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Sun & Seasons
Outline
1. Size of Stuff in the Sky
A. Angular size
B. Sun & Moon: angular diameter = 0.5o
C. Angular size () & distance (d):
 
1
d
2. Solar Motions
A. Daily Motion
a. East to west relative to horizon
b. Rising/setting
B. Motion relative to stars
a. Eastward on celestial sphere
b. Sun’s apparent path on celestial sphere: Ecliptic
c. Zodiac: zone of constellations along Ecliptic
3. Equinoxes and Solstices
A. Equninoxes
a. Autumnal: Sep 23
b. Vernal: Mar 21
c. Sun on celestial equator
B. Solstices
a. Winter: Dec 21
b. Summer: Jun 21
c. Sun at maximum distance north/south of celestial equator
4. Daily Solar Motion Changes with Season
A. Rising/setting points wander north/south of east/west
B. Noon altitude varies
a. State College
Equinoxes: altitude = 49o (= 90o – latitude)
Winter solstice: altitude = 25.5o (90o – latitude – 23.5o)
Summer solstice: altitude = 72.5o (90o – latitude + 23.5o)
C. Duration of daylight varies
a. Mar 21 – Sep 23: Sun above horizon >12 hours
b. Sep 23 – Mar 21: Sun above horizon < 12 hours
c. Mar 21 & Sep 23: Sun above horizon 12 hours
D. Changes result from change of orientation of Earth relative to Sun
E. Zones of constant daylight/darkness near Earth’s poles
5. Reasons for the Seasons
A. Temperature varies through the year
a. change in directness of sunlight
b. change in duration of sunlight
B. No significant effect due to change in Earth-Sun distance
Questions
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?
Answers
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 setting.
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. (94o, measured from due south, in summer; 4o, 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 (relative to the stars)
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. On the dates of the equinoxes, the Sun rises directly east and sets directly west. Between rising
and setting, the Sun follows an arc of a circle across the sky. This arc carries the Sun toward the south;
the Sun is closest to south at midday, when it crosses the observer’s meridian. After the Vernal
Equinox (Mar 21), the Sun’s rising and setting points migrate northward; maximum northward rising
and setting points occur on the Summer Solstice (June 21). During this period, the Sun continues to
follow an arc of a circle across the sky, but this arc carries the Sun higher and higher above the south
point on the horizon at midday. The Sun reaches its highest mid-day altitude on the date of the
Summer Solstice. After June 21, the Sun’s rising and setting points retreat southward, and its daily arc
carries it to lower & lower altitudes at midday. The Sun again rises directly east and sets directly west
on the date of the Autumnal Equinox (Sep 23). After Sep 23, the rising and setting points continue to
retreat southward, until the date of the Winter Solstice (Dec 21). On Dec 21, the Sun’s daily arc
carries it to its lowest midday altitude. After Dec 21, the Sun’s rising and setting points move
northward until the Sun once again rises directly east and sets directly west, on the date of the Vernal
Equinox.
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.
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