Usturlab ile yükseklik dairesinde gözlemler ile konum belirleme
Usturlab ile yükseklik dairesinde gözlemler ile konum belirleme
Dosyalar
Tarih
1995
Yazarlar
Kurttekin, Turgut
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Yayınevi
Fen Bilimleri Enstitüsü
Özet
Ufuk düzlemine paralel eşit yükseklikli noktaların oluşturduğu gökküre yüzeyindeki daireye Yükseklik Dairesi ( Almukantarat ) adı verilir. Jeodezik astronominin temel gözlem yöntemlerinden birisi de Yükseklik Dairesi 'nde yıldız gözlemleri ile konum belirlemektir. Önceden belirlenen sabit bir zenit uzaklığından yıldızların geçişinin astronomik yer tayininde kullanma fikri C.F. GAUSS (1808)'a dayanmaktadır. Bu_ gözlem yöntemi, gözlem aletinin belirlediği yükseklik açısından en az üç yıldızın geçiş zamanının tesbitine dayanmaktadır. Bu geçiş zamanının belirlenmesi için bir çok yaklaşım vardır ve bu yöntemler kullanılacak cihazların da çok çeşitli yapıda olmasına yol açmıştır. Bu cihazlardan biri de 'Usturlap' olarak bilinir. Büyük bir ihtimalle Astronom PTOLEMAEUS (M.S.85-160) tarafından kullanılan bu sözcük 19 ncu yüzyıla kadar birçok değişik anlamlar ifade ederek kullanılmıştır. Bu çalışmada, yıldızların Yükseklik Dairesi 'nden geçiş zamanlan ölçü olarak alınmış olup bu ölçüler kullanılarak istasyonların enlem ve boylam değerleri eş zamanlı olarak hesaplanmıştır. Bu çalışmada, konum hesabı için yaygın olarak kullanılan Astronomik Üçgen Çözümü yerine, Küresel koordinatlar ( 8, GHA ) kullanılarak, bir yıldızın Yükseklik Dairesi 'nden geçiş anındaki Kartezyen Koordinat Sistemi ( X, Y, Z ) koordinatlarının belirlenmesi tercih edilmiştir. Bundan sonraki adım gözlemcinin zenitine ilişkin değerlerin hesaplanması olup gözlemcinin zenit noktası, istasyonun enlem ve boylamı ile ilgili bilgileri taşımaktadır. Yükseklik Dairesi gözlemlerinde yıldız vektörü ile zenit vektörünün "İç Çarpım"ı dengeleme yöntemine esas olacak modelin belirlenmesini de kolaylaştırmış olup buradan elde edilen sonuçlar da halihazırda kullanılan değerler ile karşılaştırılmıştır. Bunlara ilişkin sonuçlar sunulmuştur.
In order to provide better terminology, the phrase "field astronomy" is used to cover the theory and practice necessary for third order work, and "geodetic astronomy" is used to cover the further theory and more refined practice necessary for first and second order work. Some such distinction is required in order to separate those sections and geodetic astronomy has a wider scope than field astronomy, therefore in geodetic astronomy, latitude, longitude and azimuth are measured to higher accuracy, namely with a standard error of about ± 0.3" to 0.5". and its objects are: a. To measure azimuth and longitude at Laplace stations to control azimuth in geodetic control surveys. b. To measure latitude and longitude to determine the deviation of the vertical for such purposes as: (1) Determining the geoid-spheroid separation by observation of geoid sections: (a) for the correct reduction to sphereiod level of distances measured on the surfaces of the earth. (b) to provide a direct and detailed measure of the form of the geoid. (2) The correction of horizontal angles in mauntainous terrain, or wherever the deviation of the vertical is large. (3) The study of variation in density within the crust of the Earth, eg to attempt to delineate the boundaries of tectonic plates. c. To measure latitude, longitude and azimuth at the origins of independent surveys. d. To measure latitude and longitude to demarcate astronomically defined baundaries. In geodetic astronomy, there are six main positioning methods: a. Sterneck Method (Latitude determination) b. Astrolabium Method (Latitude or time determination) c. Horrebow-Talcott Method (Latitude determination) d. Zinger Method (Time determination) e.Doellen Method (Time determination) f. Pole Star Observation for Azimuth Determination. The illustrations in geodetic astronomy are referred to the celestial sphere where the position of stars are supposed to be known and the fundemantal formulas are based on the apparent rotation of the celestial sphere around the Earth as a consequence of the Earth's rotation. Therefore, classical methods of reduction for the determination of astronomic position need the solution of the astronomical triangle which is very well-known quantity in Celestial System. This Thesis shows how the same problem can be solved using a method dealing with the location of observer's zenith on the celestial sphere and then the astro-latitude and astro-longitude of the station. All needed to be known is the right ascension and declination of the star and time of observation at the instant stars cross the almucantar of the astrolabe. Astrolabe as a measuring instrument which can be turned around a vertical axis whilst the line of sight forms a constant angle with the direction of a plumb line. When rotating the instrument, the line of sight prescribes a small cirle of equal altitude referred to as the almucantar. In other word, we are to consider a special circle of the celestial sphere parallel to the horizon connecting all points of equal altitude which is called Almucantar. Three stars on an almucantar define the plane of the almucantar and its position on the celestial sphere. In this form, the astrolabe serves to determine the time at which a star passes the altitude fixed by the instrument and then the determined time is used for the computation of latitude and longitude. Most astrolabes are attachments to be used in conjuction with a theodolite. Special astrolabes do exist, however, they can be used for no other purposes. In order to obtain a practical astrolabe,it is necessary to form a constant angle with a plumb line. Keeping this angle constant is best achieved with a prism. On principle, any angle could be chosen except zenith. Prismatic astrolabe essentially consists of a telescope which views a star through a prism by direct viewing (and simultaneously at some instruments after reflection in a pool of mercury which defines the vertical more accurately. Thus, the two star images appear to move in opposite directions in the focal plane and when they are side-by-side) the time recorder is actuated manually. At that instant, they are at altitude defined by the prism angle. If the observer should never have to wait long for a suitable star, then the lowest altitude would have to be chosen for the line of sight. Taking into account the refraction, however, it is necessary to choose an optimum altitude such as 60°. In spite of rather simple design, a remarkably high standard of accuracy can be achieved. For the computation of results, there are very well-known methods such as: a. Position Lines Method. b. A New Reduction Method Using X, Y,Z -Coordinates. The position line method was originally devised for finding position at sea, but developments proved that it became more and more popular among surveyors for finding position on land. At the begining, the position line was found the most convenient method to apply. However, this method makes it a condition that the observer's position be known approximately in latitude and longitude. This meant that two sides (the observer's co-latitude and the object's polar distance) were regarded as known, together with the included angle (the hour angle) computed from the assumed longitude. vi In position line method, basically, the observed altitude is compared with the approximate altitude of the line of observation. As might be expected a difference generally occurs, which is a measure of the error in the assumed position, and constitutes the difference in length between the radius of position circle passing through the assumed position and the radius of the positioncircle passing through the actual position. This difference is known as 'Intercept". It is often quite small, and the problem can be completed graphically. In practice, if the azimuth circle of the instrument was oriented, the star itself will appear in the field of view at the precalculated time. It will be quite obvious that the altitude under which all stars were observed was the same to within very narrow limits. The observed altitude increases when the observer travels along the vertical plane towards the star, that is if he approaches the star in its azimuth. Additionally, an observer will see the star under the same altitude from any point on a circle around the sub-stellar point which means the star is at the zenith of observer ( O = 8 and LST = RA ). This circle is referred to as the 'Position Circle" of the observer and can be taken to a straight line which forms a right angle with the star azimuth. One position line, however, is limited in its usefulness. To fix the position, it must be combined within a reasonable period of time with a second position line obtained by another observation a star. If several stars are observed this will give several position lines enclosing a rough square, inside which can be drawn the circle with a center which most nearly touches all position lines. Thus, position lines form tangents of a circle with the radius "c" around the true point of observation. If the observer's approximate latitude
In order to provide better terminology, the phrase "field astronomy" is used to cover the theory and practice necessary for third order work, and "geodetic astronomy" is used to cover the further theory and more refined practice necessary for first and second order work. Some such distinction is required in order to separate those sections and geodetic astronomy has a wider scope than field astronomy, therefore in geodetic astronomy, latitude, longitude and azimuth are measured to higher accuracy, namely with a standard error of about ± 0.3" to 0.5". and its objects are: a. To measure azimuth and longitude at Laplace stations to control azimuth in geodetic control surveys. b. To measure latitude and longitude to determine the deviation of the vertical for such purposes as: (1) Determining the geoid-spheroid separation by observation of geoid sections: (a) for the correct reduction to sphereiod level of distances measured on the surfaces of the earth. (b) to provide a direct and detailed measure of the form of the geoid. (2) The correction of horizontal angles in mauntainous terrain, or wherever the deviation of the vertical is large. (3) The study of variation in density within the crust of the Earth, eg to attempt to delineate the boundaries of tectonic plates. c. To measure latitude, longitude and azimuth at the origins of independent surveys. d. To measure latitude and longitude to demarcate astronomically defined baundaries. In geodetic astronomy, there are six main positioning methods: a. Sterneck Method (Latitude determination) b. Astrolabium Method (Latitude or time determination) c. Horrebow-Talcott Method (Latitude determination) d. Zinger Method (Time determination) e.Doellen Method (Time determination) f. Pole Star Observation for Azimuth Determination. The illustrations in geodetic astronomy are referred to the celestial sphere where the position of stars are supposed to be known and the fundemantal formulas are based on the apparent rotation of the celestial sphere around the Earth as a consequence of the Earth's rotation. Therefore, classical methods of reduction for the determination of astronomic position need the solution of the astronomical triangle which is very well-known quantity in Celestial System. This Thesis shows how the same problem can be solved using a method dealing with the location of observer's zenith on the celestial sphere and then the astro-latitude and astro-longitude of the station. All needed to be known is the right ascension and declination of the star and time of observation at the instant stars cross the almucantar of the astrolabe. Astrolabe as a measuring instrument which can be turned around a vertical axis whilst the line of sight forms a constant angle with the direction of a plumb line. When rotating the instrument, the line of sight prescribes a small cirle of equal altitude referred to as the almucantar. In other word, we are to consider a special circle of the celestial sphere parallel to the horizon connecting all points of equal altitude which is called Almucantar. Three stars on an almucantar define the plane of the almucantar and its position on the celestial sphere. In this form, the astrolabe serves to determine the time at which a star passes the altitude fixed by the instrument and then the determined time is used for the computation of latitude and longitude. Most astrolabes are attachments to be used in conjuction with a theodolite. Special astrolabes do exist, however, they can be used for no other purposes. In order to obtain a practical astrolabe,it is necessary to form a constant angle with a plumb line. Keeping this angle constant is best achieved with a prism. On principle, any angle could be chosen except zenith. Prismatic astrolabe essentially consists of a telescope which views a star through a prism by direct viewing (and simultaneously at some instruments after reflection in a pool of mercury which defines the vertical more accurately. Thus, the two star images appear to move in opposite directions in the focal plane and when they are side-by-side) the time recorder is actuated manually. At that instant, they are at altitude defined by the prism angle. If the observer should never have to wait long for a suitable star, then the lowest altitude would have to be chosen for the line of sight. Taking into account the refraction, however, it is necessary to choose an optimum altitude such as 60°. In spite of rather simple design, a remarkably high standard of accuracy can be achieved. For the computation of results, there are very well-known methods such as: a. Position Lines Method. b. A New Reduction Method Using X, Y,Z -Coordinates. The position line method was originally devised for finding position at sea, but developments proved that it became more and more popular among surveyors for finding position on land. At the begining, the position line was found the most convenient method to apply. However, this method makes it a condition that the observer's position be known approximately in latitude and longitude. This meant that two sides (the observer's co-latitude and the object's polar distance) were regarded as known, together with the included angle (the hour angle) computed from the assumed longitude. vi In position line method, basically, the observed altitude is compared with the approximate altitude of the line of observation. As might be expected a difference generally occurs, which is a measure of the error in the assumed position, and constitutes the difference in length between the radius of position circle passing through the assumed position and the radius of the positioncircle passing through the actual position. This difference is known as 'Intercept". It is often quite small, and the problem can be completed graphically. In practice, if the azimuth circle of the instrument was oriented, the star itself will appear in the field of view at the precalculated time. It will be quite obvious that the altitude under which all stars were observed was the same to within very narrow limits. The observed altitude increases when the observer travels along the vertical plane towards the star, that is if he approaches the star in its azimuth. Additionally, an observer will see the star under the same altitude from any point on a circle around the sub-stellar point which means the star is at the zenith of observer ( O = 8 and LST = RA ). This circle is referred to as the 'Position Circle" of the observer and can be taken to a straight line which forms a right angle with the star azimuth. One position line, however, is limited in its usefulness. To fix the position, it must be combined within a reasonable period of time with a second position line obtained by another observation a star. If several stars are observed this will give several position lines enclosing a rough square, inside which can be drawn the circle with a center which most nearly touches all position lines. Thus, position lines form tangents of a circle with the radius "c" around the true point of observation. If the observer's approximate latitude
Açıklama
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1995
Anahtar kelimeler
Gözlem yöntemleri,
Konum belirleme,
Vektörler,
Yükseklik dairesi,
Observation methods,
Position determination,
Vectors,
Almucantar