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Or Universal Time, Julian Date, and Celestial Coordinates.

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1 Or Universal Time, Julian Date, and Celestial Coordinates.
Watch, When, and Where Or Universal Time, Julian Date, and Celestial Coordinates.

2 Overview Universal Time Julian Date Local Coordinates
What are the things you need to know in order to give a location of the origin of a cosmic ray? Universal Time Julian Date Local Coordinates

3 Watch: UNIVERSAL TIME

4 Universal Time The times of various events, particularly astronomical and weather phenomena, are often given in "Universal Time" (abbreviated UT) which is sometimes referred to, now colloquially, as "Greenwich Mean Time" (abbreviated GMT). When a precision of one second or better is needed, however, it is necessary to be more specific about the exact meaning of UT. For that purpose different designations of Universal Time have been adopted. In astronomical and navigational usage, UT often refers to a specific time called UT1, which is a measure of the rotation angle of the Earth as observed astronomically. However, in the most common civil usage, UT refers to a time scale called "Coordinated Universal Time" (abbreviated UTC), which is the basis for the worldwide system of civil time. This time scale is kept by time laboratories around the world, including the U.S. Naval Observatory, and is determined using highly precise atomic clocks. When a precision of one second or better is needed, however, it is necessary to be more specific about the exact meaning of UT. For that purpose different designations of Universal Time have been adopted. In astronomical and navigational usage, UT often refers to a specific time called UT1, which is a measure of the rotation angle of the Earth as observed astronomically. It is affected by small variations in the rotation of the Earth, and can differ slightly from the civil time on the Greenwich meridian. Times which may be labeled "Universal Time" or "UT" in data provided by the Astronomical Applications Department of the U.S. Naval Observatory (for example, in the annual almanacs) conform to this definition. However, in the most common civil usage, UT refers to a time scale called "Coordinated Universal Time" (abbreviated UTC), which is the basis for the worldwide system of civil time. This time scale is kept by time laboratories around the world, including the U.S. Naval Observatory, and is determined using highly precise atomic clocks. The International Bureau of Weights and Measures makes use of data from the timing laboratories to provide the international standard UTC which is accurate to approximately a nanosecond (billionth of a second) per day. The length of a UTC second is defined in terms of an atomic transition of the element cesium under specific conditions, and is not directly related to any astronomical phenomena. One can think of UT1 as being a time determined by the rotation of the Earth, over which we have no control, whereas UTC is a human invention. It is relatively easy to manufacture highly precise clocks that keep UTC, while the only "clock" keeping UT1 precisely is the Earth itself. Nevertheless, it is desirable that our civil time scale not be very different from the Earth's time, so, by international agreement, UTC is not permitted to differ from UT1 by more than 0.9 second. When it appears that the difference between the two kinds of time may approach this limit, a one-second change called a "leap second" is introduced into UTC. This occurs on average about once every year to a year and a half.

5 UTC and Local Time UTC is the time distributed by standard radio stations that broadcast time, such as WWV and WWVH. It can also be obtained readily from the Global Positioning System (GPS) satellites. Countries lying on meridians east or west of the Greenwich meridian do not use GMT as their local civil time. It would obviously be impractical to do so as the local noon, the time at which the sun reaches its maximum altitude, gets earlier or later with respect to the local noon on the Greenwich meridian. To avoid confusion, the world is divided into time zones, each zone corresponding to a whole number of hours before or after UT. This time is known as your local time.

6 Conversion to UTC It is often convenient in making astronomical calculations to use UT and local time may be converted into UT in the following manner. Local Time = Universal Time - 6 hr (central standard time) - 5 hr (central daylight time) Local Time = Universal Time - 7 hr (mountain standard time) - 6 hr (mountain daylight time)

7 When: JULIAN DATE

8 The Julian timeline Julian dates (abbreviated JD) are simply a continuous count of days and fractions since noon Universal Time on January 1, 4713 BCE (on the Julian calendar). Almost 2.5 million days have transpired since this date. Julian dates are widely used as time variables within astronomical software. Calendar dates — year, month, and day — are more problematic. Various calendar systems have been in use at different times and places around the world. Primarily there are two calendars: the Gregorian calendar, now used universally for civil purposes, and the Julian calendar, its predecessor in the western world. Sometimes the modified Julian date, MJD, is quoted. This is equal to the JD ; MJD zero therefore began at 0h on November 17th 1858. Julian dates (abbreviated JD) are simply a continuous count of days and fractions since noon Universal Time on January 1, 4713 BCE (on the Julian calendar). Almost 2.5 million days have transpired since this date. Julian dates are widely used as time variables within astronomical software. Typically, a 64-bit floating point (double precision) variable can represent an epoch expressed as a Julian date to about 1 millisecond precision. Note that the time scale that is the basis for Julian dates is Universal Time, and that 0h UT corresponds to a Julian date fraction of 0.5. Calendar dates — year, month, and day — are more problematic. Various calendar systems have been in use at different times and places around the world. This application deals with only two: the Gregorian calendar, now used universally for civil purposes, and the Julian calendar, its predecessor in the western world. As used here, the two calendars have identical month names and number of days in each month, and differ only in the rule for leap years. The Julian calendar has a leap year every fourth year, while the Gregorian calendar has a leap year every fourth year except century years not exactly divisible by 400. This application assumes that the changeover from the Julian calendar to the Gregorian calendar occurred in October of 1582, according to the scheme instituted by Pope Gregory XIII. Specifically, for dates on or before 4 October 1582, the Julian calendar is used; for dates on or after 15 October 1582, the Gregorian calendar is used. Thus, there is a ten-day gap in calendar dates, but no discontinuity in Julian dates or days of the week: 4 October 1582 (Julian) is a Thursday, which begins at JD ; and 15 October 1582 (Gregorian) is a Friday, which begins at JD The omission of ten days of calendar dates was necessitated by the astronomical error built up by the Julian calendar over its many centuries of use, due to its too-frequent leap years.

9 Conversion to Julian Days
The Julian date of any day in the Julian calendar may be found by the method below. Set y= year, m = month and d = day If m = 1 or 2 subtract 1 from y and add 12 to m Calculate A= integer part of y/100; B = 2 - A+ integer part of (A/4) Calculate C = integer part of • y Calculate D = integer part of x (m + 1) Find JD = B + C + D + d Example: Calculate the Julian date for February 17.25, 1985. y=1984, m=14, d=17.25, A=19, B=-13, C= , D = 459 JD =

10 Where: ASTRONOMICAL COORDINATES

11 Types of Coordinates Topocentric System (Altitude and Azimuth)
Equatorial System (Right Ascension and Declination) Galactic System (Galactic Latitude and Longitude)

12 Viewing the Sky

13 Actual Distance and View

14 Topocentric (Horizon) System
Azimuth (A) This is the direction of a celestial object, measured clockwise around the observer's horizon from north. So an object due north has an azimuth of 0°, one due east 90°, south 180° and west 270°. Azimuth and altitude are usually used together to give the direction of an object in the topocentric coordinate system.

15 Topocentric System Altitude (h)
The angle of a celestial object measured upwards from the observer's horizon. Thus, an object on the horizon has an altitude of 0° and one directly overhead has an altitude of 90°. Negative values for the altitude mean that the object is below the horizon.

16 Equatorial (Celestial) Coordinates
The term "Celestial Sphere" describes the appearance of the nighttime sky. The stars revolve in diurnal rotation without changing their positions relative to one another. Because our eyes are not sensitive to the varying "distance of the stars" away from us, the stars appear to lie all at the same large distance away. This leads to the concept of the sky and stars as a sphere concentric with the earth and rotating around it. This apparent rotating sphere carrying the stars on its surface is known as the Celestial Sphere.

17 Equatorial Coordinates
Right Ascension (a) In the sky with right ascension (celestial longitude) we need some point to play a similar role to that of Greenwich, England for terrestrial longitude. Astronomers have chosen the Vernal Equinox to define the starting point for the measurement of right ascension. The Vernal Equinox is the point where the sun appears to cross the Celestial Equator at the beginning of spring. Right ascension in many ways works somewhat differently than longitude. First, unlike longitude, right ascension is always measured eastwards from the Vernal Equinox. There is no west right ascension in the sky. Second, we do not measure right ascension in degrees as we do, longitude, but rather in hours. One hour of right ascension corresponds to 15° of celestial longitude, and there are 24 hours all the way around the sky eastwards from the Vernal Equinox, back to the Vernal Equinox again. Each hour is subdivided into 60 minutes, and each minutes into 60 seconds, just as if we were measuring time, instead of eastwards angular distance, but you should keep in mind, that even though we are using hours, minutes and seconds to measure right ascension, we are still talking about an angular distance measured around the Celestial Sphere. On earth we have constant longitude on lines stretching from pole to pole - the meridians of longitude. However, we don't talk about meridians of right ascension. The corresponding term in the sky is hour circle. An hour circle stretches from the North Celestial Pole to the South Celestial Pole. You have the same right ascension all along an hour circle. Thus in the figure above, hour circles are shown for right ascensions of 0, 1, 2, and 3 hours. (Actually only half of each hour circle is shown, the half lying in the Northern Celestial Hemisphere.) The measurement of right ascension may seem to be set up in a rather peculiar fashion. The purpose for dealing with right ascension in this way is to make it easier to use the apparent diurnal rotation of the Celestial Sphere as a means of telling time. This is the basis of sidereal time.

18 Equatorial Coordinates
Declination (d) Declination works on the surface of the Celestial Sphere much like latitude does on the surface of the earth, that is, declination measures the angular distance of a celestial object north or south of the Celestial Equator. Lines of declination are analogous to parallels of latitude on the earth. An object lying on the Celestial Equator has a declination of 0°. The declination increases as you move away from the Celestial Equator to the Celestial Poles. At the North Celestial Pole therefore, the declination is + 90°. Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°.

19 Galactic Coordinates Here the fundamental line is the galactic circle, a great circle represented by the course of the “Milky Way”. The galactic circle or equator, intersects the celestial equator at an angle of about 63 degrees. Galactic longitude (l), is measured from the center of the galaxy, eastward along the galactic equator. Galactic latitude (b), is measure on the great circle through the object and the galactic pole, and counted north (+) or south (-) with respect to the galactic equator. Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°.

20 Referencing - Horizon View
This is an image of the night sky looking directly south from Lincoln. In the middle of the image is the object M-4, a globular cluster in Scorpius. This is how the observer would see the cluster relative to the horizon at 10:15 PM on July 5, 2001. What would be its azimuth and altitude? M-4 SW Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°. SE S Az 180 ° Alt 30°

21 Referencing - Horizon and Equatorial View
This view shows the same image as before but with the addition of the equatorial grid overlayed on the horizon view. What is M-4’s Right Ascension and Declination? M-4 Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°. 16 h 30 m -23°

22 Referencing - Equatorial and Galactic View
This view shows the horizon removed and the equatorial aligned with the celestial equator. The galactic system has been inserted over the equatorial system. What is M-4’s Galactic longitude and latitude? M-4 Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°. 350° +20°

23 Referencing - Galactic View
M-4 This view shows only the galactic system. Notice how the center of the galaxy runs along the galactic equator line. Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°.

24 Referencing - Galactic Sky
This view shows the galactic system projected for the entire sky. The galactic poles are at the top and bottom of the image. Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°.

25 Referencing - Equatorial Sky
This view shows the the galaxy projected onto the equatorial system. The celestial poles are at the top and bottom. Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°.

26 Referencing - Horizon Sky
This view shows the the galaxy projected onto the horizon system. Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°.

27 Equatorial to Galactic Coordinate Conversion
In previous pictures you should have noticed that all of the coordinate systems are based on spheres. Conversion from one system to another is based on the use of spherical trigonometry. The set of equations below forms the basis of spherical trigonometry, which governs, amongst other things, the change in coordinates consequent upon a rotation of the axes. The equations are useful when the angles are less than 180º, and the sides of the figures are formed from arcs of great circles. Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°. cos a = cos b cos c + sin b sin c cos A sin a /sin A = sin b / sin B = sin c / sin C sin a cos B = cos b sin c - sin b cos c cos A

28 Equatorial to Galactic Coordinate Conversion
In order to list a cosmic rays origin in galactic coordinate you must know its equatorial coordinates. The conversion formulas are: b = sin-1{cos d cos (27.4) cos (a ) + sin d sin (27.4)} l = tan-1{(sin d - sin b sin (27.4))/ cos d sin (a ) cos (27.4)} + 33 The numbers come from the following facts about our Galaxy: north galactic pole coordinates a = 192º 15’, d = 27º 24’; ascending node of galactic plane on celestial equator l = 33º. These are coordinates. Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°.

29 Equatorial to Galactic Coordinate Conversion
Example: What are the galactic coordinates of a star whose right ascension and declination are a = 10 h 21m 00s and d = 10º 03’ 11”? b = sin-1{cos d cos (27.4) cos (a ) + sin d sin (27.4)} l = tan-1{(sin d - sin b sin (27.4))/ cos d sin (a ) cos (27.4)} + 33 b = º or 51º 07’ 20” l = or 232º 14’ 53” Declination differs from latitude in the way that we specify north or south. Astronomers might have chosen to specify declination as N or S as with latitude, but the convention in astronomy is to specify north or south by means of sign: declinations in the Northern Celestial Hemisphere are positive. Southern hemisphere declinations are negative. If the sign is not given explicitly, it is understood to be plus. Thus we can say that the declination of Polaris is very nearly 90°, which is understood to mean +90°, placing Polaris in the Northern Celestial Hemisphere. For objects in the Southern Celestial Hemisphere we must indicate a specifically negative declination. Thus in the figure shown above, the lines of declination drawn in the Southern Celestial Hemisphere are at negative declinations of -5° and -10°. The South Celestial Pole lies at a declination of -90°.

30 Additional Conversions
Horizon Universal Time Equatorial Ecliptic Galactic

31 Good Source and More….. Practical Astronomy With Your Calculator By
Peter Duffett-Smith


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