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Precise alignment methods – a practical compact guide Great God! This is an awful place and terrible enough for us to have laboured to it without the reward of priority ... We took risks, we knew we took them ... Had we lived, I should have had a tale to tell of the hardihood, endurance, and courage of my companions. These rough notes and our dead bodies must tell the tale ... Robert Falcon Scott, 29 March 1912 Is the telescope setup after a few step the remaining task is to align the hour axis on e.g. the celestial pole. If one likes to observe visually then the star Polaris is a good mark. The accuracy of the obtained alignment is good enough because the typical field of view of a given combination telescope and eyepiece yields something between 0.5 and 1o . In the photographic case the situation is different. The primary task of an astrophotographer is not to point the telescope exactly to a desired target. The real task is to minimize the field rotation due to atmospheric refraction. The better pointing accuracy of a correctly aligned telescope is a desired by product of the precise alignment of the hour axis. The pointing accuracy of the goto telescopes can be enhanced if a software like Tpoint is applied. But it has to be mentioned that only after the movement of the hour axis according to the calculated corrections the telescope is ready for photographical purposes. The task of pointing is a complete different thing than tracking an object or better a star field. If you have doubts read the articles of A.S. Hinks and of P.T. Wallace and K.P. Tritton. On the following pages I describe precise visual methods how to align the hour axis. Precise means in this context with an accuracy better than 30 arc seconds. This tolerance makes it possible to take a two hours long exposure symmetrical to the meridian a little bit farther away from the celestial pole. Farther means about 30o. The field of view must not exceed about 1o by 1o. If one likes to picture larger field of views or closer to the celestial pole, then a better accuracy is needed. Of course the presented methods provide this higher accuracy in case where the measurement lasts simply longer. The mathematical background will not be described on these pages. The program will take over all the necessary computation. The sources are found in the literature or, when my manuscript manuscript found a publisher, there together with a cook book like guide of the procedure and many more. Overview From the numbers on the left side, these are the years when the methods were introduced, can be seen, that they are all well older than hundred years. This list is probably not complete but there is for each situation a method, e.g. for the temporary setup in the countryside as well as for a permanent setup at a real observatory. The methods were introduced by well known astronomers on both sides of the Atlantic Ocean at the time when the photographic plates replaced the eye as a detector in professional astronomy. With the exception that of J. Challis all other methods assume a perfect sidereal rate of the telescope's drive. Nowadays the telescopes fulfill this requirement within narrow limits without any problems. If one uses a telescope without any electrical drive and likes to find fainter objects with the setting circles then the method of choice is that of J. Challis, because it uses only the movement of the star in the direction of the declination measured twice. In all the other cases one star is used for the measurement and its movement in both direction, declination and rightascension is used for the data reduction. The accuracy is better in case where the measurement star is as close as possible to the celestial pole. On the celestial equator the method of A.A. Rambaut fails completely but not that of J. Challis. In the case of the method of E.S. King the measurement is carried out with Polaris. The drift drift alignment method introduced by J. Scheiner is a way too to reach the celestial pole in case where his original instructions were followed. I have to remind you that this method is zero-measurement and at the eyepiece there is a certain elbowroom if one has to interpret what zero really means. But the main drawback of the contemporary description is clearly that the refraction is not taken into account. One can make things simpler but not simpler than they are. I think these are all reasons not to use it in case one likes to take a photograph. The simplified version is simply thought as an entry point in order to grasp the basic elements of the alignment procedure and for a fast success. How I describe directions in this guide All information about directions in this guide are meant as seen by the unarmed eye that means as seen directly. If a star moves towards North then that means the declination is increasing. In the inverting astronomical telescope the star moves toward the horizon. A movement to the West means that the rightascension is increasing. Preparation If you think about measuring the position of the hour axis there is no need for additional expensive equipment. The only things which one needs are: a stop watch a calibrated eyepiece, at best with a quadratic measurement field a programmable pocket calculator The unit of the measurement eyepiece has to be calibrated in order that we obtain the length of the star trail in arc seconds. One starts by putting a star, which is in the vicinity of the celestial equator, on the western edge of the field (position A) and then one shuts down the drive and measures the time t until the star reaches position B. The the following equation d = 15 * cos(delta) * t yields the diameter d of the measurement field in arc seconds. The variable delta is the declination of the star and t is time needed the star needs to travel from the point A to B. The field diameter is then divided by the number of units and finally the scale in arc second per unit is received. The result should lie between about 5 to 10 arc seconds in the maximum. In every case the estimation of 2 arc seconds should be possible. Duration of the measurement The given numbers for the duration of the measurement are only approximations. In every case it should not be shorter than 10 minutes with the exception when the rough polar alignment was not as successful as expected. In that case the star will reach the edge of the filed and that time point has to be written down together with its position. Now continue as usual an calculate the position of the hour axis and correct it. Then start the procedure again. In case where the drive has a periodic error then it is best to choose the duration as a multiple of this error. The ordinary zero point is the true celestial pole. This is the intersection of the rotation axis of the earth with the sphere. In all methods where the refraction is eliminated by computation this point is the zero point. These methods are that of A.A. Rambaut and J. Challis. In case where the hour axis is aligned on this point it has to be moved in the direction of the zenith by the amount of the refraction. This amount R is given by the following equation R = (n – 1) * tan( 90o – phi) The refractive index n has the value of 1.0002743 and the geographical latitude phi is that of the observatory. The amount Rb in arc seconds is calculated by the multiplication and division with the following constants Rb= R * 3600 * 180 / Pi with Pi = 3.14. If one divides the obtained value by the unit of the measurement field the work at the telescope will be a little bit easier. If you use the variants of the methods introduced by E.S. King then this step is not necessary. In the vicinity of the celestial pole the correction for the refraction is superfluous and one reaches the apparent (refracted) pole directly. Guide for the visual measurement All four methods follow with tiny differences the following scheme: Leveling the tripod with the bubble level rough polar alignment of the hour axis orientation of the measurement field center the star that should be observed uncorrected tracking of the star with sidereal rate Reading the position on the measurement field and calculation of the correction At this point I have to mention that the description of this topic and presumably the reading takes longer than the effective work at the telescope later. With experience it is possible to perform all these seven steps within a hour. In that case the telescope is ready for the more interesting part before the astronomical twilight ends. Leveling the tripod with the bubble level The corrections can only be calculated in the true azimuthal coordinate system. In case where the mounting is not leveled the corrections are not really useful because we rotate along different axes. The purpose of the leveling is to coincide the axes of the telescope coordinate system with the true system. Are these requirements meet then it is possible to adjust the position of the hour axis alone by turning the mounting as a whole and by lowering or lifting the hour axis' elevation. This step is a necessary prerequisite for these methods. The needed accuracy is 1 mm on 1000mm or 0.057o. This requirement is usually met by ordinary bubble levels. If you like it more exact use a so called “Maschinenrichtwaage”, which has a tolerance of only 0.0057o or 20 arc seconds. Under these circumstances: Do not forget the mountains or the high-rise buildings in your vicinity! There are many ways for the rough polar alignment. Here my suggestion: Set the telescope to the declination of 90o. The local hour angle is in case of fork mounting irrelevant, in case of a German equatorial mounting it might be advisable to set it to the local hour angle zero. Now fix the the axes. The centering of Polaris happens only by means of the movement of the hour axis in azimuth and elevation. Calculation of the position of Polaris Rough alignment of the hour axis with the help of the calibrated measurement field of the eyepiece. Use a star close to the equator in the vicinity of the meridian and align the measurement field equatorially. You receive the azimuthal correction for the chosen star if you enter the value of its declination in the field correction star declination of the program. The corrections appears in the output and looks similarly to: Move the north end of the hour axis 771.48 units to the WEST with star at declination 20.00 degree 356.23 units to the WEST In der Elevationsrichtung können Sie die Korrektur direkt übertragen. You can download the program here. Orientation of the measurement field The axes of the measurement field must coincide with the directions either of the azimuthal or the equatorial coordinate system. Alignment with the azimuthal system: The alignment of the measurement field happens best when the star is already centered. In this case compare the horizontal axis of the field directly with the horizon. Of course this an estimation and therefore has a certain error. But for the sake of brevity, let me make the remark that we can live with this error because under any circumstances we receive the correct polar distance of the instrumental pole. We will see differences in case of the hour angle of the instrumental pole and hence if one calculates the corrections in the azimuthal coordinate system. This way of alignment is only used in the variants of E.S. King's method King B1 and King B2. There are other ways if one does not like it. Alignment with the equatorial system: Like in the case of the calibration of the measurement field center the star on the western edge (position A ) and turn the drive off. Align the field as long as the star does not reach position B. If you do not like the positional calibration of your goto telescope center the star in the middle of the field and move the telescope with the buttons of the h hand controller in the direction of the rightascension. Bring the star to the position C in the center of the field. If the star is centered then let the telescope tracki the star undisturbed. Write down the starting time point and the duration of the measurement. The star will move away from the center. Calculation of the corrections Independent from the alignment of the measurement field the correction can be calculated in both directions. The positive directions of the x- and y-axes will be explained in the dedicated sections of the different methods (see navigation bar on the left). Enter the values in both directions together in units of the grid together with the value of the grid unit The alignment of the hour axis based on the calculated correction is the remaining task. Choose a star close to the celestial equator in the vicinity of the meridian as it was already described in the above paragraph of rough polar alignment and align the hour axis in both directions according to the obtained values. The directions are the true directions and do not describe what you see in an inverting telescope. But remember that an astronomical telescope does only rotate the field bey an angle of 180o. Now the telescope is ready for the tracking of a star field! The hour axis points now to the point: Where none have gone before :-) Now we are with a higher precision at the pole than Roald Amundsen ever was.
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Comments, questions, corrections: markus.wildi@one-arcsec.org |
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