Engineering topics

Taff, L. G.

Publications and source records attributed to Taff, L. G..

29 records · Page 2

NASA NTRS1986

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.

Taff, L. G.↗

NASA NTRS1986

Bi-telescopic, deep, simultaneous meteor observations

A statistical summary is presented of 10 hours of observing sporadic meteors and two meteor showers using the Experimental Test System of the Lincoln Laboratory. The observatory is briefly described along with the real-time and post-processing hardware, the analysis, and the data reduction. The principal observational results are given for the sporadic meteor zenithal hourly rates. The unique properties of the observatory include twin telescopes to allow the discrimination of meteors by parallax, deep limiting magnitude, good time resolution, and sophisticated real-time and post-observing video processing.

Taff, L. G.↗

NASA NTRS1985

Two locations, two times, and the element set

A robust analytical formulation is developed to apply classical initial orbital determination to artificial satellites whose locations are uncertain to about 1 cu km and separated in time by no more than 30 min. An analytical simplification reduces Gauss's method, iteration on the semilatus rectum, iteration on the true anomaly, and the Lambert-Euler technique, to the solution of a single equation in one unknown, instead of the usual coupled triplet of three equations in three unknowns. The method is demonstrated for all common artificial satellite orbits over a variety of time intervals between the two location vectors, and for a varied set of position and distance errors.

Taff, L. G.↗

NASA NTRS1985

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.

Taff, L. G.↗

NASA NTRS1985

Low altitude, one centimeter, space debris search at Lincoln Laboratory's (M.I.T.) experimental test system

The majority of work performed by the Lincoln Laboratory's Space Surveillance Group, at the request of NASA, to define the near-earth population of man-made debris is summarized. Electrooptical devices, each with a 1.2 deg FOV, were employed at the GEODSS facility in New Mexico. Details of the equipment calibration and alignment procedures are discussed, together with implementation of a synchronized time code for computer controlled videotaping of the imagery. Parallax and angular speed data served as bases for distinguishing between man-made debris and meteoroids. The best visibility was obtained in dawn and dusk twilight conditions at elevation ranges of 300-2000 km. Tables are provided of altitudinal density distribution of debris. It is noted that the program also yielded an extensive data base on meteoroid rates.

Taff, L. G.↗

NASA NTRS1984

On initial orbit determination

The classical methods of initial orbit determination are brought together within a larger viewpoint. This new synthesis stresses that all such techniques follow one of three approaches. Either they seek to compute the orbital element set, or its equivalent, by attacking the differential equations of motion (Laplace), the first integrals of the equations of motion (Taff), or the solution itself (Gauss). The particular technique pursued within a given type of approach should depend upon the nature of the observational data, the amount of a priori information one is willing to presume, and the object of the exercise. This might be a binary star system, a moon, a minor planet, or an artificial satellite. The efficacy of some algorithms for each approach is discussed briefly. Unfortunately, none of them work very well. Extensions of these techniques to radars or laser radars are trivial and have provided no new insights into the overall problem.

Taff, L. G.↗

NASA NTRS1984

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. Previously announced in STAR as N83-34657

Taff, L. G.↗

NASA NTRS1984

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.

Taff, L. G.↗

NASA NTRS1983

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.

Taff, L. G.↗

NASA NTRS1983

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.

Taff, L. G.↗

NASA NTRS1981

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.

Taff, L. G.↗