Lecture 4: DM: time and Diurnal Motion

Transcription

1 Dr. W. Pezzaglia Astronomy 10, Fall 2006 Page 8 Lecture 4: DM: time and Diurnal Motion Schedules: Aug 30, Wed (today) o Homework #2 due (see solutions below) o Web Site changed to: o Handout today of all previous presentations o Start Chapter 3 in book (moon) Sep 06, Wed o Homework #3 due (see assignment below) o Download Lunar Motion presentation from new web site. Sep 11, Mon: o Quiz #1, covers homeworks 1, 2, 3, 4. Starwheel use ok. Closed book. o Homework #4 due. Notes: Office Hours: Wednesdays 11:45-12:45, room 1824 (door is locked, please knock!) WebSite: Video: Mystery of Chaco Canyon o o o Study Guide: HOMEWORK #3 due Next Lecture at beginning of class. 6. On the Ecliptic and Sun (modified from #60, page 40 in Freedman 7 th ed) Using Starry Night 4 program, GO menu, choose Guides, choose Atlas. Under Guide tab, select Ecliptic. Under View Options tab, under constellations, turn on Auto Identify and Boundaries. Using Starry Night 3 program, GO menu, choose Atlas. Find the sun. Under Constellations check the Auto Identify and Zodiac. Click the Now button. Find the sun. Note: be sure that you have set your home location to San Jose, California! (a) Move forward in time by steps of 1 day. Do this for an entire year. How does the sun appear to move against the constellations? What path does it follow? Does it ever change direction? (b) What constellation is the sun in today? Is this the same as the astrological sign for today s date? Explain in terms of precession. (c) Again follow the sun day by day for a year. What constellations does the sun appear to pass over during the year? Are any of them NOT the standard 12 astrological signs? (d) Change the date to be June 29 (at noon). Double click on sun. Look at the Position in the Sky tab. What is the RA/Dec of the sun? (e) What is the ecliptic longitude of the sun? 7. The Ecliptic Find the ecliptic (dashed line) on the starwheel. The "degrees" along this line run from 0 to 360, called ECLIPTIC LONGITUDE. NOTE this is missing on the newer plastic starwheel, so you will need to consult the xerox copy given in the first lecture. DO THIS: add (using pencil) the ecliptic longitude values to your starwheel. You will need this to figure out some things in the future. Use a TABULAR FORMAT (such as given below) to summarize all your answers!

2 Dr. W. Pezzaglia Astronomy 10, Fall 2006 Page 9 (a) Give the approximate ecliptic longitude for the following stars: Aldebaran, Al Rischa (the star in Pisces near 2 h, 3 ), Hamal, Sadalmelik (the brightest star in Aquarius, near the equator at 22 h ), Dabih (Beta Cap, the brightest star in Capricorn, at about 20 h 20 m, -15 ), Nunki (b) Put the stars in order in your table. Are they all about 30 apart? (c) Include in your table the constellation that each star is in. Star Ecliptic Longitude Constellation Nunki etc 8. Diurnal Motion: Set your starwheel to: August 25, at 3 am (PST) [HINT: Turn the wheel until August 25 lines up with 3 am in the morning] (a) What star or constellation(s) is rising in the east? (b) What star or constellation(s) is setting in the northwest? (c) What star or constellation(s) is at zenith? (i.e. overhead)? [Hint: overhead is the will be near the center of the cut out area] Xtra Credit hmk (i.e. not required, but will replace missed points on homework) 9. Arabic Star Map: You should have received a handout of an Arabic chart of the heavens. Make a copy of it, and try to label the constellations. Some hints: If you compare with your starwheel, you will have to look at the map in a MIRROR. The dot at the center is the ECLIPTIC pole (pole of revolution), while the second "dot" which is about an inch below center corresponds to the "rivet" (North Celestial Pole, Pole of Rotation, Polaris) of your starwheel. The outer circle (edge) of the map roughly corresponds to the "ecliptic" (the dashed line on your starwheel). The "Arc" on the upper half of the map corresponds to the "equator" (solid line on starwheel) Solutions to HOMEWORK #2 due today at beginning of class. 4. Seasons: (a) The equinoxes/solstices are an average of 365 d 5 h 49 m 45 s later (last year we got 5 h 44 m, previous year we got 5 h 48 m, previous year we got 5 h 51 m previous year 5 h 47 m previous year we got 365 d 5 h 50.5 m, previous year we got 5 h 48.5 m, previous year 5 h m, previous year 5 h m, so things are not always the same!). They are not all the same, differing by a few minutes, with Spring Equinox difference the greatest by 6 m less than average! (b) Our average year is 1 m longer than the true tropical year (including leap day Feb 29, 2004 does not matter, because the first date in our table, spring equinox 2004, is past that date) (c) Predict the 2006 Fall Equinox. If we add 5 h 49 m to the 2005 Fall solstice we would predict 2006 Sep 23 d 04 h 12 m. [Note we are off from the true value by a few minutes. Why are we off at all? The earth s orbit is an ellipse, and the position of the perihelion is slowly moving, which will change the lengths of the seasons].

3 Dr. W. Pezzaglia Astronomy 10, Fall 2006 Page 10 Season Difference Predict (true)** Equinox: Mar 20 d 06 h 49 m 20 d 12 h 33 m 5 h 44 m 20 d 18 h 22 m 20 d 18 h 26 m Solstice: Jun 21 d 00 h 57 m 21 d 06 h 46 m 5 h 49 m 21 d 12 h 35 m 21 d 12 h 26 m Equinox: Sep 22 d 16 h 30 m 22 d 22 h 23 m 5 h 53 m 23 d 04 h 12 m 23 d 04 h 03 m Solstice: Dec 21 d 12 h 42 m 21 d 18 h 35 m 5 h 53 m 22 d 00 h 24 m 22 d 00 h 22 m ** From (d) The 2004 season lengths (ending in spring 2005) are given below. [NOTE: Near Jan 3, just after the winter solstice, the sun is moving fastest, so indeed winter to spring is the shortest time, while half a year later the summer to fall (which contains the aphelion) is the longest. Since Jan 3 is close to the winter solstice, the time from fall to winter is nearing the perihelion, and also on the short side.] (e) These values differ from the "classic" ones (Kallippos). NOTE: In part, this is because the perihelion has moved maybe as much as 10 east over the last 3000 years (i.e. perihelion took place in the FALL making that the shortest season for Kallipos). =========================================================== Season 2004 Euktemon 433 BC Kallippos (335? BC) Sp-Su 92 d 18 h 08 m = Su-Fall 93 d 15 h 33 m = Fall-Win 89 d 20 h 12 m = Win-Sp 88 d 23 h 51 m = =========================================================== 5. Sun s Diurnal Motion (a) The length of day is slowly decreasing (by about 2.5 minute per day). This is because we have passed the Summer Solstice, and approaching Fall Equinox. (b) Sunset time is getting earlier by a 1.5 minutes a day. Sunrise is getting later by about the same amount. (c) Transit time: is just about constant at 1:09 pm, but slowly decreasing. (d) The sun is transiting about 1 minute late. [Note the analemma predicts that the sun would be about 1.5 minutes late on Aug 28, so 12:08+1=12:09 PST, or for daylight savings: 1:09 PDT] ==================================================== Date Sunrise Transit Sunset DayLength /26/ :32 13:09 19:45 13 h 13 m 8/27/ :33 13:09 19:43 13 h 10 m 8/28/ :34 13:08 19:42 13 h 08 m ==================================================== Source: Times for Livermore, California

4 Dr. W. Pezzaglia Astronomy 10, Fall 2006 Page 11 SAMPLE QUIZ QUESTIONS ON THE MOTION OF THE SUN [Quiz 1 ] Below is a starmap which has down to 3rd magnitude stars drawn in. Label North, South, East, West,Label (in words) the axes with proper names,label FIVE constellations on the map. LABEL the celestial equator, DRAW the position of the sun for the date DECEMBER 31, what is its ecliptic longitude? What is its RA and Dec? Label equator, ecliptic, first point of aries, descending solar node, north ecliptic pole. SAMPLE QUIZ QUESTIONS ON Time and Diurnal Motion (Quiz 1) 1. A star is on the prime meridian a. always b. once a day c. twice a day d. twice a year e. none of these 2. If the clock on the wall says 8 pm, the Universal time would be: a. 3 am b. 4 am c. 3 pm d. none of these 3. At the north pole, would be circumpolar. a. no stars b. all stars c. all stars above the equator d. only Polaris e. none of these 4. The sidereal time is equal to the solar time a. once a day b. once a year c. always d. never e. none of these 5. Name of the point overhead? 6. Name a constellation which is never seen at the north pole, but can be seen at Livermore. 7. At what time on May 7 will the star Regulus (leo) set? 4. Name a constellation that CAN be seen from Livermore, but NOT from the North Pole? 10. ASSUMING THAT YOUR WATCH RIGHT NOW READS 10:00 am (approximate time of quiz today): a. The time at the Greenwich observatory? b. The Local Sidereal Time (LST)? 7. If a star rose at 3 am, then one week later it would rise at what time? 8. At what time tonight will the star ALTAIR (Aquila) SET? 9. How high above the horizon (in degrees) will RIGEL (Orion) transit today? 2. The sidereal time is equal to the solar time A. once a day B. once a year C. always D. never E. none of these 3. A star will transit each successive day at altitude angle (height above the horizon) in the sky. A. later, a different B. earlier, a different C. later, the same D. earlier, the same E. none of these 5. At what time on December 1 will the sky appear the same as on October 1 at 11 pm? A. 3 am B. 1 am C. 11 pm D. 9 pm E. none of these

5 ,. The Northern Hemisphere of the Celestial Globe, designed by the Arabic astronomer Mohammud ben Helah of Monsul, 1275

6 ~ ~ ~l