AnnouncementsLast math review, tonight 4-4:45pm,

room 230

When did the sun rise this morning?From what direction did the sun rise?

yesterday

N S

E

W

When did the sun rise this morning?From what direction did the sun rise?

7:15 am113˚

• • 76.7˚76.7˚80.7˚•80.7˚•

How much later (in min.) does the sun rise in Blacksburg than Williamsburg?

Longitude difference = 4˚Longitude difference = 4˚

Recall 15˚ longitude per hourRecall 15˚ longitude per hour

4˚/15˚ per hour = 0.267 hrs =4˚/15˚ per hour = 0.267 hrs =

0.267 hrs x 60 min./hour =0.267 hrs x 60 min./hour =

16 minutes 16 minutes

N S

E

W

What path does the sun take?

N S

E

W

Local NoonFor mid-latitudes in northern hemisphere sun is directly to the SOUTH

At local noon the sun is at its highest angle of the day above the horizon

That angle is a function of the time of year and your latitude.

@ 40˚ N

@ 40˚ N

@ 40˚ N

@ 40˚ N

Inclination• tilt of the Earth’s axis• with respect to a line

perpendicular to the plane of the ecliptic

• amount of tilt affects day length and angle of sunlight, also determines declination during solstices

23.5°

Solstices and Equinoxes

June 21st

Sept 22nd

Dec 21st

Mar 21st

Earth’s position during the year: top view

March 21 June 21

Sept 22Dec 21

Angle of sunlight during the year: side view

Arctic/Antarctic CircleTropic of Cancer/Capricorn

23.5 o S

66.5 o S

66.5 o N23.5 o N

Seasons

Why is there a summer season?

A. Summer occurs when the distance between the earth and the sun is closest

B. Summer occurs when the earth’s rotational axis is tilted towards the sun, lengthening the days

C. Summer occurs because the tilt of the earth’s axis makes it closer to the sun

D. Summer occurs when the sun is higher overhead, so the rays strike the Earth more directly

Seasons: the logic

Summer

longer days

more direct sunlight

more energy

warmer temperatures

Winter

shorter days

less direct sunlight

less energy

colder temperatures

March 21 June 21

Sept 22Dec 21

How does a tilt make days longer or shorter?

1. Day lengthLongitude

SummerSolstice

WinterSolstice

AutumnEquinox

SpringEquinox

WinterSolstice

1. Day lengthLongitude

SummerSolstice

WinterSolstice

AutumnEquinox

SpringEquinox

WinterSolstice

• How long is the longest day of the year (@40o)?

1. Day lengthLongitude

SummerSolstice

WinterSolstice

AutumnEquinox

SpringEquinox

WinterSolstice

• When are the days getting shorter the fastest?

2. Sun angle: declination

• Declination: The latitude for which the sun is directly overhead at noon.

Seasons activity1. Divide into groups of 4

2. Assign each member of your group a date

- March 21, June 21, Sept 22, Dec 21

3. Answer following for your date

- How is the Earth tilted relative to the Sun?

- What is the declination?

- How many hours of daylight at NP, Eq, and SP?

4. Extra challenge: How would the seasons change if the tilt of the Earth was 0°?

2. Sun angle: declination curves

• graph of declination throughout year

• x-axis: months of the year

• y-axis: declination (90°S to 90°N)

-90

-60

-30

0

30

60

90

Dec

lin

atio

n

Ma

r21

Jun

21

Se

p2

3 De

c21

? m2

2. Sun Angle: Insolation• Watts per square meter (W/m2)

1 Watt

1 m2

1 Watt

X

2. Sun Angle

XX

Y Y

Y

X’

X’= X/sinƟ

Ɵ

sinƟ=X/X’

2. Sun Angle: insolation curves

2. Sun Angle: insolation curves

WinterWinter

SummerSummer

Autum

n

Autum

nSpr

ing

Spr

ing

WinterWinter

@ 40˚ N

@ 40˚ N

@ 40˚ N

@ 40˚ N