• Murison continued work on the first paper of the orbit-orbit distance problem, but he didn't make as much useful progress as anticipated due to the SAA effort.
• Murison implemented a Genetic Algorithms search technique to find two-orbit parameters that maximize the number of stationary points of the (2-dimensional) function that describes the distance between the orbiting bodies. The numerical program is extremely efficient. Results indicate that the maximum number is twelve, despite the theoretical upper bound of sixteen. There are also interesting geometrical configurations associated with the 12-solution orbits. A paper is in preparation.
• Murison worked on the problem of extracting orbital information of a body obtained from incomplete state vector observations (with errors) made from a moving platform. This is in support of SAA ("Space Situational Awareness") issues involving USNO MAPS and possibly the USNO FTS projects. He completed a first report, "Degradation of Error in the Longitudinal Coordinate of an Orbit from Astrometric Measurements", which considers a simplified two-dimensional geometry in order to extract an analytical expression for the degradation with time of orbital longitude errors. However, the generalization to three dimensions in order to determine the orbit orientation angles (inclination, ascending node, argument of pericenter), as well as letting the orbit(s) be eccentric instead of circular, is analytically intractable and exceedingly difficult. Murison investigated various approximations (both geometric and small-parameter) that might lead to useful analytical results, and he is implementing nonlinear least squares to calculate numerical results. Murison also found connections between this problem and his ongoing work on the orbit-orbit distance problem.
• Murison worked with M. Efroimsky (USNO), applying Efroimsky's gauge transformation ideas to the dynamical stability of natural satellites orbiting oblate, precessing planets. A paper was due to be given (Efroimsky lead author) at the 2005 DDA meeting but had to be cancelled due to illness.
• Murison is investigating the connections between the arc length of an elliptical orbit, elliptic integrals, modular functions, Fermat's Last Theorem (very obliquely!), and the orbit-orbit distance problem. The ideas for this came about while perusing the collected papers of Ramanujan. It is yet unclear what ramifications, if any, will result from this work.
• Murison implemented several web pages that contain various useful astronomical calculators.

2. Support of USNO instrumentation projects

• Murison assisted the FTS project in various ways, including the generating of observing lists of bright stars, exoplanets, and spectroscopic binaries within reach of the Clay Center telescope, where the FTS currently resides.

3. Consultation

• Murison lent assistance and expertise on various astronomical, dynamical, optical, spacecraft, and computational programming subjects to researchers and staff at USNO.

4. Professional growth and development

• Murison mentored summer student Andrei Munteanu (now at Harvard), working on fractal phase space structures in the dynamics of the elliptic restricted three-body problem and the implications for satellite capture in the Solar System.
• Murison and Efroimsky, with the probable collaboration of E. Belbruno (Princeton), are considering the writing of a book, Unconventional Celestial Mechanics. Murison has finished about two-thirds of the chapter on two-body motion.
• Murison prepared and gave a lecture on Gravity in the Solar System as part of the Smithsonian Institution's Resident Associate class, "New Astronomy at the U.S. Naval Observatory". Murison also prepared an extensive handout for the class members.
• Murison was to give a paper, on the Genetic Algorithms solutions for the 2-body distance function problem, at the DDA meeting in Santa Barbara but had to cancel due to illness.
• Murison assisted in the development of AA's new web site.
• Murison reviewed papers for Celestial Mechanics and Dynamical Astronomy.
• Murison continued his duties as Secretary of the AAS Division on Dynamical Astronomy, preparing for the 2006 DDA elections and helping the LOC with various tasks in preparation for the 2006 DDA meeting.
• Despite yet another year of relentless ineptitude, incompetence, and sheer stupidity in the Federal Exectutive Branch of what used to be our government, from which the Navy and the USNO in particular have become luckless road kill — and the budgetary, institutional reputation, and staff morale disasters that follow more predictably than the rising of the Sun — Murison, as well as other coworkers, invested correspondingly more energy into denial of reality and thereby continued increasingly pointless efforts to feign a somewhat cheerful attitude.