Comet Halley and history

A history of Halley's Comet is presented. Comets Kohoutek and Ikeya-Seki are discussed

Nongravitational forces on comets

Methods are presented and discussed for determining the effects of nongravitational forces on the orbits of comets. These methods are applied to short-period and long-period comets. Results are briefly described

Astrometric observations of comets and asteroids and subsequent orbital investigations

Comets and minor planets were observed with a 155 cm reflector. Their orbital positions are presented in tabular form

On the Size-Dependence of the Inclination Distribution of the Main Kuiper Belt

We present a new analysis of the currently available orbital elements for the known Kuiper belt objects. In the non-resonant, main Kuiper belt we find a statistically significant relationship between an object's absolute magnitude (H) and its inclination (i). Objects with H~170 km for a 4% albedo) have higher inclinations than those with H>6.5 (radii >~ 170 km). We have shown that this relationship is not caused by any obvious observational bias. We argue that the main Kuiper belt consists of the superposition of two distinct distributions. One is dynamically hot with inclinations as large as \~35 deg and absolute magnitudes as bright as 4.5; the other is dynamically cold with i6.5. The dynamically cold population is most likely dynamically primordial. We speculate on the potential causes of this relationship.Comment: 14 pages, 6 postscript figure

The study of the physics of cometary nuclei

A semiannual progress report describing the work completed during the period 1 September 1975 to 29 February 1976 on the physics of cometary nuclei was given. The following items were discussed: (1) a paper entitled ""A speculation about comets and the earth'', (2) a chapter entitled"" The physics of comets'' for ""Reviews of Astronomy and Astrophysics'', (3) continuing work on split comets, and (4) results dealing with a new application of nongravitational solar-radial forces as a measure of comet nucleus dimensions and activity

Astrometric observations of comets and asteroids and subsequent orbital investigations

The transformation of the Oak Ridge astrometry from a photographic program to a charge coupled device (CCD) program can now be considered complete, and the number of observations being made is now approaching an order of magnitude greater than in the old photographic program. Astrometric observations with the 1.5-m reflector were made at the Oak Ridge Observatory, and the progress, accomplishments, and projected accomplishments are presented

Cometary Astrometry

Modern techniques for making cometary astrometric observations, reducing these observations, using accurate reference star catalogs, and computing precise orbits and ephemerides are discussed in detail and recommendations and suggestions are given in each area

Variational Principles for Lagrangian Averaged Fluid Dynamics

The Lagrangian average (LA) of the ideal fluid equations preserves their transport structure. This transport structure is responsible for the Kelvin circulation theorem of the LA flow and, hence, for its convection of potential vorticity and its conservation of helicity. Lagrangian averaging also preserves the Euler-Poincar\'e (EP) variational framework that implies the LA fluid equations. This is expressed in the Lagrangian-averaged Euler-Poincar\'e (LAEP) theorem proven here and illustrated for the Lagrangian average Euler (LAE) equations.Comment: 23 pages, 3 figure

Orbit Fitting and Uncertainties for Kuiper Belt Objects

We present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration can be treated as a perturbation to the inertial motion of the body. These techniques are immediately applicable to Kuiper Belt Objects, for which recovery observations are costly. Our methods produce positional estimates and uncertainty ellipses even in the face of the substantial degeneracies of short-arc orbit fits; the sole a priori assumption is that the orbit should be bound or nearly so. We use these orbit-fitting techniques to derive a strategy for determining Kuiper Belt orbits with a minimal number of observations.Comment: 21 pages AASTeX5, 3 figures, accepted to AJ. Associated software available at http://www.astro.lsa.umich.edu/users/gary

Generalized Euler-Poincar\'e equations on Lie groups and homogeneous spaces, orbit invariants and applications

We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar\'e equations on Lie groups and homogeneous spaces. Orbit invariants play an important role in this context and we use these invariants to prove global existence and uniqueness results for a class of PDE. This class includes Euler-Poincar\'e equations that have not yet been considered in the literature as well as integrable equations like Camassa-Holm, Degasperis-Procesi, $\mu$CH and $\mu$DP equations, and the geodesic equations with respect to right invariant Sobolev metrics on the group of diffeomorphisms of the circle