together for any asteroid older than ~10⁶ years.

Order-of-magnitude estimate

For a typical near-Earth asteroid of radius R = 500 m, density ρ = 1500 kg/m³, low thermal conductivity K = 0.01 W/m/K, prograde rotation with obliquity 0°, period 5 h, at a = 1 AU, the diurnal Yarkovsky in-track acceleration is:

a_y ≈ (8/9) × (1 − A) × Φ / (ρ R c) × f(Θ, γ)

where A is the bolometric albedo, Φ ≈ 1361 W/m² is the solar constant at 1 AU divided by 4 (averaging over the cross-section), c is the speed of light, and f(Θ, γ) is a dimensionless function of the thermal parameter Θ and obliquity γ — typically of order 0.1 for low-conductivity regolith. Plugging numbers:

a_y ~ (1 − 0.05) × 340 / (1500 × 500 × 3 × 10⁸) × 0.1
    ~ 1.4 × 10⁻¹³ m / s²

Tiny. Over a one-year orbital period at v ≈ 30 km/s, this in-track acceleration produces a velocity change Δv ≈ 4 × 10⁻⁶ m/s and a semi-major-axis drift

da/dt ≈ (2 a / v) × a_y ≈ 9 × 10⁻⁵ m / s ≈ 3 km / yr.

Three kilometres per year sounds infinitesimal — but over a million years it is 3 × 10⁹ m, or 3 × 10⁻² AU. Over the 4.5 Gyr age of the solar system, a freshly minted 500 m fragment could drift a full AU. That is more than enough to ferry main-belt fragments into resonance and onto Earth-crossing orbits — exactly the supply chain inferred from observations.

Variants and extensions

• Seasonal Yarkovsky on high-obliquity bodies. Dominates when γ → 90°. The hibernating side that emerges after winter is asymmetric in time, producing a net along-track force that always reduces a. The Hidalgo and Damocloid asteroids may be partly evolved by this term.
• Yarkovsky-Schach effect. Eccentricity-driven modulation: an eccentric orbit makes the thermal flux change between perihelion and aphelion, introducing a small additional drift term. Important for high-e NEAs.
• Tangential YORP. A second-order torque from boulder shadowing identified in numerical simulations (Golubov & Krugly 2012) that adds a non-zero secular spin-up for symmetric bodies. Helps explain why YORP appears to be more effective than first-order theory predicted.
• Yarkovsky drag for artificial bodies. The same thermal-recoil mechanism acts on spacecraft. Pioneer 10/11's anomalous deceleration was once tentatively attributed to a thermal-recoil "Yarkovsky" force from asymmetric IR emission from the spacecraft body; the modern consensus (Turyshev et al. 2012) is that this is indeed the origin of the Pioneer Anomaly.

Where the Yarkovsky effect shows up

• Main-belt asteroid family ages. Hirayama families spread in (a, e, i) over time; the Yarkovsky-driven a-spread is the most reliable chronometer for ages from 10⁷ to 10⁹ years. The Veritas family is ~8 Myr old, Karin ~5.8 Myr, Eos ~1.3 Gyr.
• Near-Earth asteroid supply. The NEA population is sustained by Yarkovsky-driven injection of main-belt fragments into the ν₆ secular resonance and the 3:1, 5:2, 7:3 mean-motion resonances; without Yarkovsky the NEA reservoir would drain on a Myr timescale.
• Meteorite delivery. Specific meteorites have been linked to specific parent bodies via Yarkovsky-driven transit times. Most chondrite meteorites left their parent body within the last few tens of Myr and reached Earth via slow drift across a Kirkwood gap.
• Bennu ephemeris. The OSIRIS-REx team's published Bennu orbit explicitly includes a Yarkovsky transverse-acceleration parameter, fitted to 0.4% precision. Sample return on 24 September 2023 was timed against that ephemeris.
• Apophis 2029-2036 hazard retirement. Refined Yarkovsky modelling using 2021 Goldstone radar ruled out 2036 and 2068 impact resonances, removing Apophis from the impact-risk lists for the next century.

Common pitfalls

• Confusing radiation pressure with Yarkovsky. Both are photon-momentum effects, but radiation pressure is the direct push of absorbed sunlight (radial outward) while Yarkovsky is the recoil of thermally re-emitted photons (in-track). For sub-cm dust, radiation pressure and Poynting-Robertson dominate; for metre-to-kilometre rocks, Yarkovsky dominates; for asteroids 100 km+ neither matters much.
• Assuming the drift sign from the spin sense alone. The diurnal drift sense flips with obliquity, not just spin sense. A retrograde-spinning body with obliquity > 90° (i.e. its spin pole points roughly antiparallel to the orbital angular momentum) drifts inward; flip the obliquity past 90° and it drifts outward. Spin sense is shorthand for the sign of cos γ, not the literal hand of rotation.
• Forgetting the seasonal term for high-obliquity bodies. When γ is within ~10° of 90°, the diurnal term vanishes and the seasonal term takes over. Models that include only the diurnal piece systematically misfit such asteroids.
• Using bolometric albedo where Bond albedo is needed. The thrust scales as (1 − A_Bond), the fraction of incident energy that is absorbed and re-emitted thermally; using the geometric or visible-band albedo over-predicts the force by 10-30% for typical S-type asteroids.
• Treating Yarkovsky as a constant. Both YORP-driven obliquity evolution and changing heliocentric distance during the orbit modulate the instantaneous Yarkovsky thrust. For a body older than its YORP timescale, the present-day Yarkovsky drift is not its historical mean.