1. Size of Stuff in the Sky
* Angular size
* Moon & Sun: angular diameter = 0.5 deg
* Angular size & distance:
2. Solar Motions
* Daily motion
> east to west; rising/setting
* Eastward relative to stars
> Apparent path: Ecliptic
3. Equinoxes & Solstices
* Vernal/Autumnal Equninoxes (Mar 21/Sep 23): Sun on equator
* Winter/Summer Solstsices (Dec 21/Jun 21): Sun maximum south/north of equator
4. Daily Solar Motion Changes With Seasons
* Rising/setting points vary
* Noon altitude varies
> State College
~ Equinoxes: altitude = 49 deg ( = 90 deg - latitude)
~ Summer solstice: altitude = 72.5 deg ( = 90 - latitude + 23.5 deg)
~ Winter solstice: altitude = 25.5 deg ( = 90 - latitude - 23.5 deg)
* Duration of daylight varies
> Mar 21 - Sep 23: Sun above horizon > 12 hrs
> Sep 23 - Mar 21: Sun above horizon < 12 hrs
> Mar 21 & Sep 23: Sun above horizon exactly 12 hrs
* Changes result from change in orientation of Earth relative to Sun
* Zones of constant darkness/daylight near poles
5. Reasons for the Seasons
* Temperature varies over seasons
> change in directness of sunlight
> change in hours of daylight
* No significant temp change due to change in Earth-Sun distance
1. Earth's Moon is slowly moving farther from Earth. Thus, in the past, it would have been closer. Would the Moon's angular diameter have been larger or smaller in the past than at present? Explain your answer.
2. A penny held 1 foot in front of your eye subtends an angle of 3.6o. At what distance from your eye should we place the penny so that it subtends the same angle as the Moon or Sun (0.5o)? If you now move the penny twice this distance from your eye, what angle will it subtend? What angle is subtended by the penny at 10 times the distance?
3. As viewed from Earth, Sun and Moon have the same angular diameter, yet we know the Sun's linear diameter exceeds the Moon's linear diameter by a factor of 400. Does this not present a paradox? Explain.
4. Ques. #13, pg. 26.
5. Why is it warmer in summer than in winter?
6. (a) Prob. #3, pg. 26.
(b) Suppose Earth's axial tilt were 45o instead of 23.5o. Do you think seasonal temperature differences would be more or less extreme than at present in State College? Explain
7. What is the difference between the daily ('diurnal') and annual motion of the Sun?
8. What is the ecliptic, and why is it tilted with respect to the celestial equator?
9. By how many degrees does the Sun move along the ecliptic each day? Explain your answer.
10. Describe how the daily path of the Sun across the sky changes with the seasons.
11. At latitude 29o North on Earth, where should I look in the sky to view the (astronomical) noon Sun on the dates of the Equinoxes? Summer Solstice? Winter Solstice?
12. Where do you have to be on Earth (i.e., at what latitude(s)) to see the Sun appear in the zenith (i.e., straight overhead) at least once per year?
13. What is the Zodiac?
1. Viewed from Earth, the Moon's angular diameter would have have been larger in the past.
2. The distance would be 7.2 ft (3.6/0.5 = 7.2, so the penny must
be 7.2 times farther away when it subtends an angle of 0.5 degrees.)
At a distance of 14.2 ft, the penny will subtend an angle of 0.25o.
(0.5/2 = 0.25 - twice the distance means one-half the angle). At
10 times the distance (72 ft), the angle subtended is 0.05o.
(0.5/10 = 0.05)
3. There is no paradox. The Sun is simply 400 times farther from Earth than the Moon, so it appears just the same size (in degrees) as does the Moon.
4. The cause of Earth's seasons is very nicely described on pgs. 19 - 20, beginning with the last paragraph on pg. 19.
5. Summer is warmer than winter for two reasons: 1) Sun is higher in the sky in summer, thus sunlight is more direct. 2) Sun spends more time above the horizon in summer, thus exposing Earth's surface to warming sunshine for longer period of time.
6. a) There would be no seaons. For all locations
on Earth (except at the poles), the sun would rise and set each day and
follow exactly the same path across the sky the year-around. At the
poles the sun would perpetually circle the horizon, neither rising nor
b) Seasonal differences in temperature would be more extreme as the sun would rise higher in the sky in summer, and dip lower in winter. (94 deg, measured from due south, in summer; 4 deg, measured from due south in winter.)
7. Daily motion carries the sun from east to west relative to the horizon, each day. Annual motion carries the sun eastward, relative to the stars; the sun completes a circle on the sky once per year.
8. The ecliptic is the Sun's annual path among the stars, as viewed from Earth. That is, the ecliptic is the projection of Earth's orbit on the sky, as viewed from Earth. The celestial equator is the projection of Earth's equator on the sky. As Earth's equator (plane) is tilted by 23.5o to Earth's orbit plane, so too must the celestial equator be tilted by 23.5o to the ecliptic.
9. The Sun moves about 1o/day eastward along the ecliptic.
10. Seasonal changes in the Sun's motion across the sky are well-summarized by FIG 3 above.
11. In all cases, you're looking south to view the noon sun elevated above the horizon. Equnioxes: elevation = 61o. Winter Solstice: elevation = 37.5o. Summer solstice: elevation = 84.5o.
12. You must be located within 23.5o latitude of the equator to see the Sun in the zenith at least once per year.
13. The Zodiac consists of the 13 constellations that form the
background of the ecliptic.