Orbital YORP and asteroid orbit evolution, with application to Apophis

Photon thrust from shape alone can produce quasi-secular changes in an asteroidʹs orbital elements. An asteroid in an elliptical orbit with a north–south shape asymmetry can steadily alter its elements over timescales longer than one orbital trip about the Sun. This thrust, called here orbital YORP (YORP = Yarkovsky–OʹKeefe–Radzievskii–Paddack), operates even in the absence of thermal inertia, which the Yarkovsky effects require. However, unlike the Yarkovsky effects, which produce secular orbital changes over millions or billions of years, the change in an asteroidʹs orbital elements from orbital YORP operates only over the precession timescale of the orbit or of the asteroidʹs spin axis; this is generally only thousands or tens of thousands of years. Thus while the orbital YORP timescale is too short for an asteroid to secularly journey very far, it is long enough to warrant investigation with respect to 99942 Apophis, which might conceivably impact the Earth in 2036. A near-maximal orbital YORP effect is found by assuming Apophis is without thermal inertia and is shaped like a hemisphere, with its spin axis lying in the orbital plane. With these assumptions orbital YORP can change its along-track position by up to ± 245  km , which is comparable to Yarkovsky effects. Though Apophisʹ shape, thermal properties, and spin axis orientation are currently unknown, the practical upper and lower limits are liable to be much less than the ± 245  km extremes. Even so, the uncertainty in position is still likely to be much larger than the ∼ 0.5  km “keyhole” Apophis must pass through during its close approach in 2029 in order to strike the Earth in 2036.