The Four Seasons. A Warm Up Exercise. A Warm Up Exercise. A Warm Up Exercise. The Moon s Phases

The Four Seasons

A Warm Up Exercise

What fraction of the Moon’s surface is illuminated by the Sun (except during a lunar eclipse)?

a) Between zero and one-half b) The whole surface c) Always half

d) Depends on the lunar phase

e) Depends on the angle between the Earth, the Moon and the Sun.

A Warm Up Exercise

What fraction of the Moon’s surface is illuminated by the Sun (except during a lunar eclipse)?

a) Between zero and one-half b) The whole surface c) Always half

d) Depends on the lunar phase

e) Depends on the angle between the Earth, the Moon and the Sun.

The Moon’s Phases

Earth

This Way

A Warm Up Exercise

If the Earth did not rotate a) The Sun would rise once a year b) Stars would rise in the West c) Stars would rise in the East

d) We could see all parts of the Moon from the Earth

A Warm Up Exercise

If the Earth did not rotate

a) The Sun would rise once a year

b) Stars would rise in the West c) Stars would rise in the East

d) We could see all parts of the Moon from the Earth

A Warm Up Exercise

The synodic month is longer than the sidereal month because

a) Tides slow the Earth Down b) The Moon moves around the Earth c) The Earth moves around the Sun d) All of the above

A Warm Up Exercise

The synodic month is longer than the sidereal month because

a) Tides slow the Earth Down b) The Moon moves around the Earth c) The Earth moves around the Sun

d) All of the above

Key Ideas From Last Time:

•The Moon always keeps the same face towards the Earth.

–Rotation and Revolution are synchronous.

•Phases of the Moon:

–Fraction of the sunlit side visible to us.

•Sidereal & Synodic Periods:

–Sidereal Period: 27.3 days –Synodic Period: 29.5 days

Key Ideas:

•The Four Seasons

–Due to the tilt of the Earth’s axis relative to the plane of its orbit.

–NOT due to changes in the distance of the Earth from the Sun!

•The tilt of the Earth’s axis affects

Recall the Obliquity of the Ecliptic

•The Earth’s rotation axis is tilted relative to the plane of its orbit around the Sun:

– Tilted about 23.5º from perpendicular relative to the Ecliptic.

•The Earth’s axis points towards the same general direction in space as we orbit around the Sun:

– Currently points near Polaris.

– Changes slowly with time...

December

March

June

September The Seasons Are Due to the Tilt of the Earth

There are two (major) physical effects:

• It makes the length of the day vary – how long the Sun is up to warm the surface,

• It changes the angle between the ground and the sun, which changes the amount of sunlight per unit area

Length of the Day

•Vernal & Autumnal Equinoxes:

–Sun rises due East and sets due West.

–Day and Night are equal length (12 hours)

•Summer Solstice:

–Sun rises in the Northeast, sets in the Northwest –Day is longer than Night

•Winter Solstice:

–Sun rises in the Southeast, sets in the Southwest –Day is shorter than Night

Equinoxes

•In March & September:

–Axis is at right angles to the Earth-Sun line.

–The Sun is seen on the Celestial Equator.

–Day and Night are equal length (12 hours).

•March: Vernal Equinox

–Northern Spring & Southern Autumn.

•September: Autumnal Equinox

Equinoxes: March 20 & Sept. 22

Northern Spring/Fall

Southern Fall/Spring

Winter Solstice

•In December:

–The North pole tilts away from the Sun.

–The Sun is at its maximum southern declination

•Northern Winter:

–The Sun is low in the sky.

–The day is shorter than the night

•Southern Summer:

–The Sun is high in the sky.

–The day is longer than the night

December 21: Winter Solstice

Northern Winter

Southern Summer

Summer Solstice

•In June:

–The North pole tilts towards from the Sun.

–The Sun is at its maximum northern declination

•Northern Summer:

–The Sun is high in the sky.

–The day is longer than the night

•Southern Winter:

–The Sun is low in the sky.

–The day is shorter than the night

June 21: Summer Solstice

Northern Summer

Southern Winter

Just for fun…. An exciting math slide

This is the actual expression for the length of the day





daylight

cos 



 



•YOU DO NOT NEED TO KNOW THIS FOR ANY TEST!!!

•It depends only on your latitude and the Sun’s declination

•At an equinox the solar declination is zero and at the equator your latitude is zero, so

•At the summer solstice the solar declination is +23.5^o daylight in Columbus (latitude=+40^o) is 14.9 hours

•At the winter solstice the solar declination is 23.5^o daylight in Columbus (latitude=+40^o) is 9.1 hours

hours 12 daylight12hours daylight

The length of the day

Autumnul equinox

Vernal equinox Summer solstice

Winter Solstice

Columbus at latitude +40^o

Insolation

•If the Sun is up, what matters for solar heating is how directly the rays of the sun hit the ground:

•Sun directly overhead (at Zenith):

–Maximum concentration of sunlight.

–Get ~1000 Watts/meter² of heating.

•Sun 30º above the Horizon:

–Sunlight spreads out over 2 meter² –Get only 500 Watts/meter² of heating.

The Angle of the Sun At Noon

At noon, the angle between the Zenith and the Sun is (your latitude) – (declination of the Sun) = l

For Columbus (latitude l=40^o) this angle is:

•Either equinox (Sun at declination = 0^o ) it is at l=40^o

•Summer solstice (Sun at declination = +23.5^o) it is at l=16.5^o

•Winter solstice (Sun at declination = 23.5^o) it is at l=63.5^o

Equator and Celestial Equator N Pole

l=latitude

=Declination of Sun To the Sun l

Zenith

Parallel to equator

The angle alters the amount of solar radation we get per unit area

L 

If we send a fixed amount of stuff S between the two purple lines, then the amount hitting line L’ per unit length is

(amount of stuff)/(length of L’)=S/L’

The most you can get per unit length is S/L when the line is perpendicular to the direction the stuff is coming from – this corresponds to having the Sun at your zenith – away from zenith the same amount of Sunlight is spread over more area (larger L’)

L’

S

With Perspective

L L’>L

zenith

sun l=60^o

For Columbus at Noon

•Either equinox (sun at declination =0^o) it is l==40^o

(flux/flux if sun at zenith)=0.77

•Summer solstice (sun at declination =23.5^o) it is l=16.5^o (flux/flux if sun at zenith)=0.96

•Winter solstice (sun at declination = 23.5^o) it is l=63.5^o (flux/flux if sun at zenith)=0.45

Crudely, the solar flux (light per unit area) is about twice as high in summer compared to winter

29 . 0 9~ . 14 1 . 9 96 . 0 45 .

~0 summer in daylight

in winter daylight summer in flux

in winter flux summer~ in heating solar

in winter heating solar

This is all due to the 23.5^o tilt between the equator and the ecliptic.

L

sun

Rick Pogge

2000 Dec 21: Winter Solstice

2001 June 21: Summer Solstice

2001 Mar 20: Vernal Equinox

2001 Sept 22: Autumnal Equinox Winter

Summer

Summer

Winter

Spring

Autumn

Autumn

Spring

Seasons are not due to the shape of the Earth’s orbit!

The Earth-Sun Distance

•The Earth’s orbit is slightly elliptical:

•Aphelion (greatest distance):

–152.1 Million kilometers –Occurs in July (in 2004: on July 5)

•Perihelion (closest approach):

–147.1 Million kilometers

–Occurs in January (in 2004: on January 4)

•5 Million km difference makes only ~7% difference in the amount of solar radiation.

Summer vs. Winter in Columbus

•December 21 –Sun’s altitude at noon: 26.5º –Insolation: 450 W/m²

–Average temperature (1948-1996): 32º F –Length of the Day: 9^h

–Distance from the Sun: 147 Million km –Coldest Month: Jan (28º F average)

•June 21 –Sun’s altitude at noon: 73.5º –Insolation: 960 W/m²

–Average temperature (1948-1996): 70º F –Length of the Day: 15^h

–Distance from the Sun: 152 Million km –Hottest Month: July (74º F average)

Distance Doesn’t Matter

• The Earth is 5 Million kilometers closer to the Sun in January than in July, yet January is the coldest month in the North!

–7% more solar radiation in January than July

–Factor of 2 less insolation in the North in January than in July.

• Seasonal temperature variations have nothing to do with changes in the distance of the Earth from the Sun.

Seasons Cannot Be Due to Distance

One simple way to remember is that it is Summer in the Southern hemisphere when it is Winter in the Northern hemisphere

•Naturally explained by the tilt of the Earth relative to its orbit

If it was due to the variation in the distance from the Sun, then it should be the same season in both hemispheres – if it is Winter in the Northern hemisphere it has to be winter in the Southern hemisphere

Eclipses

The Moon’s orbit is tilted out of the ecliptic by 5^o So you also need to have the “line of nodes” pointing at the Sun

5 degrees at radius of Moon is about 32000 km

Radius of Moon 1700 km Radius of Earth 6300 km

Sun Moon Earth

Line of nodes aligned with Earth-Sun line – solar eclipse occurs

Line of nodes not aligned with Earth-Sun line – no eclipse occurs Line of nodes not aligned with Earth-Sun line – no eclipse occurs

NOT TO SCALE – WOULD NOT FIT ON PAGE!

Possibilities at a new Moon

Angle of up to 5 degrees

So you need a double coincidence

For a solar (lunar) eclipse you need a new (full) moon and the line of nodes pointing at the sun

You have a chance of an eclipse twice per eclipse year

What’s an eclipse year?

It’s the time between intervals when the line of nodes points at the Sun. If the line of nodes were fixed, it would be the same as

the normal year.

However, the line of nodes precesses westward with a period of 18.6 years (19^o/year), so you get an eclipse year of 346.6 days

Why is the eclipse year shorter than the sidereal year?

(the next few slides are only of interest if you want to dig a bit deeper )

Wait a minute!

Noon Not to Scale

The Earth rotates on its axis and the Moon orbits the Earth in the same sense that the Earth goes around the Sun but faster

This makes the solar day longer than the sidereal day and the synodic month longer than the sidereal month

no precession Line of nodes at start

Not to Scale

The line of nodes and the Earth’s axis both precess Westward, which is the reverse direction, but slowly compared to the year

This makes the solar year and the eclipse year shorter than the sidereal year

So for Westward precession

Line of nodes – precesses in 18.6 years (19^o/year), so you get an eclipse year of 346.6 days

19 degrees  about 19 days so the eclipse year is 365-19=346 days

Precession of Equinoxes – precesses in 26000 years (0.01^o/year) Which corresponds to 20 minutes of time – the sidereal year is 20

minutes longer than the solar year (equinox to equinox)

Eclipse Seasons

You get two chances of an eclipse each eclipse year, so there is an “eclipse season” every 173.3 days (half an eclipse year) because it doesn’t matter which “side” of the line of nodes you

use

It lasts about 37 days because of the relative sizes of the Sun, Earth and Moon

start

Half an eclipse year later

Line of nodes

One eclipse year later

Predicting Eclipses Is Hard, But….

An eclipse can occur

•when you have a new or full moon

•Once every synodic month=29.53 days

•the line of nodes points towards the sun

•Twice every eclipse year=346.62 days

Once you have had one, you will have almost the same geometry after:

223(synodic months) = 6585.32 days 19(eclipse years) = 6585.78 days

So every 18 years, 11 days and 8 hours, the Sun, Moon and Earth return to an almost (but not quite) identical configuration – there is a good chance of another eclipse on the Earth, but at a DIFFERENT location

The Geometry of Eclipses

The finite size of the sun leads to a shadow composed of two parts

•The umbra where the shadowing is complete, and

•The penumbra where parts of the sun are still visible

Lunar Eclipses

The umbra and penumbra created by the Earth are larger than the moon

•Angular diameter of the Earth as seen from the Moon= 2R/D_M=1.90^o

•Angular diameter of the Sun as seen from the Moon = 2R_/D_=0.53^o

•Diameter of Earth’s umbra at the moon 

DM(angular diameter of earthangular diameter of sun)  9200 km

•Diameter of Earth’s penumbra at the moon 

D_M(angular diameter of +angular diameter of sun)  16000 km

•Compared to the 3500km diameter of the moon umbra

penumbra

total partial penumbral moon

Lunar Eclipses –pictures 1

Lunar eclipses are more common than solar eclipses because the Earth casts a bigger shadow than the Moon – penumbral lunar eclipses are easy to miss since all you see is a dimming of an otherwise full moon.

Full eclipse

(Freedman & Kaufmann)

The red color at full eclipse is due to the refraction of sunlight by the Earth’s atmosphere

Lunar Eclipses –pictures 2

Lunar Eclipses –pictures 3 Lunar Eclipses – last

In real life, it takes the moon 2.5 hours to cross the full width of the umbra

Solar Eclipses

The umbra and penumbra created by the Moon are much smaller than the Earth

• Angular diameter of the Moon = 2R_M/ D_M=0.52^o ranges from 0.49^o to 0.55^o because of the ellipticity of the Moon’s orbit

• Angular diameter of the sun = 2R/D=0.53^o

• Diameter of Moon’s umbra at the Earth 

D_M(angular diameter of moonangular diameter of sun)  0 to 150 km

• Diameter of Moon’s penumbra at the Earth 

D_M(angular diameter of moon+angular diameter of sun)  7100 km

• Compared to the 13000km diameter of the earth

umbra penumbra

Earth

Solar Eclipse From Space

1999 from the Russian space station Mir

Animation of April 8 2024 Eclipse (Rick Pogge)

The Umbra

Total Solar Eclipse – Moon Near Pericenter (umbra exists)

Totality never lasts more than 7 ½ minutes….

Annular Solar Eclipse – Moon Near Apocenter (no umbra)

O. Staiger

Partial Eclipse – in the penumbra

Solar Corona

Total Solar Eclipse Paths

Annular Solar Eclipse Paths