Y

TARGET OBJECT(S)

2 1997 WL23

3 A0054

pixels pixels

143.643 168.991

093.155 108.174

114.022 047.391

mag RAS

13.47 04 00 15.694

16.99 04 00 22.365

DEC S

ASTROMETRIC RESIDUALS RArms DECrms (arcsec) (arcsec) 000.368 000.401

Plate center, RAS: 04 00 19.500

Plate center, DEC: +21 21 16.90

X of plate center: 126.00

Y of plate center: 121.00

Figure 9.6 This report summarizes the process used to derive the positions for the three asteroids seen on Brian Manning's images in Figures 9.3 and 9.4. In a complete report, the date, time, epoch, pixel size, and reference stars used are all shown. For this image, the residuals were only 0.4 arcseconds.

• Tip: If you know the orientation and focal length of an image, you can use AIP4Win Distance Tool to measure the precise angular separation and position angle between any two points on that image.

Few observers know the actual focal length of their telescopes, yet this parameter is an easily computed by-product of astrometry. Given a reasonably well-separated set of reference stars, a single measurement of the focal length is good to about 0.1%.

9.4.5 Astrometry in Education

There is virtually no limit to educational projects based on astrometry—projects that would have been either very difficult or impossible for amateur astronomers and educators before the advent of CCD imaging. What CCD images bring to astrometry is high sensitivity, star images that yield accurate centroids, and software programs that make the reduction of data fast and easy.

One feature of astrometric projects that makes them especially valuable in the educational setting is the analysis of observational errors. The parallaxes of nearby stars, for example, are comparable to the errors of measurement, so that only by making careful measurements, reducing data intelligently, and understanding sources of observational error can an individual or class expect to obtain credible results.

Proper Motion of Stars. There are thousands of stars whose annual proper motion exceeds 0.2 of a second of arc—which is just about the limit that an observer with an 8-inch//10 telescope could detect using a given set of reference stars. The greatest known stellar proper motion is that of Barnard's Star in Ophi-uchus, a red dwarf that moves 10.34 arcseconds per year. A careful observer could (in theory) detect the motion of this object over the course of one week!

In many cases, stars that are near enough to Earth to show appreciable proper motion will also show parallax, substantially enhancing the educational value and interest in making the observations and reducing the data.

A proper motion observing program would consist of imaging a chosen star every couple weeks for several years. When its astrometric positions were plotted, they would describe a looping curve on the sky, a combination of the parallactic oval and the linear motion of the star. The Gliese Catalog of Nearby Stars lists some 3800 potential subjects for such study.

Stellar Parallax. The German astronomer Friedrich Wilhelm Bessel was the first to publish a widely accepted distance to a star (61 Cygni) in the year 1838. Bessel used trigonometric parallax to measure the apparent displacement of the nearby star against the background of more distant ones. Parallax shifts are small—only 0.7 arcsecond for a Centauri, the nearest star. If we accept the limit of 0.2 arcsecond for a single measurement made with a CCD camera, then it should be possible for an observer with an 8-inch//10 telescope to measure the parallax of any star closer than about 15 light years.

The most intriguing aspect of this project would be developing effective techniques to reduce observational error. Such techniques might include using image-motion reduction to make the smallest possible star images, shooting multiple images at each observing session and stacking them to reduce noise and improve the accuracy of centroids, and working at large image scales.

The methodology of the project consists of making images of the star as Earth moves around its orbit, with the greatest number made when the Earth-Sun line is perpendicular to the Sun-star line, but with enough images between the extremes to fill in the oval path described by the parallax star against the background of distant ones.

Determination of Orbits. There has probably always been a small band of amateur astronomers interested in the determination of the orbits of comets and asteroids. In the past, however, good positions were hard to come by. With the advent of CCD astrometry, a single observer can track and shoot images of an aster oid for three to six months, measure its positions on the images, and compute an orbit. To add spice to the project, the asteroid (or comet) could be a newly discovered object for which no previous orbit existed.

The project would consist of making images over an appreciable arc of the object's orbit. The astrometric positions would then become feedstock for an orbit determination program to make a least-squares fit to the best orbit possible, and they would be used to predict future positions for the object. As the measured orbital arc becomes longer, the quality of the solution improves, until eventually you have produced a definitive orbit.

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