Group 7 CHEN MING SHEN ALEXANDER (U041436L) CHENG SUH JENG (U042983R) GAO HE (U052142J) NG LIN YIN (U032435W) YANG JIE (U058644M)

Transcription

1 Group 7 CHEN MING SHEN ALEXANDER (U041436L) CHENG SUH JENG (U042983R) GAO HE (U052142J) NG LIN YIN (U032435W) YANG JIE (U058644M)

2 SUNSET OBSERVATION Objective On a day in August, September and October, determine the rising or setting position of the Sun. Take a picture showing this event, and use a compass (the magnetic declination is negligible in Singapore) and a protractor (or something similar) to estimate the number of degrees the rising/setting point is from due East/West. Compare the observations and explain any differences. Tools Used Compass: to allow us to find the direction of the setting sun (in this case due west) as a reference point. Method: Our Choice of Location King Edward VII Hall rooftop, NUS. This locale gave us a vantage point from which to have as the foreground certain reference points (the immovable buildings, trees and rooftops) and a relatively convenient view. The sun is still visible even with the wide spread of tree tops obscuring the otherwise clear horizon (not taking into account weather conditions and clouds). Observations 1 st Observation W Figure 1: North of West, approximately by 7hN Time taken: 19:02 Date: 04 September

3 2 nd Observation W Figure 2: just about due West Time taken: 18:48 Date: 24 September rd Observation W Figure 3: South of West, approximately by 8hS Time taken: 18:46 Date: 15 October

4 Discussion From the three pictures it can be seen that before the September equinox, the position where the sun sets lies north of the celestial equator. Similarly, after the equinox has passed, in October, the sun sets south of the celestial equator. On or around the equinox, the sun sets near west, the position not being perfectly due west by taking into account the time of the photograph taken (not exactly on the equinox) and the compass magneti c devi ati on fr o m tr ue nort h. We ackno wl edge that this causes certain inaccuracies in our setup and findings. Early Sept 2005 Sept Equinox 2005 W Oct 2005 Figure 4: The three black lines reveal and juxtapose the relative sunset positions 4

5 RING OBSERVATION Objective Figure 5: Lastly, a side by side comparison of the setting sun from August to October On a day in August suspend a ring-shaped object vertically in the East-West plane. Observe what does the shadow of the ring look like on the ground and where does the shadow of the half of the ring closest to the Sun fall with respect to the other half of the ring? Repeat this activity around the time of the fall equinox (usually 23 September) and in October. Compare the observations and explain any differences. Tools Used Compass: To measure the direction Black line: To indicate the direction of East-West Ring-shaped object: To observe the shape of the shadow in different months Additional tools (two stones, two chairs, and a straw): To improve our observation. Method We chose a ring-shaped object which was suspended East-West according to instruction, with a black tape to line the ground below the ring to indicate the direction of East-West. From August to October, the sun shifts across the equator towards the south. Due to the movement of the sun, the shadow of an object in the same position of the earth also changes with it. Figure 6: Observe at the equator 5

6 1 st Observation Date: 31 st August 2005 Time: 13:01 Declination: 8 o 42.6 N Figure 7 The shadow cast of the ring in Figure 7 is an ellipse: it fell to the south of the black line (the indicator of west-east), and the lower portion was close to the line. 6

7 2 nd observation Date: 24th September 2005 Time: 13:05 Declination: 0 o 30.0S Figure 8 The shadow cast of the ring in Figure 8 was much different from Figure 7, it was almost a straight line. As we know that the latitude of Singapore is 1.27 o N, therefore, when the equinox falls on 23 rd September (when the sun crosses the celestial equator moving southward), the sun is not in the vertical direction over us, it is in south of us. Then we will find the shadow is in north of the black line, and it will be very close to the line. In order to observe the shape of the shadow clearly, we didn t place the black line in the vertical direction below the ring, because the line is simply used as a reference to indicate the east- 7

8 west direction and therefore we got the shadow which was in south of the black line instead. The shadow of one side fell exactly on the other side and formed a straight line. 3 rd Observation Date: 21st October 2005 Time: 12:40 Declination: 10 o 43.4S Figure 9 The shadow cast of the ring in Figure 9 was an ellipse, it fell to the north of the black line (the indicator of west-east), and the lower portion was also close to the line. 8

9 SHADOW OF THE STICK Objective For this task, we were asked to: On a day in August put a stick in the ground. Take at least five photos of the shadow of the stick in the course of the day. Mark the shadow points on the ground, and draw a curve on the ground estimating the path of the shadow. Take a photo of this path, too. Repeat this activity around the time of the fall equinox (usually 23 September) and in October. Compare the observations and explain any differences. Tools used Dustpan: We chose it as the tool which can be erected still on the ground Sticker: To mark the shadow of the stick s top end Compass: To measure the tilted angle *Improvements made: Figure 10 1) For the first observation, we chose one roof of Kent Ridge Hall. However, since there was some other construction located at the roof, sometimes its shadow covered the stick s. Therefore, we moved to the multi-purpose court of King Edward VII Hall for the other two observations where the shadow of the stick would not be disturbed in the course of a day. 2) In the first observation, we used stones in order to make the marked shadow points more easily visible in the picture. But it turned out that because of the size and the irregular shape of the stones, the accuracy of the final curve was somewhat affected. As a result, we changed to use round-shape stickers in the observations afterwards. 9

10 Observations 1 st Observation Date: Aug.31 st Location: The roof of Block D, Kent Ridge Hall, NUS Figure 11 Point P1 P2 P3 P4 P5 P6 Time 9:31 10:35 11:28 12:40 14:31 16:41 The six points are aligned in a convex curve to the north of the east-west plane. 10

11 2 nd Observation Date: Sep.25 th Location: Multi-purpose Court, King Edward VII Hall, NUS Figure 12 P1 P2 P3 P4 P5 P6 P7 P8 Time 10:17 11:15 11:44 12:14 13:12 14:16 15:50 16:42 The eight points almost formed a straight line in the east-west direction. 11

12 3 rd Observation Date: Oct.22 nd Location: Multi-purpose Court, King Edward VII Hall, NUS Figure 13 P1 P2 P3 P4 P5 P6 P7 P8 P9 Time 10:43 11:08 11:55 12:37 13:19 13:41 14:15 14:49 15:29 The ten points are aligned in a convex curve to the south of the east-west plane. 12

13 Discussion 1) Comparison Observations Time Aug.31 th Sep.25 th Oct.22 th Declination of the sun 8.52 (Northern hemisphere) (Celestial Equator) (Southern hemisphere) Shape of the path curve Convex to the North Almost a straight line Convex to the South 2) Explanation We know that a shadow is formed when the ray of the illuminating object is obstructed by another object. Moreover, the shadow and the illuminating object will always be on the opposite sides with respect to the obstructing object. From this simple theory, we can easily judge the position of the sun by observing the shadow of the stick erected on the ground. In the first observation, which was made on Aug.31st, the shadow was to the south of the eastwest plane. If we divide the sky into northern half and southern half by the due east-zenith- due west plane, then from the phenomenon we can judge that the sun was at the northern half of the sky during the course of that day. When it came to Sep.25th, the path of the shadow was almost a straight line pointing to due east and west. This illustrates that the sun was almost right above head on that day, rising and setting from due east and due west respectively. On Oct.22nd, the shadow was to the north of the east-west plane. This means that on that day, the sun was at the southern half of the sky. All these three observations add up to show that there is a southward shift of the sun during the period of August to October. We can use the knowledge we have learned in class to explain it: After the Summer Solstice which is around June.21th, the sun begins moving southwards towards the celestial equator speaking from the view of the earth. It then crosses the celestial 13

14 equator at Autumnal Equinox around Sep.23rd and goes on moving south until it reaches the Tropic of Capricorn around Dec.22th. Furthermore, for people living on the equator, at the Autumnal Equinox, the sun will be right above head at true noon. Because Singapore s latitude is 1 degree north, the day the sun is right above head, that is, at zenith at true noon will be earlier than the Autumnal Equinox. Therefore, when we made our second observation on Sep.25th, the sun should have already passed our head for several days. As a result, the path of the shadow could only be a straight line theoretically which was indeed slightly convexing to the south. This is the path of the shadow we estimate to be: 3) Error Analysis Figure 14 There is still some discrepancy between the direction and shape of the theoretical curve and the curve we have obtained. Nevertheless, we insist on conforming to the original result without any artificial modification. We regard this as the right attitude towards science. Here are some reasons we have come up with that may result in the discrepancy: 1) Error from the compass The compass itself is not accurate enough at the time it is manufactured. The magnetic declination effect the difference between true north (the axis around which the earth rotates) and magnetic north (the direction the needle of a compass will point). The ground was not quite flat which is a requirement for the measurement with compass 2) Besides, in the first observation, we used stones to indicate the path of the shadow in order to make it clearer on the picture. However, the size and irregular shape of the stones affected the accuracy of the targeted curve more or less. Conclusion From August to October, there is a southwards-shifting movement for the sun seen from the earth. 14

15 APPENDIX Pictures for Shadow of the Stick Observation 1 st Observation Figure 1 August.31st :38 Figure 2 August.31 st :37 15

16 Figure 3 August.31 st :28 Figure 4 August.31 st :40 16

17 Figure 5 August.31 st :32 Figure 6 August.31 st :47 17

18 2 nd Observation Figure 7 Sep.25 th 10:17 Figure 8 Sep.25 th 11:15 18

19 Figure 9 Sep.25 th 11:44 Figure 10 Sep.25 th 12:14 19

20 Figure 11 Sep.25 th 13:12 Figure 12 Sep.25 th 14:16 20

21 Figure 13 Sep.25 th 15:50 Figure 14 Sep.25 th 16:42 21

22 3 rd Observation Figure 15 Oct.22 nd 10:32 Figure 16 Oct.22 nd 11:08 22

23 Figure 17 Oct.22 nd Figure 18 Oct.22 nd 12:37 23

24 Figure 19 Oct.22 nd 13:19 Figure 20 Oct.22 nd 13:41 24

25 Figure 21 Oct.22 nd 14:15 Figure 22 Oct.22 nd 14:49 25

26 Figure 23 Oct.22 nd 15:29 Figure 24 Oct.22 nd 16:20 26

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