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The full program with abstracts in PDF format is here.
Especially intriguing to me was one that featured a masterful presentation entitled; ‘Analytic Theory of the YORP Effect for Near –Spherical Objects. This talk appeared in Session 02, starting at 10:45 a.m. and held everyone spellbound. The YORP Effect was named after Yarkovsky-O'Keefe-Radzievskii-Paddack – or the physicists that discovered it. It is a phenomenon that occurs when photons from the Sun are absorbed by a body and reradiated as heat. In the process, two forces influence the object: one from the impact of the photons, providing a tiny push, and the other as a recoil effect when the object emits the absorbed energy. See figure below:
Synopsis diagram of YORP Effect (From Wikipedia)
Since photons possess momentum, p = Ec , each of these interactions leads to changes in the angular momentum of the body relative to its center of mass. If considered for only a short period of time, these changes are very small, but over longer periods of time, these changes may integrate to significant changes in the angular momentum of the body.
The primary author, David Nesvorny, emphasized consideration of an irregularly -shaped small object in interplanetary space (i.e. typical asteroid) heated by sunlight and for which the temperature T of the object's surface element is set by the balance of absorbed, conducted and emitted radiation energies. The sketch given in the talk approximately appeared as shown below:
dt = r x d f
where r is the radius vector pointing from the center of mass of the object to dS. and F the force supplied. The element of asteroid surface area is dS. The total torque is obtained by integrating over the body's surface, e.g.
t = òs r x d f
and is called the thermal (YORP) torque. This can produce important effects on the spin rate ( w) and the obliquity ( e ) of the object over planetary timescales. In his presentation Nesvorny noted it was convenient to average t over the spin and orbit periods of the small object and thereby determine the mean YORP torque which controls the long term behavior of the spin vector. In bis approach Nesvorny said he also found it convenient to split into two parts: ts and te .
Where d w /dt = ts / I
And: d e /dt = te / Iw
And I denotes the principal moment of inertia. A key step is to take the surface integral over the torque (general) such that:
M » a òs dS (r x n ) ( n· n o)
The thermal YORP torque on an object with a vanishingly small value of surface thermal conductivity is expressed:
t = - 2/3 (1 - pv) vc òs dS (r x n ) ( n· n o)
Where pv is the thermal conductivity and vc the velocity of light. This can alternatively be expressed:
t = -a òW dW
/sin q
(r x N )max (0, n·
n o)
In the talk Prof. Nesvorny pointed out the main complications arose from the shapes of the asteroids considered, since these shapes would affect the solar insolation, thermal conductivity and related parameters. The analytical approach therefore made use of spherical harmonics in the form:
å ¥ q=0 å ¥ f=0 a n Gk (q, f)
Where the a, k are shape coefficients, and Gk (q, f) is a gamma function relating the angles, q and f.
Nesvorny emphasized the situations considered were confined to the cases where the impinging solar radiation was at right angles to the asteroid’s spin axis. Three separate detections of the effect were announced, including for a nearly spherical object (1998 KY), and on two more irregular objects, (1862 Apollo, and 25143 Itokawa).
In the case of the Apollo object the observed effect was approximately 3.0 x 10 -4 deg/day, vs. the theoretically –predicted YORP effect magnitude of 2.6 x 10 -4 deg/day. Earlier, Cornell graduate student Patrick Taylor and assistant professor of astronomy Jean-Luc Margot mapped the shape and located the spin pole of a 100-meter-diameter (about 300 feet) near-Earth asteroid called (54509) 2000 PH5 (abbreviated to PH5) between 2001 and 2005, using radar at the National Science Foundation's (NSF) Arecibo Observatory in Puerto Rico and NASA's Goldstone telescope in California.
On average, asteroids rotate every four to 12 hours. But the smallest asteroids (with a diameter of less than 10 kilometers, or about 6 miles) tend to spin either unusually slowly or unusually quickly -- and astronomers have long wondered why. YORP analytics could also explain why some asteroids come in pairs. Most asteroids are actually loosely bound clumps of rubble with very little internal cohesion, so an object with an increasing spin rate could eventually spin faster than its own strength and gravity can endure -- ultimately flying apart to form two objects.
The presentation ended by asking the question 'How to calculate best the YORP parameters? Three approaches were given:
i) Numerically: Write a consistent numerical code using the key torque and other associated parameters and compute the results and compare with the observations.
ii) Analytically: Use spherical harmonics to tie asteroid properties etc. to the approximated shapes, which can then ne analytically handled.
iii) Combine methods (i) and (ii), i.e. assume initial ellipsoid shape, e.g.
Then from this choose initial a,k values by which to compute the YORP torque, then refine by accommodating 2nd order effect. (E.g. sum over Legendre polynomials of even orders).
For small, irregularly
shaped objects , it was found that the YORP effect can cause measurable changes in motion. Taken together the sheer power of the Nesvorny presentation had the astronomers who attended his talk glad they did. It totally reinforced the power and depth of dynamical astronomy and celestial mechanics in an era in which the threat oof near Eaarth asteroids is finally being grasped.
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