Engineering & Science
Yarkovsky Effect Formula: Asteroid Thermal Recoil & Orbital Drift (da/dt)
Calculate diurnal thermal-photon recoil acceleration a_Y and secular semimajor axis drift da/dt (m/yr) driving near-Earth asteroids like (101955) Bennu and Apophis.
How afternoon infrared photons push 500-meter asteroids hundreds of meters per year!
Ivan Osipovich Yarkovsky (1900) realized that a rotating sunlit asteroid re-emits absorbed solar energy in the thermal infrared AFTER thermal lag carries its warmest "afternoon" hemisphere away from the subsolar line—producing a tiny net transverse photon thrust a_trans = (3 * (1 - A) * S_0 * f_Y) / (2 * D * ρ * a_AU^2 * c)! Through Gauss’s planetary perturbation equation da/dt = 2 * a_trans / n (where orbital mean motion n = SQRT(μ_☉ / a^3)), prograde rotators spiral outward while retrograde rotators like OSIRIS-REx target (101955) Bennu spiral inward!
Model a carbonaceous rubble-pile NEA with diameter D = 500 m, bulk density ρ = 1,190 kg/m^3, semimajor axis a = 1.126 AU, Bond albedo A = 0.04, and effective thermal-lag projection factor f_Y = 0.14: secular orbital drift reaches |da/dt| = 459.5 m/yr—halving to 229.8 m/yr for a 1,000 m body due to strict 1 / D surface-to-mass scaling!
| Asteroid Diameter D (ρ = 1190 kg/m³, a = 1.126 AU, f_Y = 0.14) | Transverse Recoil Scaling | Semimajor Axis Drift |da/dt| (m/yr) | Planetary Defense Impact |
|---|---|---|---|
| D = 500 m (Bennu-Scale Rubble Pile) | 1 / D baseline | 459.5 m/yr | Dominates keyhole trajectory uncertainty |
| D = 1,000 m (Kilometer NEA) | 0.5× recoil | 229.8 m/yr | Exact inverse-diameter 1/D law |
| Invalid D <= 0, ρ <= 0, or A >= 1 | Error Guard | "Invalid Asteroid Parameters" | Physical Bounds Guard |
Secular Yarkovsky Semimajor Axis Drift Rate |da/dt| (Meters per Julian Year)
Evaluates (2 * a_trans / n) * 31,557,600 s/yr from asteroid diameter B2 (m), bulk density B3 (kg/m^3), semimajor axis B4 (AU), Bond albedo B5, and thermal-lag projection factor B6.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 < 0, B5 >= 1, B6 <= 0), "Invalid Asteroid Parameters", ROUND(2 * ((3 * (1 - B5) * 1361 * B6) / (2 * B2 * B3 * (B4 ^ 2) * 299792458)) / SQRT(1.3271244E20 / ((B4 * 1.4959787E11) ^ 3)) * 31557600, 1))Transverse Thermal-Recoil Acceleration a_trans (pm/s² = 10^-12 m/s²)
Outputs the raw photon-recoil acceleration in picometers per second squared (× 10^12).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 < 0, B5 >= 1, B6 <= 0), "Invalid Asteroid Parameters", ROUND(((3 * (1 - B5) * 1361 * B6) / (2 * B2 * B3 * (B4 ^ 2) * 299792458)) * 1E12, 3))Try the example
Use the original values or change them to test your understanding.