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Monthly Reports — 2008 January
 
Murison finished his analysis of and technical memo describing a laboratory calibration method for the new Trex geodetic astrolabe. A way of overcoming the calibration accuracy limitation due to the 1-arcsecond alignment precision of the best available retroreflectors is to spin the retro and determine the center of the resulting arc on the CCD. Murison had concerns that the spot position at the detector as a function of retro spin angle is much more complicated, due to the inevitable combination of misaligned retroreflector mirror planes and misaligned retro spin axis, than presumed by the Trex people. Unfortunately, the inclusion of a small misalignment of the retro spin axis from the system optical axis complicates the analytical analysis such that a ray tracing cannot be done with current computing technology. This is unfortunate not so much because an analytical trace cannot be done but because it confirms that the function of spot position with spin angle is indeed complicated. Nevertheless, the laboratory calibration method appears to be both sound and useful, even at the 1-arcsecond level.

With regard to the Kepler equation paper (wherein Murison describes a new optimal method for numerically solving the equation), Murison ran into difficulties with the hyperbolic orbit case. The problem is that, by definition, the eccentricity can no longer be considered a small quantity, so the iteration scheme that works so well for the elliptical orbit case probably cannot be made to work. Given that, in practice, the proportion of hyperbolic to elliptical orbits one generally tends to work with is vanishingly small, this is not a major setback. But it is annoying, and Murison is currently investigating how best to deal with it from an optimal numerical point of view.

Murison worked on his new restricted three-body code for satellite capture. He resolved a longstanding problem in the correct conversion of orbital elements from the "rotating-pulsating" coordinate frame to a local frame centered on either of the primary masses. The program now can calculate satellite capture timespan as a function of initial orbital elements with respect to either primary and hence investigate in three dimensions the origin (in terms of sun-orbiting bodies) of planetary captured satellites. Almost all previous satellite capture investigations ignore inclined orbits, which is a potentially important omission. Collaborating with Efroimsky, Murison will also introduce planetary tidal dissipation to determine if, despite being small in magnitude, it could have played a role in effecting permanent captures. (Murison thinks it is unlikely, but this avenue has not previously been investigated.)

Murison spent increasing amounts of time in his duty as Secretary of the AAS Division on Dynamical Astronomy, due to the upcoming DDA meeting and the upcoming DDA elections.