March 21 Sun Observer located at 42 N Horizon 48
June 21 March 21 A 48 90 S 23.5 S 0 23.5 N 42 N 90 N Equator
(June 21) C (March 21) B A 71.5 48 Horizon 24.5 Observer
Sun 40 Observer
Sun 22 Observer
Sun 31 Observer
Sun 54 Observer
Flashlight Flashlight Area B Area A Globe
50
70
30
90
Apparent Diameter of the Sun During the Year Date Apparent Diameter ( ' = minutes '' = seconds) January 1 February 10 March 20 April 20 May 30 June 30 August 10 September 20 November 10 December 30 32'32'' 32'25'' 32'07'' 31'50'' 31'33'' 31'28'' 31'34'' 31'51'' 32'18'' 32'32''
Duration of Daylight (hr) 18 17 16 15 14 13 12 11 10 9 8 7 Duration of Daylight Hours Throughout the Year at Various Locations Spring equinox March 21 Summer solstice June 21 Fall equinox September 23 Winter solstice December 21 J F M A M J J A S O N D Months Caracas 11 N Mexico City 19 N New Orleans 30 N Denver 40 N Edmonton 54 N
Observer Duration of Insolation March 21 Duration of Insolation June 21 W 12 hr 0 hr X 12 hr 12 hr Y 12 hr 18 hr Z 12 hr 24 hr
N Sun s rays S
Diagram 1 N Equator C N Day Arctic Circle Night B N Sun D Night Day N A
6 p.m. 8 p.m. 4 p.m. 10 p.m. 2 p.m. Midnight North Pole Noon Sun s rays 2 a.m. 10 a.m. 4 a.m. A 6 a.m. 8 a.m. Direction of rotation
Diagram 2 Sun s rays Noon E March 21
Point X North Pole Sun s rays Direction of rotation
Point X North Pole Sun s rays Direction of rotation
Mars Earth Sun (Not drawn to scale)
Earth Light rays from Sun North Pole
Sun s apparent path z Sun s actual position S Observer N
N Sun s rays S
66 o N North Pole Sun s rays 23 o N Equator 23 o S 66 o S South Pole
Ceiling of room Pivotal point of attachment Swinging pendulum Floor Ring of pegs
Swing Floor 0 2 Apparent change in pendulum direction 4 6 8 hours
Stick Pail Weight Stool
Wire 200 feet long Swing Steel ball 0 2 4 6 8 hours Floor
B A H C Star G D E F
Force of Gravity J F M A M J Month J A S O N D
Gravitational Attraction Distance
Star Distance = 1 Planet B Mass = 2
d
Date Data Table Hours of Daylight Altitude of the Sun at Noon ( ) January 21 9.5 32.3 February 21 10.8 40.1 March 21 12.0 47.3 April 21 13.7 55.1 May 21 14.8 62.5 June 21 15.3 70.4 July 21 14.8 63.3 August 21 13.7 55.5 September 21 12.1 47.7 October 21 10.8 39.9 November 21 9.5 32.1 December 21 9.0 24.4
City Panama City, Panama Mexico City, Mexico Tampa, Florida Memphis, Tennessee Winnipeg, Canada Churchill, Canada Fairbanks, Alaska Data Table Latitude ( N) Duration of Daylight (hr) 9 11.6 19 11.0 28 10.4 35 9.8 50 8.1 59 6.3 65 3.7
Intensity of Insolation Noontime Altitude of the Sun
Intensity of Insolation 0 90 Angle of Insolation
Latitude Day 1 Duration of Insolation (hours) Day 2 Duration of Insolation (hours) Day 3 Duration of Insolation (hours) 90 N 24 12 0 80 N 24 12 0 70 N 24 12 0 60 N 18 1 2 12 5 1 2 50 N 16 1 4 12 7 3 4 40 N 15 12 9 30 N 14 12 10 20 N 13 1 4 12 10 3 4 10 N 12 1 2 12 11 1 2 0 12 12 12
2d
90 Altitude of Sun ( ) 45 0 12 a.m. 6 a.m. noon 6 p.m. midnight Time on December 21
Sun s actual position z Sun s apparent path S Observer S
Sun s Sun s actual apparent position path z S Observer N
W Location A Mar 21 Sep 23 Jun 21 Dec 21 N E Observer S
Location C S S Observer Jun 21 S Mar 21 Sep 23 S
W Location B Jun 21 Mar 21 Sep 23 Dec 21 E N Observer S S
Pin 8 a.m. Noon 10 a.m. Pin shadows (Drawn to scale)
B N D A N Sun N N C
A D Sun C Earth B (Not drawn to scale)
N Earth at perihelion S Sun N S Earth at aphelion (Not drawn to scale)
Equator A North Pole Equator I I I D Sun I I I I North Pole I I North Pole North Pole C Equator B Equator (Not drawn to scale)
N Equator C N Day Arctic Circle Night B N Sun D Night Day N A
A E Equator B North Pole Arctic Circle Sun D C
C NP B NP A Sun NP D NP
C D Satellite Planet B A (Not drawn to scale)
Position D N Position A N S Sun N Position C S N S S Position B
D B A Sun C
A B H Equator C North Pole Arctic Circle Sun G D F E
D N A N Sun N N C B
A North Pole B North Pole Sun North Pole D North Pole C
Diagram I September 23 Shadow Vertical stick N Cardboard Shadow Vertical stick Diagram II December 21 N Cardboard Shadow Vertical stick Diagram III March 21 N Cardboard Shadow length = 10 cm Shadow length = 17.5 cm Shadow length = 10 cm
Length of Shadow Sunrise Noon Sunset
C B A D
Zenith Noon Sun West South July 21 Observer North East Horizon
Earth on May 1 90 N 45 N 30 N 15 75 N 60 N 30 45 60 Sun s rays 15 N 75 0 Equator 90 75 Night Day
N Sun s rays S
Sun s rays A North Pole Axis B Arctic Circle Tropic of Cancer Antarctic Circle South Pole Equator Tropic of Capricorn
Sept 10 Sept 19 Sept 30 Oct 8 Oct 25 Nov 20 Nov 25 Dec 9 Dec 21 Horizon
A B C Horizon Northeast East Southeast
Latitude 30 N 40 N 50 N 60 N Data Table Azimuths of Sunrise and Sunset sunrise 69 sunset 291 sunrise 66 sunset 294 sunrise 61 sunset 299 sunrise 51 sunset 309 Letter Code A B C D E F G H
Solar noon Solar noon Solar noon September 23 June 21 Sun s apparent path December 21 S W Observer N E
Polaris S E W Observer N
March 21 June 21 Dec 21 West Sunset South Observer North East Sunrise
Shadow Cast on March 21
Sun's apparent path Sun's present position Zenith Apparent position of Polaris South North
June March, September December N S
Sun directly overhead at noon South West Sun Path of Observer East North
Sun's present position Sun's apparent path Zenith Apparent position of Polaris South South
Sun's present position Zenith Apparent position of Polaris South Sun's apparent path North
Solar noon Polaris 50 60 70 80 90 80 70 60 50 40 Sun s path 40 30 30 20 West 20 10 10 South 0 Observer 0 North East
Sun's present position Zenith Apparent position of Polaris South Sun's apparent path North
Sun s apparent path Zenith 2 South 1 3 West 4 Observer North East
Sunrise Noon Sunset
Noon Sun N Observer E Dec 21 S W
W S N E
N Pole Sun s rays
S Pole Sun s rays
S Pole N Pole Sun s rays
N Pole Sun s rays S Pole
Horizon Sun South West
Equator Tropic North Pole Arctic Circle of Cancer
North Pole Sun s rays Equator
N Sun s rays S
B A Sun's direct rays C Equator D E Earth
160 140 120 100 80 60 40 20 0 20 40 60 80 100 120 140 160 180 66.5 N Equator A 66.5 S
North Pole 0 1 25 2 41 N 1 23 2 N 1 66 2 N A Night B Equator Day 43 Sun s rays 90 0 C Sun s apparent positions at noon 1 23 2 S D 1 66 2 S (Not drawn to scale) 1 232 47 South Pole