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Celestial Coordinate System Fall 2007 Updated 09/07/2007 Purpose The purpose of this lab is to familiarize the student with determining sidereal time, both through calculation and observation, and applying this system of time to locating stars and other objects using the celestial coordinate system. Introduction Early in the history of astronomy it became necessary to devise a system for describing the positions of the stars on the celestial sphere. The most obvious system was one based on the local horizon and named simply the Horizon System. It gives the star’s position in terms of the observer’s horizon pane, with one coordinate (azimuth) measured in terms of compass directions along this plane. However, this system of coordinates has disadvantages in that the azimuth and altitude of a star change both with the time of day and the location of the observer. It is desirable to have a system of coordinates permanently attached to the celestial sphere. Such a system is the Celestial Equatorial System (Fig. 1). The polar axis of the earth is projected outwards, defining the poles of the celestial sphere. The equatorial plane of the earth is projected outward and it defines the celestial equator. The coordinates of this system are right ascension (analogous to longitude on the earth), measured along the celestial equator and declination (analogous to latitude), measured north and south from the celestial equator. The coordinates of stars in this system are constant rather than dependent on the observer’s time of day and place. Figure 1. Sidereal time You are already familiar with solar time – you use it every day. The earth makes one complete revolution in 24 hours, and the sun crosses the observer’s meridian at noon, local mean time. The sidereal day, however, is 3 minutes, 56 seconds shorter than the solar day. Sidereal time is based on one rotation of the earth in relation to any star (other than the sun), starting with the star on the observer’s meridian, and returning to the meridian one earth rotation later. The reason for the star returning to the meridian in less than 24 hours is that the earth orbits about the sun. The rate of this orbit is 360 degrees/ 365.25 days, or about 1 degree per day. One degree per day is equal to 4 minutes of time and averages two hours per month. (See Fig.2) Figure 2 Application to Astronomy Simply put, the sidereal time is equal to the right ascension of an astronomical object lined up with the observer’s meridian. The sidereal day begins at 0 hours, a time when the vernal equinox crosses the celestial meridian. On or about March 21, the sun is located at the vernal equinox, and will be on the meridian at noon. We can therefore assume that the sidereal time on March 21 is 0h at noon, local mean time. One sidereal hour later, stars with a right ascension of 1 h will cross the meridian. Sidereal time can be calculated for an observer’s location, using the formulas and table provided with this lab. Once determined, the sidereal time will be used, in conjunction with the celestial coordinate system, to locate astronomical objects with an equatorially aligned telescope. (Fig. 3) Standard Time Zones Terminology Standard Time: is the mean time of a time zone, which is 15 degrees wide. At the central meridian of a time zone, standard time coincides exactly with mean solar time. Simply, this means the sun will be on the meridian at noon (or nearly so), as observed from the central meridian of the time zone. Elsewhere in the time zone, the sun will be no more than 30 minutes from the meridian. Local Mean Time: This is the mean solar time applied to your exact location. L.M.T. is calculated by applying a correction equal to four minutes for each degree you are away from the central meridian of your time zone. The central meridian for the Eastern Time zone is 75 degrees. Providence is located 71 degrees, 25 minutes longitude. This is about 3 ½ degrees east of the central meridian. (3 ½ degrees times 4 minutes = 14 minutes times correction) Because we are east of the central meridian, we add this time correction to standard time. This means that our watches, set to L.M.T., will read 14 minutes later than Eastern Standard Time. Local Sidereal Time (L.S.T.): Indicates how much time has passed since the vernal equinox crossed the observer’s meridian. Sidereal time is also equal to the right ascension of any star currently on the observer’s meridian. To calculate L.S.T. with an approximate correction, use this formula: L.S.T.= L.M.T. + G.S.T at 0h next day (see table # 1 ). If the answer is greater than 24 hours, subtract 24 hours for the answer. For example, if it is 8:00 PM E.S.T. (remember to subtract 1 hour from daylight savings time) on October 1st, then… L.M.T. = E.S.T. + time correction (14 minutes) = 20h 14m (Providence, R.I.) L.S.T.= L.M.T. + G.S.T at 0h next day L.S.T. = 20:14 + 0h 41m (table 1) L.S.T. = 20h 55m @ 8:00 P.M. (EST) on October 1, 2007 Sidereal Time (rounded to nearest minute) at 0h Greenwich Mean Time (G.M.T.) October through December, 2007. (Table 1) Day Oct Nov Dec 2h 40m 4h 38m 0h 37m 1 0h 41m 2 2h 44m 4h 42m 0h 45m 3 2h 48m 4h 46m 4 0h 49m 2h 51m 4h 50m 5 0h 53m 2h 55m 4h 54m 6 0h 57m 2h 59m 4h 58m 7 1h 1m 3h 3m 5h 2m 8 1h 5m 3h 7m 9 1h 9m 3h 11m 10 1h 13m 3h 15m 11 1h 17m 3h 19m 12 1h 21m 3h 23m 13 1h 25m 3h 27m 14 1h 29m 3h 31m 15 1h 33m 3h 35m 16 1h 37m 3h 39m 17 1h 40m 3h 43m 18 1h 44m 3h 47m 19 1h 48m 3h 51m 20 1h 52m 3h 55m 21 1h 56m 3h 58m 22 2h 0m 4h 2m 23 2h 4m 4h 6m 24 2h 8m 4h 10m 25 2h 12m 4h 14m 26 2h 16m 4h 18m 27 2h 20m 4h 22m 28 2h 24m 4h 26m 29 2h 28m 4h 30m 30 2h 32m 4h 34m 31 2h 36m Equipment needed for this lab Equatorially mounted telescope, equipped with setting circles. Accurate time signal http://www.time.gov/timezone.cgi?Eastern/d/-5/java Accurate watch set to L.S.T. Star atlas and catalog. Rotating Star Chart Procedure (Indoors): 1) The first thing you need to do is to determine the current sidereal time, and set your watch to it. Although your watch will run slower than sidereal time, about 10 seconds per hour, it will be accurate enough for the duration of this lab. Refer to table # 1 for G.S.T. at 0h, not for today’s date, but the following day. Use this time in the formula above. Make sure to calculate the local mean time (LMT) correction for the location you plan to do your observations from. The coordinates for Providence are given above, and the coordinates for Jerimoth Hill are 41 50 58N, 071 46 45W. Once you have your watch set to sidereal time, you are ready for the next step. 2) Sidereal time equals the RA of objects currently on the meridian. In this lab, we will be trying to find objects throughout the sky. To do this, we will need to determine the angular separation of the object from the meridian, measured in hours, minutes and seconds. This is called the Hour Angle. 0 hours will define the meridian, and objects will either east or west of the meridian. 3) To determine the hour angle (HA) of an object, use the following equation: HA=ST-RA Let’s say it is December 1st at 11:00 PM, EST. Using the equation to determine sidereal time, we come up with ST = 3h 56m. We want to locate M42, the Orion Nebula. The coordinates for M42 are RA=5h 34m, DEC= 5.4 degrees south. HA=3h 56m – 5h 34m HA= (-2h 22m) A negative hour angle means M42 is east of the meridian. If you were to try to locate M42 later in the evening, say at 6h (L.S.T.), then the equation would read: HA= 6h - 5h 34 m HA= 0h 26m A positive hour angle means M42 is west of the meridian. (If the answer is greater than 12h, it must be subtracted from 24h to give the answer in negative hour angle.) Orion on Dec 1st, at 3h LST and 6h LST (Fig. 4) 4) Practice indoors, using “Starry Nights” Determine the HA for the three objects in the table below, setting the time to 9:00PM this evening. You will need to calculate the sidereal time. Object NGC 884 Alberio M15 RA 2h 22.6m 19h 30.7m 21h 30.3m Dec +57 8m +27 58’ +12 10’ ST HA (east/west) Using “Starry Nights”, select the following in the tool bar: “View” -“Alt/Az Guide” - “Meridian” “View” -“Celestial Guides” - “Equator” - “Grid” Verify that the calculations you entered in the table above are correct, by locating the objects in the “Starry Night” program, and noting where the objects are located on the celestial grid. Which object most recently crossed the meridian? _______________________________ Which object is currently located in the eastern most part of the sky? ________________ Which object is currently located in the western most part of the sky? ________________ Doing the above exercise should help you to find your way around the sky, which will be useful for the next, outdoor part of this lab. Procedure (outdoors): 1) You will need to use a telescope with an equatorial mount, and align the mount with the celestial pole. Please refer to “Polar Alignment Procedure for Meade ETX” for directions on properly setting up the Meade telescope. If you are using a telescope that is already aligned to the pole, you may skip this step. 2) You know the current local sidereal time, and the telescope is properly aligned to the pole. Level the declination axis using a level (your TA will show you how to do this); set the RA circle to the current sidereal time. 3) To locate an object in the table above, turn the telescope mount in RA to the RA coordinates of the object sought. Then turn the telescope mount in DEC until the circle matches the coordinates. 4) If the object you are looking for does not appear in the eyepiece, try looking in the small finder telescope to see if the object is close by – then move the telescope to center the object in the eyepiece. This might happen if the polar alignment is a little off. 5) Note the appearance of each object in your notebook. Answer the following questions: (This part will be done indoors, using “Starry Nights”.) (Providence is located at 71 degrees, 25 minutes west longitude; 41 degrees, 50 minutes north latitude) I) From our location on Earth, is it possible to locate an object more than 6 hours east or west of the meridian? Are there any limitations on how many hours of RA can be seen if you look in different directions (east, west, north and south)? II) How many hours of RA, east and west of the meridian could you see from the earth’s equator, and from the poles? III) Looking due north, along the meridian, from our location, what is the declination of the horizon? Looking due south, along the meridian, what would the southern most declination be? Polar Alignment Procedure for Meade ETX Part of Celestial Coordinates Lab Star trails around the celestial pole. 1) The ETX telescope is set-up, with telescope mounting roughly pointing north. Note that the optical in the photo is pointing towards the south. 2) Turn fork arms until the telescope is pointing south. Check this with a level. 3) Turn RA circle (the moveable dial located on the drive base of the mount) until it reads the current local sidereal time. Example shown is 3h, for January 1 at 8pm, EST. 4) Rotate mount until the RA circle reads the coordinates for Polaris: 20h 30m. Turn the telescope in declination until the setting circle (the smaller dials located at the top of the fork arms) reads 89 degrees N. 5) First, try to sight Polaris along the side of one of the fork arms. Turn the adjustment screws on the tripod head to align the mount with Polaris. Once Polaris is close, look through the eyepiece; continue to turn the adjustment screws in azimuth and altitude until Polaris is centered in the eyepiece. 6) Turn the mount back towards the south, place a level across the fork arms, and continue to turn the mount until the bubble is level. 7) Turn the RA circle until it reads the current sidereal time. You are ready to begin finding astronomical objects using the setting circles on your telescope. Follow the directions in the “Celestial Coordinates” lab.