How many Earth-approaching asteroids are there?

The discovery process of Earth-approaching asteroids is formulated as a periodic sampling problem from an urn with replacement. It presumes as unchanging number of such objects over recent historical times, a fixed limiting magnitude/angular speed combination for detection probability, and allows for the possibility of the lack of detection or the lack of sufficient observations to refine an orbit at the first noticed apparition. While simple, the model is sufficiently powerful to show that an estimate of the number of Earth-approaching minor planets is impossible. This conclusion is insensitive to uncertainties in perturbing influences, celestial mechanics, or a model for the distribution of the orbital element sets of these minor planets

Optimal searches for asteroids

Optimal searches for a fixed object are discussed, and the rigorous analytical results of discrete search theory are presented. The totally optimal, the uniformly optimal, the locally optimal, and the fastest searches are shown to be identical under not too restrictive assumptions. The mathematical formalism is illustrated by an Earth-approaching asteroid search and optimal searches for such objects are explicitly constructed. The approximation that Earth-approaching asteroids are fixed is equivalent to having a very high ( equiv 100 sq degs/hour) search rate. Generalizations to other types of astronomical search are briefly mentioned

An analysis of the Hubble Space Telescope fine guidance sensor fine lock mode

There are two guiding modes of the Hubble Space Telescope (HST) used for the acquisition of astronomical data by one of its six scientific instruments. The more precise one is called Fine Lock. Command and control problems in the onboard electronics has limited Fine Lock to brighter stars, V less than 13.0 mag, instead of fulfilling its goal of V = 14.5 mag. Consequently, the less precise guiding mode of Coarse Track (approximately 40 milli-arc seconds) has to be used fairly frequently. Indeed, almost half of the scientific observations to have been made with the HST will be compromised. The only realistic or extensive simulations of the Fine Lock guidance mode are reported. The theoretical analysis underlying the Monte Carlo experiments and the numerical computations clearly show both that the control electronics are severely under-engineered and how to adjust the various control parameters to successfully extend Fine Lock guiding performance back to V = 14.0 mag and sometimes beyond

The discovery circumstances of Earth-approaching asteroids

The discovery circumstances are analyzed for all Earth-approaching asteroids detected in the last twenty-four years. In particular, topocentric angular velocities, opposition distance, geocentric and heliocentric distances, phase angle, and lunar phase at discover were calculated in an effort to separate any selection effects between chance and purposeful (i.e., as the result of a systematic search) discoveries. Another motivation was the possibility of discerning useful clues how to search more efficiently for such objects. There are 60 minor planets in the sample. The principal result is that the discovery of Earth-approaching asteroids is dominated by serendipity. Therefore, searching for them at the current relatively bright limits at less than a very high rate seems pointless

A search for Earth-crossing asteroids

Improvements made in both resolution element size and sensitivity in EBSICON cameras are discussed. An up-to-date illustration of what an asteroid detection now looks like is provided. Shown are four phases during the realignment of the live (white) and reference (black) frames. As one passes through the sequence the stars' images overlap and become grey, while the displaced images of the asteroid do not cancel

Gamma ray burst astrometry 2: Numerical tests

Since the announcement of the discovery of sources of gamma ray radiation in 1973, many more reports of such bursts have been published. Numerous artificial satellites have been equipped with gamma ray detectors including GRO. Unfortunately, almost no progress has been made in identifying the sources of this high energy radiation. Only one visible counterpart is known. It is suspected that this is a consequence of the methods currently used to define gamma ray burst source 'error boxes'. An alternative procedure was proposed in 1988 by Taff. Herein, Monte Carlo simulations are reported of the efficacy of this technique using realistic burst timing uncertainties and satellite location errors as well as a variety of satellite constellations. Since these are controlled numerical experiments, the dependence is examined of the statistics of the errors in the deduced burst wavefront normal as a function of the timing inconsistencies, detector location standard deviations, and especially the number and distribution of the detectors. The results clearly show that an arc minute prediction of a unique burst location is routinely obtainable once there are at least two interplanetary detectors

Analyzing Space-Based Interferometric Measurements of Stars and Network Measurements of Gamma-Ray Bursts

Since the announcement of the discovery of sources of bursts of gamma-ray radiation in 1973, hundreds more reports of such bursts have now been published. Numerous artificial satellites have been equipped with gamma-ray detectors including the very successful Compton Gamma Ray Observatory BATSE instrument. Unfortunately, we have made no progress in identifying the source(s) of this high energy radiation. We suspected that this was a consequence of the method used to define gamma-ray burst source "error boxes." An alternative procedure to compute gamma-ray burst source positions, with a purely physical underpinning, was proposed in 1988 by Taff. Since then we have also made significant progress in understanding the analytical nature of the triangulation problem and in computing actual gamma-ray burst positions and their corresponding error boxes. For the former, we can now mathematically illustrate the crucial role of the area occupied by the detectors, while for the latter, the Atteia et al. (1987) catalog has been completely re-reduced. There are very few discrepancies in locations between our results and those of the customary "time difference of arrival" procedure. Thus, we have numerically demonstrated that the end result, for the positions, of these two very different-looking procedures is the same. Finally, for the first time, we provide a sample of realistic "error boxes" whose non-simple shapes vividly portray the difficulty of burst source localization

A search for Earth-crossing asteroids, supplement

The ground based electro-optical deep space surveillance program involves a network of computer controlled 40 inch 1m telescopes equipped with large format, low light level, television cameras of the intensified silicon diode array type which is to replace the Baker-Nunn photographic camera system for artificial satellite tracking. A prototype observatory was constructed where distant artificial satellites are discriminated from stars in real time on the basis of the satellites' proper motion. Hardware was modified and the technique was used to observe and search for minor planets. Asteroids are now routinely observed and searched. The complete observing cycle, including the 2"-3" measurement of position, requires about four minutes at present. The commonality of asteroids and artificial satellite observing, searching, data reduction, and orbital analysis is stressed. Improvements to the hardware and software as well as operational techniques are considered

Sub-Plate Overlap Code Documentation

An expansion of the plate overlap method of astrometric data reduction to a single plate has been proposed and successfully tested. Each plate is (artificially) divided into sub-plates which can then be overlapped. This reduces the area of a 'plate' over which a plate model needs to accurately represent the relationship between measured coordinates and standard coordinates. Application is made to non-astrographic plates such as Schmidt plates and to wide-field astrographic plates. Indeed, the method is completely general and can be applied to any type of recording media

Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals

We present a method to integrate the equations of motion that govern bound, accelerated orbits in Schwarzschild spacetime. At each instant the true worldline is assumed to lie tangent to a reference geodesic, called an osculating orbit, such that the worldline evolves smoothly from one such geodesic to the next. Because a geodesic is uniquely identified by a set of constant orbital elements, the transition between osculating orbits corresponds to an evolution of the elements. In this paper we derive the evolution equations for a convenient set of orbital elements, assuming that the force acts only within the orbital plane; this is the only restriction that we impose on the formalism, and we do not assume that the force must be small. As an application of our method, we analyze the relative motion of two massive bodies, assuming that one body is much smaller than the other. Using the hybrid Schwarzschild/post-Newtonian equations of motion formulated by Kidder, Will, and Wiseman, we treat the unperturbed motion as geodesic in a Schwarzschild spacetime whose mass parameter is equal to the system's total mass. The force then consists of terms that depend on the system's reduced mass. We highlight the importance of conservative terms in this force, which cause significant long-term changes in the time-dependence and phase of the relative orbit. From our results we infer some general limitations of the radiative approximation to the gravitational self-force, which uses only the dissipative terms in the force.Comment: 18 pages, 6 figures, final version to be published in Physical Review