Objectives/HW

The student will be able to:		HW:
1	Explain and utilize constellations and asterisms as means of mapping and organizing the stars.	1 – 4
2	Explain and utilize the concept of the celestial sphere as a means of understanding the appearance of the universe as seen from Earth.
3	Explain the significance of the pole star, Polaris, and its connection with the apparent motion of the celestial sphere.
4	Explain, define, and utilize the celestial equatorial coordinate system of right ascension and declination, celestial equator and celestial poles.
5	Describe changes in position and appearance of the stars through time and explain in terms of the actual motion and position of the Earth.	5
6	Define, apply, and relate to astronomical events or cycles the following time concepts: sidereal and solar day, sidereal and tropical year, mean solar time, standard time, daylight savings time, and universal time.	6
7	Use a planisphere to locate celestial objects for a particular date and time and/or determine the date and time of certain celestial events.	7 – 8
8	Describe changes in position and appearance of the Sun through time and explain in terms of the actual motion and position of the Earth.	9
9	State the constellations of the zodiac in order and explain the relation between the zodiac and the Sun.	10 – 14
10	Explain, define, and utilize the concept of the ecliptic and the ecliptic plane.	10 – 14
11	Illustrate and describe the connection between the seasons and the motion and orientation of the Earth in its orbit.	15
12	Explain the cause and effect of Earth’s precession and state and apply the period of this cycle to solve problems.	16
13	Describe changes in the appearance of the Moon over the course of one day and night, from one night to the next, from one week to the next, from one month to the next, and from year to year.	17 – 20
14	Explain the apparent motion and changing appearance of the Moon in terms of the actual motions of the Earth and Moon relative to the Sun.
15	Explain and illustrate how the motion and position of the Moon relative to the Earth and the Sun result in the phases: new Moon, waxing crescent, first quarter, waxing gibbous, full Moon, waning gibbous, third quarter, and waning crescent.
16	Define, apply, and relate to astronomical events or cycles the following concepts: sidereal month, synodic month, lunar sidereal and solar days.	21 – 22
17	Explain and illustrate how the motions and positions of the Earth, the Sun, and the Moon result in lunar and solar eclipses – partial, total, and annular.	23
18	Explain and illustrate the concepts of umbra and penumbra in relation to eclipses.	24

1. Given its coordinates, determine the star and state the constellation in which it lies:
(a) RA: 5^h 17^m, d: 45° 59′, (b) RA: 6^h 45^m, d: -16° 43′, (c) RA: 14^h 04^m, d: 64° 22′

2. Determine the coordinates of each of the following stars: (a) Fomalhaut (Piscis Austinus)
(b) Regulus (Leo), (c) Antares (Scorpius), (d) Algol (Perseus)

3. (a) Name five constellations that lie on the celestial equator. These constellations will pass directly overhead only for certain locations on Earth. (b) Name two cities at which you could observe these constellations pass through the zenith.

4. (a) Determine the brightest star to pass within five degrees of our zenith here in Knoxville. (b) Determine the brightest star to pass within five degrees of the zenith in Sydney, Australia.

5. Describe each of the following as east to west or west to east and explain the actual motion that causes the apparent motion: (a) direction of the stars’ hourly motion across the observer’s sky, and (b) direction of the stars’ monthly motion across the observer’s sky.

6. Suppose you observe the bright star Procyon crossing the sky during the night. This star is quite close to the celestial equator. (a) Calculate the approximate angular distance that Procyon moves across the sky in 1.0 hour of time. (b) In what direction does it move across the sky? (c) If it crosses the meridian at 11:00 p.m. on one night at what time will it cross the meridian on the next night? (Crossing the meridian is sometimes called a transit.)
Hint: use the length of the sidereal day to determine parts (a) and (c).

7. Use a planisphere to determine the approximate dates on which the following events would occur at midnight mean solar time for an observer at 40°N latitude: (a) Betelgeuse (Orion) transits (crosses the meridian), (b) Arcturus (Bootes) transits, (c) the “pointers” (Merak and Dubhe) in the big dipper reach maximum altitude, (d) the “Summer Triangle” (Vega, Deneb, and Altair) reaches maximum altitude.

8. Use a planisphere for observer at 40°N latitude on August 14, 11 p.m. mean solar time, to find: (a) the most prominent constellation and/or bright star at or near the observer’s zenith, (b) the zodiac constellation on the observer’s meridian, (c) the most prominent constellation and/or bright star just above the observer’s northeast horizon, and (d) the most prominent constellation and/or bright star just above the observer’s southeast horizon.

9. Describe each of the following as east to west or west to east and explain the actual motion that causes the apparent motion: (a) direction of the Sun’s hourly motion across the observer’s sky, (b) direction of the Sun’s monthly motion across the celestial sphere.

10. Refer to the given ephemeris for the Sun. (a) Using the symbol ¤, plot the Sun’s position on the given chart for each date. Label the date on some of the dots. (b) Connect with a smooth curve – what is the result called? (c) Use the table and graph to determine which equinox and which solstice occurs during this time interval and estimate the date of each. (d) Discuss the patterns illustrated by the azimuth and altitude values – what changes occur and why?

Sun from Knoxville
Date	Time	RA	Decl.	Az.	Alt.	Ang. Dia.	Dist. (AU)
03/19	3 pm	23^h 58^m	- 00° 08′	210.6°	49.7°	32.1′	0.996
03/24	3 pm	00^h 16^m	+01° 50′	212.4°	51.4°	32.1′	0.997
03/29	3 pm	00^h 35^m	+03° 47′	214.4°	52.9°	32.0′	0.999
04/03	3 pm	00^h 53^m	+05° 42′	216.5°	54.5°	32.0′	1.000
04/08	3 pm	01^h 11^m	+07° 36′	218.7°	55.9°	31.9′	1.001
04/13	3 pm	01^h 30^m	+09° 25′	220.9°	57.3°	31.9′	1.003
04/18	3 pm	01^h 48^m	+11° 11′	223.2°	58.6°	31.9′	1.004
04/23	3 pm	02^h 07^m	+12° 53′	225.5°	59.9°	31.8′	1.006
04/28	3 pm	02^h 26^m	+14° 29′	227.8°	61.0°	31.8′	1.007
05/03	3 pm	02^h 45^m	+15° 59′	230.0°	62.1°	31.7′	1.008
05/08	3 pm	03^h 04^m	+17° 22′	232.1°	63.1°	31.7′	1.009
05/13	3 pm	03^h 24^m	+18° 38′	234.1°	64.0°	31.7′	1.011
05/18	3 pm	03^h 44^m	+19° 47′	235.9°	64.8°	31.6′	1.012
05/23	3 pm	04^h 04^m	+20° 46′	237.5°	65.6°	31.6′	1.013
05/28	3 pm	04^h 24^m	+21° 37′	238.8°	66.3°	31.6′	1.013
06/02	3 pm	04^h 45^m	+22° 19′	239.8°	66.8°	31.5′	1.014
06/07	3 pm	05^h 05^m	+22° 51′	240.5°	67.4°	31.5′	1.015
06/12	3 pm	05^h 26^m	+23° 12′	240.8°	67.8°	31.5′	1.016
06/17	3 pm	05^h 47^m	+23° 24′	240.8°	68.1°	31.5′	1.016
06/22	3 pm	06^h 07^m	+23° 25′	240.4°	68.3°	31.5′	1.016
06/27	3 pm	06^h 28^m	+23° 16′	239.7°	68.4°	31.5′	1.017
07/02	3 pm	06^h 49^m	+22° 57′	238.6°	68.3°	31.5′	1.017

11. As the Earth moves in its orbit the position of the Sun relative to the backdrop of stars changes from our perspective on Earth. Through how many arc minutes does the Sun move relative to the stars in 1.0 hour of time? (Hint: relate this to the amount of time for the Sun to make a “complete trip around” the celestial sphere.)

12. What would be the length of the mean solar day if the sidereal day was still 23 hours 56 minutes but the Earth was rotating in the opposite direction while still revolving around the Sun in the same direction? (Note: assume the second, minute, and hour are the same as they are now – i.e. based upon atomic properties and not defined by the Earth’s motion.)

13. Use a planisphere to determine approximate values of the following for an observer in Knoxville on August 1^st: (a) mean solar time of sunrise, (b) EDT of sunrise, (c) mean solar time of sunset, (d) EDT of sunset.

14. For August 1^st determine the approximate celestial coordinates of the Sun. Hint: note the position relative to stars on planisphere and/or consult star map.

15. Suppose the Earth had no tilt to its axis – i.e. suppose its axis of rotation was perfectly perpendicular to its orbit. (a) What would happen to the ecliptic on the celestial sphere?
(b) Would there still be seasons? If so, would the seasons be more or less intense?
(c) Would the Earth still have tropic regions and arctic regions? (d) How would the Sun’s appearance in the sky be different? Or would it be the same?

16. Consult a sky map and note the location of the vernal equinox. Due to precession this point on the map shifts along the ecliptic relative to the stars in a cycle 25800 years long. (a) Determine the time for it to shift by one degree (or 4^m). (b) Determine the constellation in which the vernal equinox is located in the year AD 8450. (c) Repeat for the year AD 14,900. (d) Find the declination of Polaris in AD 14,900 (hint: the change is related to the 23° tilt of Earth’s axis).

17. Describe each of the following as east to west or west to east and explain the actual motion that causes the apparent motion: (a) direction of the Moon’s hourly motion across the observer’s sky, (b) direction of the Moon’s daily motion across the celestial sphere.

18. On a certain year a full Moon occurs above Knoxville on January 1 at 12:01 a.m. EST. For the same month determine the date and approximate times for each of the following phases: (a) full Moon, (b) new Moon, (c) 1^st quarter, (d) 3^rd quarter.

19. Suppose you see, from Knoxville, the Moon in the sky on a Friday right after the sun has set. And at that time the Moon can barely be seen because only a very narrow strip of it is illuminated. (a) State the phase of the Moon – waning/waxing, crescent, gibbous, 1^st/3^rd quarter, etc. (b) Describe the Moon’s approximate location in the sky – N, W, E, W, near the horizon, near the zenith, etc. (c) Determine the approximate phase and location in the sky on the following Friday right after sunset.

20. Use the given ephemeris. (a) Plot the given positions on the same chart as prob #10 and connect with a smooth curve. Label the dates of each new and each full Moon. (b) Explain why this path is similar but not quite the same as the ecliptic. (c) By at most how many degrees is it different from the ecliptic? How is this related to the orbit of the Moon? (d) Does the Moon’s path appear to repeat itself? Explain.

Moon from Knoxville
Date	Time	RA	Decl.	Az.	Alt.	phase	ang. dia.	dist. (km)
03/19	3 am	07^h 42^m	+26° 04′	288.0°	20.5°	70.22%	30.2′	396100
03/21	3 am	09^h 23^m	+19° 22′	269.0°	35.7°	86.03%	29.8′	400400
03/23	3 am	10^h 54^m	+09° 34′	242.8°	46.1°	96.36%	29.7′	401600
03/25	3 am	12^h 19^m	-01° 41′	210.0°	48.2°	100.00%	29.8′	400600
03/27	3 am	13^h 45^m	-12° 56′	179.7°	41.1°	96.32%	30.0′	397800
03/29	3 am	15^h 21^m	-22° 30′	156.8°	27.9°	85.51%	30.4′	393300
03/31	3 am	17^h 10^m	-28° 22′	138.5°	11.7°	68.66%	30.9′	387000
04/02	3 am	19^h 11^m	-28° 26′	121.1°	-5.9°	47.83%	31.5′	378900
04/04	3 pm	21^h 32^m	-19° 33′	243.4°	2.6°	22.43%	32.7′	365500
04/06	3 pm	23^h 23^m	-06° 51′	234.7°	29.4°	6.15%	33.5′	356500
04/08	3 pm	01^h 11^m	+07° 37′	218.8°	55.9°	0.00%	33.7′	354600
04/10	3 pm	03^h 04^m	+20° 06′	161.6°	73.4°	5.89%	33.1′	360900
04/12	3 pm	05^h 04^m	+27° 16′	97.3°	60.2°	21.06%	32.0′	372900
04/14	3 pm	07^h 04^m	+27° 40′	80.6°	37.8°	40.63%	30.9′	386600
04/16	3 pm	08^h 52^m	+22° 22′	73.4°	15.6°	60.51%	30.0′	398100
04/18	3 am	09^h 57^m	+15° 59′	276.8°	18.4°	72.92%	29.7′	401900
04/20	3 am	11^h 24^m	+05° 32′	255.2°	28.3°	87.79%	29.7′	402600
04/22	3 am	12^h 49^m	-05° 52′	230.0°	34.1°	97.27%	29.9′	400000
04/24	3 am	14^h 18^m	-16° 46′	202.4°	34.2°	99.86%	30.2′	395400
04/26	3 am	16^h 00^m	-25° 19′	175.7°	28.6°	94.63%	30.6′	389800
04/28	3 am	17^h 55^m	-29° 15′	151.7°	18.6°	81.73%	31.1′	383800

21. As the Moon moves around its orbit its position relative to the backdrop of stars changes from our perspective on Earth. Through how many arc minutes does the Moon move relative to the stars in 1.0 hour of time? (Hint: use the length of the sidereal month.)

22. Suppose the Moon’s sidereal orbital period (sidereal month) was 7 solar days (instead of 27.3 solar days). What would be the synodic period (synodic month) (instead of 29.5 solar days)?

23. Consult the ephemerides and charts of problems 10 and 20. (a) Determine the date on which a solar eclipse occurs – explain how you can tell. (b) Based on the information given what type of solar eclipse would an observer in Knoxville witness on that date? Explain. (c) A new moon after the one shown in the table occurs on May 8 and has about the same RA and declination as shown for April 10. This will not be an eclipse – explain. (d) A penumbral lunar eclipse occurs on at least one of the dates in the table – which one(s)? Explain.

24. (a) About how often does the Moon enter the Earth’s umbra or penumbra? (b) About how often does the Earth enter the Moon’s umbra or penumbra? (c) About how often do you enter the Earth’s umbra? (d) About how often do you enter the Earth’s penumbra? (e) About how often do you enter the Moon’s umbra? (f) About how often do you enter the Moon’s penumbra?

Selected Answers