Astronomy Assignment – The Visible Sky

 

Reading:  Chapter 1 - Charting the Heavens

 

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.

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: 5h 17m, d: 45° 59¢,  (b) RA: 6h 45m, d: -16° 43¢, (c) RA: 14h 04m, 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 for an observer 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) Through what approximate angular distance will Procyon move 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: to answer part (a) relate 1.0 hour to the amount of time for the star to make a complete trip “around the observer.”)

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.      For an observer at 40°N latitude on August 14, 11 p.m. mean solar time, determine the following:  (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?

 

Viewing from Knoxville:

All values are for the year 2017 and local time 2 pm.

Sun (HW Problem #10)

Date

Az

Alt

RA

Dec

Distance

Size

8/1

229°

64°

8h 49m

17° 49'

1.0148 au

32'

8/6

227°

63°

9h 08m

16° 29'

1.0141 au

32'

8/11

225°

62°

9h 27m

15° 02'

1.0133 au

32'

8/16

224°

60°

9h 46m

13° 29'

1.0125 au

32'

8/21

222°

59°

10h 04m

11° 51'

1.0115 au

32'

8/26

221°

57°

10h 23m

10° 08'

1.0104 au

32'

8/31

220°

56°

10h 41m

8° 21'

1.0092 au

32'

9/5

219°

54°

10h 59m

6° 31'

1.0080 au

32'

9/10

218°

52°

11h 17m

4° 38'

1.0067 au

32'

9/15

217°

50°

11h 35m

2° 44'

1.0055 au

32'

9/20

216°

48°

11h 53m

0° 47'

1.0041 au

32'

9/25

215°

46°

12h 11m

-1° 09'

1.0027 au

32'

9/30

215°

45°

12h 29m

-3° 06'

1.0012 au

32'

10/5

214°

43°

12h 47m

-5° 02'

0.9998 au

32'

10/10

213°

41°

13h 05m

-6° 56'

0.9984 au

32'

10/15

212°

39°

13h 24m

-8° 48'

0.9970 au

32'

10/20

212°

37°

13h 42m

-10° 37'

0.9956 au

32'

10/25

211°

36°

14h 01m

-12° 22'

0.9942 au

32'

10/30

210°

34°

14h 21m

-14° 02'

0.9928 au

32'

11/4

209°

33°

14h 40m

-15° 36'

0.9915 au

32'

11/9

209°

31°

15h 00m

-17° 04'

0.9903 au

32'

11/14

208°

30°

15h 21m

-18° 25'

0.9892 au

32'

11/19

207°

29°

15h 42m

-19° 38'

0.9882 au

32'

11/24

206°

28°

16h 03m

-20° 42'

0.9872 au

32'

11/29

205°

28°

16h 24m

-21° 36'

0.9863 au

32'

12/4

205°

27°

16h 46m

-22° 20'

0.9855 au

32'

12/9

204°

27°

17h 07m

-22° 53'

0.9848 au

32'

12/14

203°

27°

17h 29m

-23° 15'

0.9843 au

32'

12/19

202°

27°

17h 52m

-23° 25'

0.9839 au

33'

12/24

202°

27°

18h 14m

-23° 24'

0.9835 au

33'

12/29

201°

27°

18h 36m

-23° 11'

0.9833 au

33'

 

 

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 1st:  (a) mean solar time of sunrise, (b) EDT of sunrise, (c) mean solar time of sunset, (d) EDT of sunset.

14.  For August 1st determine the approximate celestial coordinates of the Sun.  Hint: note position relative to stars on planisphere!

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 the precession of the Earth’s axis this point on the map will shift relative to the stars over the course of thousands of years.  (Actually it is constantly shifting but at a very slow and almost imperceptible rate.)  (a) The vernal equinox will be closest to what constellation in the year AD 8450?  (b) What about AD 14,900?

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) 1st quarter, (d) 3rd 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, 1st/3rd 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.  Similar to the ecliptic, this line represents the path of the Moon relative to the stars.  (b) Why is it 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 repeat itself?  Explain. 

 

Viewing from Knoxville:

All values are for the year 2017 and local time 2 pm.

Moon (HW problem #20)

Date

Az

Alt

RA

Dec

Distance

Size

Phase

8/1

102°

-11°

16h 13m

-16° 14'

405636 km

29'

71%

8/2

98°

-21°

17h 02m

-18° 12'

407228 km

29'

79%

8/3

93°

-30°

17h 51m

-19° 23'

407642 km

29'

86%

8/4

86°

-40°

18h 41m

-19° 45'

407001 km

29'

92%

8/5

78°

-49°

19h 32m

-19° 15'

405463 km

29'

96%

8/6

65°

-57°

20h 23m

-17° 52'

403199 km

30'

99%

8/7

45°

-63°

21h 13m

-15° 41'

400374 km

30'

100%

8/8

19°

-66°

22h 03m

-12° 45'

397129 km

30'

99%

8/9

352°

-63°

22h 53m

-9° 12'

393574 km

30'

96%

8/10

332°

-56°

23h 42m

-5° 11'

389787 km

31'

91%

8/11

319°

-47°

0h 32m

-0° 53'

385827 km

31'

84%

8/12

310°

-37°

1h 23m

3° 31'

381749 km

31'

75%

8/13

302°

-26°

2h 14m

7° 47'

377628 km

32'

65%

8/14

296°

-14°

3h 08m

11° 42'

373587 km

32'

54%

8/15

291°

-2°

4h 04m

15° 00'

369806 km

32'

42%

8/16

285°

10°

5h 03m

17° 25'

366529 km

33'

31%

8/17

278°

21°

6h 03m

18° 44'

364038 km

33'

21%

8/18

270°

33°

7h 05m

18° 47'

362622 km

33'

12%

8/19

259°

44°

8h 07m

17° 33'

362522 km

33'

5%

8/20

244°

53°

9h 07m

15° 08'

363876 km

33'

1%

8/21

222°

59°

10h 05m

11° 47'

366674 km

33'

0%

8/22

195°

60°

11h 00m

7° 47'

370751 km

32'

1%

8/23

171°

56°

11h 52m

3° 26'

375796 km

32'

5%

8/24

154°

49°

12h 43m

-0° 59'

381407 km

31'

11%

8/25

142°

41°

13h 32m

-5° 15'

387136 km

31'

18%

8/26

133°

32°

14h 21m

-9° 11'

392553 km

30'

27%

8/27

126°

22°

15h 09m

-12° 39'

397281 km

30'

36%

8/28

120°

13°

15h 57m

-15° 32'

401025 km

30'

46%

8/29

115°

3°

16h 46m

-17° 45'

403588 km

30'

55%

8/30

109°

-6°

17h 35m

-19° 12'

404877 km

30'

64%

8/31

103°

-16°

18h 26m

-19° 50'

404897 km

30'

73%

9/5

50°

-55°

22h 39m

-10° 21'

391570 km

31'

100%

9/10

320°

-34°

2h 57m

10° 51'

375453 km

32'

77%

9/15

279°

19°

7h 48m

17° 59'

368917 km

32'

23%

9/20

205°

51°

12h 23m

0° 38'

379971 km

31'

0%

9/25

136°

24°

16h 28m

-17° 17'

400298 km

30'

29%

9/30

99°

-18°

20h 40m

-17° 32'

398587 km

30'

75%

 

 

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:  you shouldn’t need a hint this time!)

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 chart of problems 10 and 20. (a) Determine the date on which a solar eclipse likely occurs – explain how this is apparent.  (b) Assuming the Moon and Sun perfectly align on that day, will it be a total eclipse or annular?  How can you tell?  (c) Explain why a solar eclipse does not occur at every new moon by referring to the data and chart.  (d) Determine the date on which a lunar eclipse likely occurs – 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

 

 

 

1.      a.
b.
c.

2.      a.
b.
c.
d.

3.      a.
b.

4.      a.
b.

5.      a.
b.

6.      a. 15.04°
b.
c. 10:56 pm

7.      a.
b.
c.
d.

8.      a.
b.
c.
d.

9.      a.
b.

10.  a. graph
b.
c.
d.

11.  2.46¢

12.  23 hrs 52 min.

13.  a.
b.
c.
d.

14.   

15.  a.
b.
c.
d.

16.  a. sag.
b. vir. 

17.  a.
b.

18.  a. Jan. 30, 12 noon 
b. Jan. 15, 6 pm
c. Jan. 8, 9 am
d. Jan. 23, 3 am

19.  a.
b.
c.

20.  a. graph
b.
c.
d.

21.  33¢

22.  7.14 days

23.  a.
b.
c.
d.

24.  a.
b.
c.
d.
e.
f.