Photon thrust fro
m shape alone can produce quasi-secular changes in an asteroid's orbital ele
ments. An asteroid in an elliptical orbit with a north–south shape asy
mmetry can steadily alter its ele
ments over ti
mescales longer than one orbital trip about the Sun. This thrust, called here orbital YORP (YORP = Yarkovsky–O'Keefe–Radzievskii–Paddack), operates even in the absence of ther
mal 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 asteroid's orbital ele
ments fro
m orbital YORP operates only over the precession ti
mescale of the orbit or of the asteroid's spin axis; this is generally only thousands or tens of thousands of years. Thus while the orbital YORP ti
mescale 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 i
mpact the Earth in 2036. A near-
maxi
mal orbital YORP effect is found by assu
ming Apophis is without ther
mal inertia and is shaped like a he
misphere, with its spin axis lying in the orbital plane. With these assu
mptions orbital YORP can change its along-track position by up to
me="mml2">method=retrieve&_udi=B6WGF-4PJCYH3-1&_mathId=mml2&_user=10&_cdi=6821&_rdoc=15&_acct=C000050221&_version=1&_userid=10&md5=dc8418066c4b865a2352522e8f5a1885" title="Click to view the MathML source">±245 km, which is co
mparable to Yarkovsky effects. Though Apophis' shape, ther
mal properties, and spin axis orientation are currently unknown, the practical upper and lower li
mits are liable to be
much less than the
me="mml3">method=retrieve&_udi=B6WGF-4PJCYH3-1&_mathId=mml3&_user=10&_cdi=6821&_rdoc=15&_acct=C000050221&_version=1&_userid=10&md5=24fee77be47c7ed91a3212b094915d19" title="Click to view the MathML source">±245 km extre
mes. Even so, the uncertainty in position is still likely to be
much larger than the
me="mml4">method=retrieve&_udi=B6WGF-4PJCYH3-1&_mathId=mml4&_user=10&_cdi=6821&_rdoc=15&_acct=C000050221&_version=1&_userid=10&md5=71145e1edaf87df0d169fddb4f9ae6e3" title="Click to view the MathML source">mg src="http://www.sciencedirect.com/scidirimg/entities/223c.gif" alt="not, vert, similar" border=0>0.5 km “keyhole” Apophis
must pass through during its close approach in 2029 in order to strike the Earth in 2036.