# LOCATING CELESTIAL OBJECTS: COORDINATES AND TIME. a. understand the basic concepts needed for any astronomical coordinate system.

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1 UNIT 2 UNIT 2 LOCATING CELESTIAL OBJECTS: COORDINATES AND TIME Goals After mastery of this unit, you should: a. understand the basic concepts needed for any astronomical coordinate system. b. understand the basis of the equator and horizon systems. c. understand the ideas involved in conventional telescope mounting. d. understand the various definitions of time and how each is determined by astronomical events. Text References 4.2 through 4.6 See the Online Text Guide to DOSC to find the link to the listing by Objective. Mastery will be evaluated in two Parts: Part I will be a 15-question multiple-choice evaluation with 13 correct responses required. Part II will be performing the laboratory Celestial Coordinates. Part I will be based upon the following: Objectives You should be able to recognize: +1. the following about coordinates on spheres: (a) that all coordinate systems for spheres are based upon a reference plane (or reference circle) and a reference direction (or reference point) (b) the name of the reference plane and reference direction for terrestrial latitude and longitude (c) the approximate latitude and longitude of your location +(d) the relation between your latitude and the altitude of the projection of the Earth s axis (celestial pole) 2. the definition of the following terms: (a) zenith (b) equinox and solstice (c) ecliptic (d) celestial equator (e) celestial and ecliptic poles +(f) hour circle (g) meridian (h) horizon +(i) north point (j) vernal equinox 2-1

2 3. a description of the reference plane, reference direction, and coordinate names for the equator coordinate system (also known as the equatorial system) and the horizon coordinate system (also known as the altitude-azimuth [alt-azm] system) coordinate systems. You should also be able to recognize the definition of each of the coordinate names (i.e., what planes or directions they are measured along and the units of measurement used); +4. the following about the hour angle: (a) the definition of hour angle (b) why the equator system is the best to use for night-to-night observations (c) that a telescope that uses the coordinates hour angle (or Right Ascension) and declination is said to have an equatorial mount 5. the correct value of the angle between the celestial equator and the ecliptic, and that this angle has the same value as the one between the north celestial pole and the north ecliptic pole. You should also be able to recognize that the height of the celestial pole above the horizon is the same as your latitude and recognize an explanation of this equality; 6. a description of precession and that precession causes a slow change in the Right Ascension and Declination of stars; +7. the definition of the following times and days: (a) astronomical time in general (b) atomic time (c) Terrestrial Dynamical Time (TDT) (d) the three kinds of days and the time associated with each (e) universal time (f) mean solar time 8. a description and approximate date for the following astronomical events: (a) spring (vernal) equinox (c) autumnal equinox (b) summer solstice (d) winter solstice Streaming Videos Unit 2, Prelab Unit 2 USC: Finding Your Way in the Sky NOTES If there are no notes, all the information is in the relevant sections of the text. Obj. 1. The astronomical coordinate systems, like the terrestrial coordinates, describe the surface of a sphere. The most common way of specifying the stars is to ignore their various distances and to pretend that they are on a vast sphere, the celestial sphere, which surrounds us. The terms reference plane and reference circle are interchangeable as are the terms reference direction and reference point. All the astronomical coordinates you will study are based upon the great circle produced by some reference plane intersecting the sphere and some reference direction (or point) on that circle. One coordinate is always measured in the reference plane, and the other is measured perpendicular to the reference plane. 2-2 LOCATING CELESTIAL OBJECTS: COORDINATES AND TIME

3 UNIT 2 Figure SG 2-1 By defi nition the angle L is your latitude. The elevation A of the north celestial pole above the horizon equals the latitude L. To understand this principle better, draw this fi gure for an observer at the equator (L = 0 ) and at the north pole (L = 90 ). For the Earth the reference plane is the equatorial plane and the reference direction is the intersection of the circle that passes through the poles and Greenwich, England with the reference plane. Longitude is measured east west along the equator and latitude plus minus toward the poles. Columbia, S.C., for example, is at longitude 81 W, latitude 34 N. You should consult an atlas for the coordinates of other locations. Obj. 1d. This relation is shown in Fig. SG 2-1. In the northern hemisphere your latitude is equal to the angular height of the North Celestial pole above the horizon. Obj. 2. The terms local meridian and meridian of the observer are interchangeable. The north point is the intersection of local meridian with northern horizon. The ecliptic poles are the two points on the sphere equidistant from the ecliptic. An hour circle is any circle on the celestial sphere that passes through the north and south celestial poles. Read the discussion in DOSC Chapter 4. These are good sets of cluster concepts. Obj. 3. See Figure SG 2-2. Equator system (also called the equatorial system) Defining plane celestial equator. Reference point vernal equinox. Coordinates: Right Ascension [α or RA] east from the vernal equinox along celestial equator: 0 h to 24 h. declination [δ](+) toward north celestial pole, ( ) toward south celestial pole: 0 to ±90. Horizon system (also called the altitude-azimuth system or the alt-azm system) Defining plane horizon. Reference point northern intersection of local meridian with horizon (north point). Coordinates: azimuth [A] east along horizon from north point: 0 to 360. altitude [h] (+) toward zenith, ( ) toward nadir: 0 to ±

4 EV tip : These are two cluster concepts. Consider the terms for each coordinate system as a cluster of concepts. When asked about any one item, you could write the cluster of ideas on scratch paper. Figure SG 2-2 Two astronomical coordinate systems. Obj. 4a. The hour angle of an object is the angle measured to the west along the celestial equator. It is measured from the local meridian to the hour circle through the object. Hour angle is defined positive to the West because the Earth turns toward the East, and hence hour angle increases. Obj. 4b. There are three reasons the equator system is the best to use for night-to-night observations: a. For a few years the changes in RA and d caused by the precession of the Earth's axis are small enough to ignore (for most purposes). b. As the Earth rotates, we need to change only the hour angle to follow the star. c. The Right Ascension of a star can be subtracted from the hour angle of the vernal equinox to give the hour angle of the star. Figure SG 2-3 Equatorial mountings. 2-4 LOCATING CELESTIAL OBJECTS: COORDINATES AND TIME

5 UNIT 2 Obj. 4c. Until the advent of reliable electronic computers, nearly all large optical astronomical telescopes had equatorial mounts (see Figure SG 2-3 ). An equatorially mounted telescope turns about an axis parallel to the Earth's axis and also about another axis perpendicular to the Earth's axis. Thus rotating the telescope about one axis (parallel to the Earth s) moves the telescope in Right Ascension, or hour angle. Rotating the telescope about the other axis moves it in declination. To follow a star, the declination axis is held fixed and the hour angle is slowly increased. With the development of computers, the mechanical stability of altitude-azimuth (alt-azm) mounts encouraged astronomers to choose them for the new large telescopes. Obj. 5. All angles between planes are measured in a plane perpendicular to the line of intersection of the two planes. Thus referring to Figure SG 2-4, the choice B is used, not choice A. See Figures DOSC 1-8 and 1-9 to understand why the elevation of the celestial pole is the same as your latitude. Figure SG 2-4 Proper measurement of an angle. The plane of the angle must be perpendicular to the line of intersection of the two planes forming the angle. Obj. 7. Astronomical time is the hour angle of a reference object (plus possibly a constant). Each different astronomical time uses a different reference object. Until the advent of modern physics devices similar sand clocks, water based clocks, or mechanical clocks were available. All of these were designed to keep astronomical time. The problem with astronomical time is that the Earth's rotation is neither constant nor uniform. The current standard of time is currently the cesium-beam atomic clock with a stability and accuracy of better than one part in As we will later see, this time is based upon the speed of light. Another time system used in astronomy is called Terrestrial Dynamical Time (TDT). It is based on the motions of the planets and tied to atomic time. TDT averages out some of the Earth s irregularities of rotational motion. Each 6 months a second may be added or subtracted to keep this time system in phase with atomic time. The three usual types of days and time are: a. Sidereal day the interval between successive transits of the vernal equinox. Sidereal time is the hour angle of vernal equinox, it begins at sidereal noon with the vernal equinox on the meridian. b. Apparent solar day the interval between successive sunrises or sunsets. The apparent solar time is the hour angle of Sun plus twelve hours. c. Mean solar day the average of the apparent solar day. Mean is used in the sense average. d. Universal Time An atomic clock time that is nearly the same as the local mean solar time at Greenwich, England, is called Universal Time (UT) or Coordinated Universal Time (UTC). All of these times are broken into 24 hours and each hour into 60 minutes and each minute into 60 seconds. 2-5

6 The apparent solar day has a variable length (the reasons are discussed in the Notes for Unit 9, Obj. 17c). We are not discussing the variations in sunrise and sunset times (which are latitude effects). It is the amount of time from noon to noon that varies. To avoid the problems of a variable day, we use a day and a time whose lengths do not vary during the year. This average day is called a mean solar day. The mean Sun is a fictitious point in the sky that moves uniformly to the East along the celestial equator with the same average eastern rate as the true Sun. Mean solar time is the hour angle of the mean Sun plus 12 hours, and a mean solar day is the interval from midnight to midnight of the mean Sun. This day and time have the same rate as normal clocks. The value of mean time depends upon the observer s longitude. Obj. 8. DOSC Chapter 4 material. Note that the spring equinox is often referred to as the vernal equinox. We will use both of these terms; but, in the southern hemisphere, the vernal equinox heralds fall. Concepts from Unit 2 Objectives, Notes, and Text longitude on Earth latitude on Earth zenith hour angle meridian local meridian north point equinoxes as locations vernal equinox as a time vernal equinox as an event ecliptic celestial equator reference plane equator system Right Ascension declination precession reference direction altitude azimuth hour circle equatorial mount sidereal time astronomical time apparent solar time mean solar time This Unit has a laboratory portion, which must be completed for Unit 2 to count toward your grade. 2-6 LOCATING CELESTIAL OBJECTS: COORDINATES AND TIME

7 UNIT 2 UNIT 2 LOCATING CELESTIAL OBJECTS: COORDINATES AND TIME Word Practice 1. The of the equator system is the celestial equator. 2. The of a star is the height of the star above the horizon. 3. Right Ascension is measured along the to the east from the vernal equinox. 4. Ordinary clocks run at the same rate as time. 5. The apparent path of the Sun against the stars is the. 6. The uses the celestial equator as its reference plane. 7. The of a star is measured perpendicular to the celestial equator. 8. The hour circle passing through your zenith is the. 9. of the Earth s axis causes the values of Right Ascension and declination of stars to change. 10. The is the point directly overhead. 11. is measured to the west along the celestial equator from the local meridian. 12. The of the observer is the hour circle through the observer s zenith. 13. A circle on the celestial sphere passing through the North and South celestial poles is called a(n). 14. The angle of a star measured east from the north point along the horizon is the star s. 15. Most telescopes for astronomical use are supported by a(n). 16. Right is measured eastward from the vernal equinox. 17. The are the locations in the sky where the Sun crosses the celestial equator. 18. time is the hour angle of the vernal equinox. 19. The vernal equinox is the for the equator system. 20. The east or west angle of an object on the Earth s surface, measured along the equator from the meridian of Greenwich England is the object s. 21. The is the place where the Sun crosses the celestial equator going north. 22. is measured North or South on the Earth s surface. 23. The occurs when the Sun crosses the celestial equator going north. 24. The is defined as the hour angle of a reference object. 25. time is the hour angle of the Sun plus 12 hours. 26. The is the northern intersection of the local meridian with the horizon. 2-7

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