Astronomy Laboratory Exercise 22 Solar Lab The Sun (or Sol) is the nearest star to Earth. In fact, it is about 300,000 times closer to Earth than the next nearest star, Proxima Centauri. It is the only star whose surface features are clearly visible from Earth, and so it provides a glimpse into the workings of other stars. The Sun's importance can not be overstressed, for without the Sun there would be no life on Earth. This lab explores some of the features and motions of the Sun. The "surface" of the Sun can be viewed safely by projecting it onto a screen or looking through heavy filtering (such as welder's glass #14 or a special solar filter). NEVER LOOK DIRECTLY AT THE SUN, AS PERMANENT DAMAGE TO VISION MAY OCCUR! The Solar Observing Lab, Exercise 23, provides several observing exercises involving the Sun. The Sun is not a solid object, but a huge globe of glowing plasma. The "surface" that is seen through a filtered telescope or in a solar projection is the photosphere. The photosphere is that layer of the Sun from which light seems to come. But the energy of the light originates in thermonuclear fusion reactions in the core of the Sun, where hydrogen nuclei are fused into helium. The interior of the Sun can be divided into three principal parts: the core, the radiative zone, and the convective zone. In the radiative zone, light is absorbed and reemitted by the solar material. The direction in which the light is reemitted is random, so it may take millions of years for light to leave the radiative zone. At the outer boundary of the radiative zone, however, the density of the solar material is low enough for convection to occur. Material that absorbs the light is heated, rises, transmits its heat to higher materials, and falls to be heated again. The convective zone consists of loops of rising and falling material. At the photosphere, the density is low enough that the hot, rising material radiates its heat away as light then sinks to be reheated. The Sun's rotational period is not uniform across its surface; material near the equator moves about the solar axis more rapidly than material near the poles. This is called differential rotation. The sidereal rotational period of the Sun increases from about 25 days near the equator to about 34 days near the poles. However, since Earth revolves about the Sun at about 1 degree per day in the same direction that the Sun rotates, the synodic period is longer. As viewed from Earth, material near the Sun's equator takes about 27 days to complete one rotation, while material near the solar poles takes about 3 8 days. The solar rotational period at the latitude of a sunspot may be determined by measuring the sunspot's change in solar longitude (~L) over a number of days (~T) . The Sun rotates 360° in one period. Thus, the solar rotational period (P) at the latitude of the sunspot is given by P=llT·e:] . (1) 22 - 1 Example 1: A sunspot is seen to move 24 o in 2. 0 days. What is the period of rotation for material at the same latitude as the sunspot? P= (2.0· df;;o) = 30.-d Figure 22-1 illustrates the Solar Angle Device (SAD). The SAD is designed to facilitate recording the Sun's movements in the sky. It consists of a flat surface (the recording platform) mounted with a perpendicular mast. The mast may be topped by a horizontal plate with a 'V' shaped cut-out. The 'V' points toward the mast. If the 'V' is placed far enough from the mast, its shadow can be seen from the equator at solar noon on both of the solstices without reorienting the SAD. The SAD is oriented so that the recording platform is level with the ground and the shadow of the 'V' falls on the surface. The recording platform is covered with paper so a new record of the Sun's motions can be made each year. A mark is placed directly below the point of the 'V' to indicate the location of the zenith as seen from the tip of the 'V'. Also, it is convenient to mount the SAD at exactly the same location and in the same orientation each time it is used. to zenith to Snn a recording platfonn 1 tano=-} / zenith/ IE b mark Figure 22-1: Solar Angle Device (SAD) seen edge-on. The length of the shadow cast by a vertical pole can be used to determine the Sun's position in the sky. Solar noon is the time when the Sun is on the meridian. The Sun is highest in the sky at this time and shadows are shortest. During the day, the shadow of the 'V' is seen to move across the surface of the SAD. If this shadow is marked every few minutes (and the time of each mark recorded), the solar noon time can be determined later by finding the time when the shadow was shortest. The angle (8) between the Sun and the zenith is calculated using 8 =arctan(:), (2) where a is the height of the vertical mast and b is the distance of the shadow of the 'V' from the zenith mark. 22-2 Example 2: The shadow cast by the Sun of the 'V' atop a 50. em high vertical mast is 20. em north of the zenith mark at solar noon. What is the altitude and azimuth of the Sun? The angle of the Sun from the zenith is 2 8 = arctan( 0.-cm) = 22°. 50.-cm Since this shadow is measured at solar noon and the shadow is north of the zenith mark, the azimuth of the Sun is 180° (i.e., the Sun is south of the zenith). The zenith is +90° in altitude, so the Sun must be at +68° in altitude. The Sun's position in the sky depends on the location of the observer, the time and date, and the axial tilt ofEarth. Earth's rotational axis tilts with respect to the axis of the plane of its orbit (the ecliptic) by about 23.5°. On the summer solstice, the Sun appears overhead at solar noon only for people located at 23.5°N. People north of this latitude see the Sun south of the zenith and people south of this latitude see the Sun north of the zenith. After the summer solstice, the Sun's position at solar noon appears to move southward each day. On the autumnal equinox, the Sun is overhead as viewed from the equator at solar noon. On the winter solstice at solar noon, the Sun is 23.5° south of the plane ofEarth's equator and can be seen at the zenith from 23.5°S latitude. The Sun then appears to move to the north again, passing the equator on the vernal equinox. Figure 22-2 shows the changing position of the Sun in the sky during the year. The Sun is closest to the north celestial pole on the summer solstice (Figure 22-2.a) and is farthest on the winter solstice (Figure 22-2.b ). north celestial pole to zenith Figure 22-2(a): The position of Sun on the summer solstice. to ztnitl1 north cele:stial pole equator Figure 22-2(b ): The position of Sun on the winter solstice. 22- 3 The angular distance between the Sun and the zenith for a given location can be measured using the Solar Angle Device, but the latitude of the location and the axial tilt of Earth can not be measured directly. However, these values can be determined from the position of the Sun in the sky. At solar noon on the summer solstice (Figure 22-2.a), the Sun's angular distance from the zenith (8sum) is given by 8Sum = 8Lat - 8Tilt' (3) where 8Lat is the latitude angle ofthe observer's location and 8Tilt is the axial tilt ofEarth. On the winter solstice (Figure 22-2. b), the Sun's angular distance from the zenith at solar noon (8win) is given by e Win = e Lat + e Tilt · ( 4) Solving these two equations simultaneously, gives 8 = eWin + eSum (5) Lat 2 and 8 _ eWin- eSum Tilt- (6) 2 Example 3 : The angular distance of the Sun from the zenith is measured at solar noon on the winter solstice and on the summer solstice to be 58.5° and 11.5°, respectively. The Sun was south of the zenith on both occasions. Determine the latitude from which the measurements were made and the axial tilt of Earth. e = ss.so+ 11.50 = 35 oo Lat · 2 e . = 58.50-11.50 = 23 so T1lt · 2 Thus, Earth's axis tilts 23.5° and these measurements were taken from a latitude of35.0°N. The time of solar noon is different for different dates and for different locations on Earth. The daily variation in the time of solar noon is expressed by the equation of time (EOT). The equation of time gives the number of minutes that the Sun is early or late in reaching the meridian. Three factors affect the equation of time: the position ofEarth along its elliptical orbit, the axial tilt of Earth, and the location of the observer. If Earth had no axial tilt and traveled in a circular orbit, solar noon would always occur at 1200 hours for a location on a time zone line. However, Earth travels in an elliptical orbit about the Sun.