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By J. B. Tatum

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Additional resources for Celestial Mechanics Vol.2

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The coordinates (ξ , η) are called the standard coordinates of the star, and our first task is to find a relation between the equatorial coordinates (α, δ) on the surface of the celestial sphere and the standard coordinates (ξ , η) on the tangent plane or the photograph. 1, and, in addition to the star Q and its projection Q', I have also drawn the north Celestial Pole P and its projection P'. The point P' is on the η axis. The spherical triangle PQC maps onto the plane triangle P' Q'C. On the spherical triangle PQC, the side PQ = 90o − δ and the side PC = 90o − D.

The reason is that the image of every star sits already on a certain pixel, and all that has to be done is for the computer to read which row and which column that pixel is on. As soon as the 5 exposure is made, the position is already determined! In fact, the situation is even better than that. As described, the positional precision of the measurement is determined by the pixel size. If the pixel measures one arc second by one arcsecond at the focal plane of the telescope, then the precision of the measurement, as we have described it, will be no better than one arcsecond.

The asteroid appears as two adjacent spots on the screen – one white and one black. Although any of these three techniques is far quicker and less tiring for the measurer than "blinking" or "stereoing" a pair of photographic films, they are by no means the last word in locating asteroid images on CCD exposures, for computer software is available that can detect any object that has moved between two exposures, and can indicate any such objects to the operator. One problem with CCD images is that the occasionally faulty pixel on a CCD array can look like as asteroid image on the screen, and also it is common for several pixels to be hit by a cosmic ray particle during the exposure, and this also produces a blemish on the image which looks a bit like an asteroid.

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Celestial Mechanics Vol.2 by J. B. Tatum


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