Time and the Sky. The Basics

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1 Time and the Sky How do we know when and where can we find a celestial object in our sky? A knowledge and use of the concepts of time and our Celestial Coordinate System offers the best, systematic approach to resolve this problem. In fact, these concepts are fundamental to an understanding of the apparent motions of the celestial objects as seen from Earth. The Basics The conventional method of measuring angles in astronomy is to divide a full circle into 360 o, then divide each degree into 60 minutes of arc(60'), and each minute of arc divided into 60 seconds of arc(60"). There are thus 3600"(seconds of arc) in one degree, and 1,296,000" in a full circle(360 o ). Because Earth turns 360 o on its axis once a day and the day is divided into 24 hours, often written as 24h, anglescan also be measured in terms of time. In this case, 1h =15 o. Each hour is divided into 60 minutes of time(60m) and each minute further divided into 60 seconds of time(60s). There are thus 1440 minutes of time, or 86,400 seconds of time, in a circle(or in a day). You can use your fist to roughly measure a celestial objects angular size. Held out at arms lengthit is about 10 o across the knuckles. The tip of your index finger measures about 2 o. Viewed from Earth, the Sun and Moon are each 1/2 o across. They can also be measured in minutes of arc(30'), seconds of arc(1800") and minutes of time(2 m ). Coordinate Systems Perhaps the most commonly used system to locate an object in the sky is that of - also called horizon, or altazimuth - coordinates. This system designates the location of an object with respect to the location of the observer. There are also three main systems of celestial coordinates: The equatorial, ecliptic, and galactic. In each of these systems the frame of reference is located in the sky rather than on Earth. Before we discuss these systems, it may be useful to refresh you memory of terrestial coordinates. A location on Earth is specified in terms of longitude and latitude. Latitude is measuredin degrees, from 0 o at the equator to +/- 90 o at the poles; positive latitude are in the Northern Hemisphere, negative ones in the Southern Hemisphere. Longitude is the measurement of the east- west angle between the meridian( a line which extends from pole to pole) running through a given location and a a standard" meridian," which is customarily considered to be the imaginary line running through Greenwich, England. Locations have a longitude between 0 o (on the Prime Meridian) and +/- 180 o (at the International Dateline, running approximately down the middle of the Pacific Ocean. To avoid confusion, longitude is often referred to as "east" or "west"(of Greenwich). The poles mark the axis of Earth's rotation. Earth rotates in a west to east direction.

2 A point on the equator moves eastward at about 1,670 kilometers per hour; locations at higher latitudes(north or south) move more slowly. There is no eastward movement at the poles. Topocentric Coordinates - are a pair of measurements, altitude and azimuth, are used to refer to the position of an object in the sky in relation to the observer. The altitude, or elevation of an object is its angle above or below the plane of the observers horizon (the angle of the horizon is 0 o ). The point directly, or 90 o, overhead is the viewers zenith, and the point directly below is the nadir. Objects below the horizon (and therefore not visible) have a negative elevation. The azimuth, the compass direction of an object, is an angle measured along the horizon to a vertical line drawn from the object to the horizon. The angle is measured clockwise from north, which is 0 o,, through east at 90 o, south at 180 o, west at 270 o, and back to north at 360 o or 0 o. The celestial meridian is a line that runs from the exact north point on your horizon up through the zenith, and down to the exact south point on your horizon, the nadir, dividing the sky into eastern and western halves. A celestial object is said to culminate when it appears to cross the celestial meridian. Celestial Coordinate Systems. Astronomers have derived coordinate systems fixed on the celestial sphere, the "dome" of the heavens. These coordinates do not change with Earth's movements, although our ability to observe an object at a designated point in the sky will, of course, still depend on the date and time of the observation. The celestial sphere is an infinitely large imaginary sphere surrounfing Earth onto which are "glued" all the objects in the sky. The celestial equator is a projectionof Earth's equator onto the celestial sphere. Similarly, the celestial poles are projections of Earth's north and south geographic poles onto the celestial sphere. The ecliptic can be seen as the projection of Earth's orbit onto the celestial sphere (this path is tilted 23.4 o to the celestial equator because of Earth's 23.4 o tilt). One commonly used set of celestial coordinates, called equatorial coordinates, is based on the celestial equator. The north-south coordinate, the celestial equivalent of latitude on Earth, is called declination; it is measured, like latitude, in degrees, minutes, and seconds of arc from 0 o at the celestial equator to 90 o north and 90 o south at the celestial poles. Declination is often abbreviated "Dec.", or is denoted by the lowercase Greek letter delta (d). The east-west coordinate, the celestial equavalent of longitude on Earth, is called right ascension; it is usually measured eastward around the sky in hours, minutes, and seconds of time but can also be measured in degrees. Since Earth rotates 360 o in 24 hours, one hour of right ascension or time, equals 15 o of arc; and one second of right ascension equals 15 seconds of arc. The "zero-point" of right ascension, celestial kin to Earth's Prime Meridian of longitude, is the point at which the Sun (and thus the ecliptic) crosses the celestial equatoron its way north each spring; this point is called the vernal equinox and is sometimes called the first point of Aries, because in ancient Greek times the Sun was in the constellation Aries(see Constellations) on the first day...of spring. Right Ascension is often abbreviated "R.A." or is denoted by the lowercase Greek letter alpha (α).

3 The equatorial coordinate system is one of the most frequently used systems to specify the positions of celestial objects. Catalogues of stars and deep sky objects will specify the R.A. and Dec.'s of these objects at some particular time or epoch. These coordinates change very slowly because of precession. Sometimes it is easier to find the planets and other solar system objects among the constellations by using ecliptic coordinates. This system is based on the ecliptic, the plane of the Earth's orbit. The north-south, or perpendicular coordinate in this system is called celestial latitude and is measured from 0 o at the ecliptic to +/- 90 o at the ecliptic poles. Celestial latitude is sometimes denoted by the lowercase Greek letter beta (b). The east-west coordinate is called celestial longitude and is measured in degrees eastward from the point of the vernal equinox. Celestial longitude is sometimes denoted by the lowercase Greek letter lambda (l). Since all the superior planets except Pluto(see Planets) maintain their orbit close to the ecliptic, their celestial latitudes are always small, usually only a few degrees. Their celestial longitudes are changing continually. To specify the position of an object in the Milky Way galaxy, as observed from Earth, astronomers use measurements of galactic latitude and galactic longitude. The line of 0 o galactic latitude is the plane of the galaxy, which runs along the middle of the band of light that we call the Milky Way. The zero-point of galactic longitude is located in the direction of the center of the galaxy, toward the constellation Sagittarius. We make little use of galactic coordinates. Time. Astronomers recognize two ways of measuring time, one based on the distant stars and the other based on the Sun. Th first, sidereal time, is based on the motion of the Earth with respect to the stars. Since the starsare essentially infinitely distant, they form a fixed set of points in the sky. As Earth turns on its axis, any given star (except the North Star) will pass over some meridian of longitude (and corresponding celestial meridian) once every complete 360 o rotation of our planet. The period between 2 successive transits of a star across the meridian is called a sidereal day and it is divided into 24 sidereal hours. This system of time measurement is mainly used to point telescopes and to calculate celestial phenomena. The other system of time measurement, used in the everyday world and measured by ordinary clocks, is based on the Sun. One solar day is the time between two successive transits of the Sun across a meridian, and is divided into 24 solar hours. The solar day is slightly longer than a sidereal day. The reason for this is that Earth is moving about the Sun. As seen by us on Earth the Sun seems to move eastwardin the sky from day to day. Since Earth make one 360 o revolution about the Sun in a year, each day the Sun appears to move about 1 o in our sky as measured against the seemingly fixed stars. In other words, after Earth has made one complete rotation(one sidereal day) it must turn an extra 1 o to bring the Sun back to the meridian. This takes about 4 minutes, and so a solar day is about 4 minutes longer than a sidereal day ( one sidereal day equals 23h56m4s of solar time). Because the sidereal day is shorter than the solar day, each star(except circumpolar stars, which never set or rise) rises four minutes earlier each night than it did the night before.

4 After a week it rises about a half hour earlier; in two weeks, an hour earlier; in a month, two hours earlier. This is why the stars are in the same topocentric positions, say at 10:00pm tonight, that they were at midnight just one month ago, and that they will be in at 9:00pm two weeks from now. It is the interplay of the rotation of the Earth on its axis and the revolution around the Sun that brings all the celestial objects visible from our latitude into view at different times of the year and times of the night. DETERMINATION OF SIDEREAL TIME Various methods can be used to determine the observer's Sidereal Time. The method we use to calculate the Sidereal time comes from the Observers Handbook, edited by R. Bishop of the Royal Astronomical Society of Canada. I suggest that you purchase a copy of this handbook each year. Don't count on an up to date copy being in the dome all the time. Have your own copy ready for use. You will also need a calculator that accepts degrees! THE FOLLOWING IS THE GREENWICH MEAN SIDEREAL TIME (GMST) ON THE DAY 0 hours UT OF EACH MONTH (day 0 is the last day of the previous month): July h Oct h Aug h Nov h Sept h Dec h GMST at hour t UT on day d of the month = GMST at 0h UT on day 0 + 0h (d) (t) For Example: You are asked to check the sidereal clock in the dome on Dec. 15 at 8:00pm EST. STEP 1: Dec. 0 is so punch that in to the calculator. STEP 2: the formula says add that number to 0h multiplied by the day which is the 15th. The answer so far is STEP 3: take and add it to multiplied by the time which is 8:00pm but you need to use military time, so its 20h 00m 00s. You get The answer remaining is your sidereal time. Since time can only be 24 hours, if your number comes out to be more than 24 hours, simply subtract 24h 00m 00s. So your final answer is , then change it to degrees and you should come up with 1h 36m 58.5s. This will be your correct answer. Don't forget about the hour you lose to daylight savings time in the summer.

5 REFERENCES * THE ASTRONOMICAL ALMANAC, Published annually by the United States Naval Observatory. Available from The U. S. Government Printing Office. * THE OBSERVER'S HANDBOOK, Published annually by the Royal Astronomical Society of Canada. Available from AAI Sales and Promotion Committee. * TIME IN ASTRONOMY, Edmund Scientific Company, Barrington, NJ. Also available from AAI Sales and Promotion Committee.