Yarkovsky and YORP Effect — How Sunlight Slowly Steers Asteroids

Radiation Pressure vs. Thermal Re-emission

Sunlight carries momentum. When photons strike a surface and are absorbed or reflected, they exert a force — solar radiation pressure. For an airless body this force always points roughly away from the Sun, along the Sun–object line, and it is the dominant thermal-related force for dust grains and thin solar sails. But for a rotating, finite-conductivity asteroid there is a second, subtler effect: the body does not re-radiate the absorbed energy immediately or isotropically. It takes time to heat up, and that delay means the hottest point on the surface is not the point facing the Sun — it trails behind by an amount set by the rotation rate and thermal inertia. Because outgoing thermal photons also carry momentum, an asymmetric temperature distribution produces a net force that is not aligned with the Sun direction. This recoil force is the Yarkovsky effect, named after the Russian civil engineer Ivan Osipovich Yarkovsky, who first proposed the idea around 1900 in a private pamphlet, decades before it could be tested.

The Diurnal Yarkovsky Effect

The diurnal variant arises from the asteroid’s rotation about its own spin axis, on a timescale of hours. Consider a spherical, dark asteroid spinning with period P. As a surface element rotates into sunlight it begins absorbing energy, but because rock and regolith have finite thermal conductivity, the surface temperature peaks not at local noon but some time after — the thermal analogue of the fact that the hottest part of an Earth day is mid-afternoon, not solar noon.

That temperature lag means the afternoon (post-noon) hemisphere is hotter than the morning hemisphere and radiates more strongly in the infrared. The excess thermal photons leaving the afternoon side push the asteroid forward relative to that hemisphere — which, combined with the geometry of prograde vs. retrograde rotation, translates into a force with a component along the orbital velocity vector:

• Prograde rotators (spin axis obliquity < 90°, spinning the same sense as their orbit): the diurnal effect adds orbital energy, so a (semi-major axis) increases over time — the asteroid spirals slowly outward.
• Retrograde rotators (obliquity > 90°): the diurnal effect removes orbital energy, so a decreases — the asteroid spirals slowly inward, toward the Sun.

The Seasonal Yarkovsky Effect

The seasonal variant operates on the timescale of one orbital period rather than one rotation, and it depends on the obliquity of the spin axis relative to the orbital plane — the same geometry that gives Earth its seasons. Picture an asteroid whose spin axis lies roughly in the orbital plane. As it moves along its orbit, first one pole faces the Sun and warms up, then (half an orbit later) the other pole does. Each pole re-radiates its absorbed heat with a delay set by the body’s thermal inertia, and because the whole hemisphere in \"summer\" is systematically hotter than in \"winter\", the resulting thermal photon flux is asymmetric along the direction of orbital motion.

Unlike the diurnal effect, the seasonal effect always removes orbital energy, regardless of the sense of rotation — it acts like a drag force and always shrinks the semi-major axis very slightly. It typically matters most for asteroids with high obliquity (spin axis near the orbital plane) and for those with long rotation periods, where the diurnal component is otherwise suppressed.

In practice the two effects superpose. Small, fast-spinning, low- obliquity asteroids are dominated by diurnal drift; large or slow-rotating, high-obliquity bodies are dominated by seasonal drag.

The Underlying Physics: Thermal Lag and Momentum

The key parameter that controls how strong the thermal lag is — and therefore how strong Yarkovsky drift is — is the thermal parameter Θ, which compares how quickly heat is conducted into the body against how quickly the surface radiates it away:

Here ω is the rotation angular frequency (2π/P), ε is the infrared emissivity, σ is the Stefan–Boltzmann constant, and T₃ₛₜₓ⁾ is the subsolar equilibrium temperature. Two limits are instructive:

• Θ → 0 (very low thermal inertia, e.g. a fine-regolith surface that radiates heat almost instantly): the temperature peaks almost exactly at local noon, the thermal lag angle approaches zero, and the Yarkovsky force nearly vanishes.
• Θ → ∞ (very high thermal inertia, e.g. bare metallic or solid rock): heat conducts into the interior so efficiently that the surface never gets much hotter than the average, again suppressing the day – night temperature contrast and the resulting force.

The Yarkovsky force is maximised at intermediate Θ ≈ 1, roughly when the thermal skin depth is comparable to the distance heat can diffuse in one rotation. This is why Yarkovsky drift rates depend sensitively on surface regolith properties, not just size and orbit.

The resulting acceleration scales approximately as:

Because the accelerating force scales with surface area (D²) while the asteroid’s inertia scales with mass (D³), the effect scales as 1/D: small bodies drift much faster (per unit semi-major axis) than large ones. A 100 m asteroid can drift ~10₃ times faster in a/yr terms than a 10 km asteroid of the same composition.

The YORP Effect: Spinning Bodies Up and Down

The YORP effect — named for Yarkovsky–O’Keefe–Radzievskii–Paddack, the four scientists whose work established it — is the rotational sibling of the Yarkovsky effect. Where Yarkovsky is a net linear force from asymmetric thermal emission, YORP is a net torque from the same emission, arising whenever an asteroid’s shape is not perfectly smooth and symmetric (a perfect sphere or ellipsoid would radiate symmetrically and feel zero net torque).

Real asteroids are irregular: craters, concavities, boulders, and non-uniform albedo patches all cause the reflected-plus-thermally- emitted photon flux to carry a small net angular momentum. Summed over a full rotation and a full orbit, the torque does not average to zero for an irregular body, and it very slowly changes the asteroid’s spin rate and the direction of its spin axis (obliquity).

YORP was first measured directly on asteroid (54509) YORP itself (formerly 2000 PH5), whose rotation period was found to be shortening by about 1 ms/year — exactly the kind of secular spin-up the theory predicted. Similar direct detections followed for (1862) Apollo and (1620) Geographos.

Asteroid Families, Meteorites and the Yarkovsky – YORP Cycle

Collisional asteroid families — clusters of fragments sharing a common parent body, first identified by clustering in proper orbital elements by Kiyotsugu Hirayama in 1918 — provide some of the best evidence for Yarkovsky drift. Immediately after a family-forming collision, fragments share almost identical semi-major axes. Over hundreds of millions of years, Yarkovsky drift spreads them out: small fragments drift fastest (recall the 1/D scaling), so a plot of family members’ semi-major axis vs. inverse diameter (1/D) shows a characteristic V-shaped border in (a, 1/D) space, with the slope of the V directly proportional to family age. This "Yarkovsky V-shape" method is now a standard technique for dating asteroid families independent of crater-counting or dynamical modelling.

Yarkovsky drift is also the accepted mechanism that feeds meteorites and near-Earth asteroids from the main belt into resonance "escape hatches" — narrow regions in semi-major axis (such as the ν₆ secular resonance near the inner edge of the belt, or the 3:1 mean-motion resonance with Jupiter at 2.5 AU) where gravitational perturbations rapidly pump up orbital eccentricity until the object crosses Earth’s or Mars’s orbit. Without Yarkovsky drift slowly walking small bodies into these resonances over millions of years, the observed flux of meteorites and small near-Earth asteroids could not be sustained from the main belt’s collisional debris alone.

Why It Matters for Planetary Defense

For an asteroid on a trajectory that will make a close approach to Earth decades from now, the accumulated Yarkovsky drift over that time can shift its predicted position by a significant fraction of an Earth radius — enough to change whether a "keyhole" gravitational resonance is crossed, and therefore whether a future impact is possible. The most famous case is (99942) Apophis: early orbit solutions in 2004 suggested a small but non-negligible chance of a 2029 Earth impact; refining the solution with the Yarkovsky effect included (and later with direct radar astrometry) ruled out impact for at least the next century.

(101955) Bennu, the target of NASA’s OSIRIS-REx sample-return mission, is the best-characterised case: its Yarkovsky acceleration has been measured to be (-19.02 ± 0.10) × 10⁻¹&sup4; AU/day² from Doppler radio tracking, allowing JPL’s Sentry impact-monitoring system to compute a cumulative impact probability through 2300 with confidence that would be impossible using gravity alone. Every catalogued asteroid used for long-term risk assessment by JPL’s Sentry and ESA’s CLOMON systems now carries an explicit Yarkovsky uncertainty term in its orbit solution when the observational arc is long enough to constrain it.

Putting Numbers on It: An Order-of-Magnitude Model

A useful order-of-magnitude estimate for the diurnal Yarkovsky semi-major-axis drift rate, valid for a spherical asteroid with low-to-moderate thermal parameter, is the Rubincam approximation:

Plugging in typical near-Earth-asteroid numbers — D = 1 km, ρ = 2000 kg/m³, aₖₕ = 1.5 AU, α ≈ 0.9, cosγ ≈ 1 — gives da/dt ≈ a few × 10⁻&sup4; AU/Myr, matching the values recovered from real orbit-determination campaigns to within a factor of a few. Over the ~10 Myr dynamical lifetime typical of a near-Earth asteroid, this integrates to a semi-major-axis walk of order 0.01–0.1 AU — comparable to the width of the resonance "escape hatches" that ultimately deliver these bodies to Earth-crossing orbits.

Because YORP torque and Yarkovsky force share the same physical origin — asymmetric thermal photon emission — both effects are frequently modelled together in modern N-body + thermophysical integrators, which combine a shape model, a rotation state, a thermal-inertia value and a full gravitational force model to predict both orbital drift and spin evolution self-consistently over centuries to millions of years.

Try the simulations: Asteroid Deflection lets you compare a kinetic-impactor Δv against slow thermal drift; Orbital Mechanics shows how a tiny non-gravitational acceleration compounds over many orbits.