See also Technical Reports (preprints and reprints) in Publications.

Asteroid Ephemerides and Masses

An extensive set of observations, some going back into the 19th century, have been analyzed to provide ephemerides and masses of some of the largest asteroids. (Ephemerides are predicted coordinates of celestial bodies as a function of time.) These asteroid ephemerides have been used in the The Astronomical Almanac since the 2000 edition. Additionally, all asteroids that have measurable gravitational effects on their neighbors are being studied for possible mass determinations; the feasibility of such determinations depends on the strength of the dynamical interactions and the availability of good historical observations. There are, currently, about a dozen asteroids with masses determined in this way, and there are about nine others that are candidates for future work. If we know both the mass and size of an asteroid, we can calculate its density, which is a clue to the way it was formed. Having good asteroid mass determinations is also important for computing accurate ephemerides of the major planets in the solar system. This project is partially funded by NASA.

Also being explored is a way to more efficiently identify asteroids that are members of a "family" - that is, those that have common physical and dynamical properties. The members of an asteroid family undoubtedly have a common origin, probably in a collision of two larger asteroids when the solar system was young.

Gauge Freedom in Celestial Mechanics

"Gauge freedom" is a term for a specific property of the mathematics used to describe a physical system, such as a group of orbiting bodies. It emerges when the number of mathematical variables exceeds the number of physical degrees of freedom, allowing the system to be mathematically described in different ways that are physically equivalent. For example, for a group of orbiting bodies, the computed trajectories will all be identical even though the variables used are different. In certain cases, properly exploiting this freedom allows for simplifications in the calculations, as well as fresh insights into the physics of the systems. This approach is being applied to several difficult dynamical problems.

Orbit-Orbit Distance Function

For two small bodies orbiting a much larger one (such as two planets orbiting the Sun), when is the distance between the orbiting bodies least and greatest? The answer is easy if the two orbits are circles in the same plane, but is unexpectedly complex in the more general case of non-coplanar elliptical orbits. The mathematical solution is being explored. If an efficient algorithm can be found, it would have many practical applications, such as estimating the times of possible close approaches of inner-solar-system asteroids to Earth, or correcting the trajectories of interplanetary spacecraft.

Earth Rotation Modeling

Several projects are in progress to enhance the accuracy with which we calculate the orientation of the Earth in space as it spins, including the short- and long-term variations in the direction of its axis. The fundamental equations of the Earth's rotation, as affected by the gravitational attraction of the Sun and Moon, are being redeveloped to ensure that the underlying physics is correctly represented. Separately, several recent theories of the Earth's precession have been analyzed as part of an international effort (International Astronomical Union Working Group on Precession and the Ecliptic) to develop a new standard theory of precession for the astronomical and geodetic communities. Finally, in response to recent International Astronomical Union recommendations that change the basic representation of the Earth's rotational angle and its relationship to astronomical time, algorithms and associated software are being developed that efficiently and accurately implement the new scheme.

Solar System Ephemeris Program Development

Ephemerides of solar system objects are usually computed using software that solves the equations of motion numerically, in a step-by-step fashion, where each step is a small increment of time. These programs are generally referred to as "integrators". A new object-oriented ephemeris integrator, based on experience with the decades-old Planetary Ephemeris Program (PEP), is being built. The program, called Newcomb, is is a long-term project without a specific timetable. An overall design has been developed and some modules have already been coded and tested. It will be first applied to studies of the motions of asteroids, since the observational data - almost all of it consisting of right ascensions and declinations measured with respect to background stars - are the simplest to process and the results most easily tested.

Celestial Navigation

A device that automatically observes stars, day or night, with respect to the local gravity vector (i.e., the true "down" direction), could provide a high-precision location and attitude solution for ships and aircraft, independent of GPS. Two prototype units with different designs have been constructed, one that operates in the far-red optical part of the spectrum, the other in the near-infrared. Accuracies better than 100 meters in position and several arcseconds in attitude should eventually be achievable with such devices. This project is jointly managed by the U.S. Naval Observatory in Washington and the Navy's SPAWAR System Center in San Diego. The prototype units were built by two California contractors. A follow-up device is being built for surveying applications (fixed points on land) by one of the contractors, funded by the National Geospatial-Intelligence Agency (NGA). The feasibility of using similar devices to precisely align Navy Aegis ship radar is also being investigated.

The navigation software for the project is based on some innovative algorithms for celestial navigation developed at the Naval Observatory about a decade ago. These algorithms are based on the solution to a familiar astronomical problem - determining the orbit of a body from a series of observations. In this case, the body in question is a ship and its "orbit" is a rhumb-line track over the spheroidal surface of the Earth.