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 A Warm Up Exercise Earth This Way 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 1
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 The Four Seasons Key Ideas: 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 The amount of direct sunlight (Insolation) The length of the day 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... 2
September The Seasons Are Due to the Tilt of the Earth June 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 December March 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 Northern Autumn & Southern Spring. 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 3
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 tan 24hours solar declination tan(your latitude) 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 daylight 12 hours daylight 12 hours 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 The length of the day Columbus at latitude +40 o Autumnul equinox Summer solstice Vernal equinox Winter Solstice 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/meter 2 of heating. Sun 30º above the Horizon: Sunlight spreads out over 2 meter 2 Get only 500 Watts/meter 2 of heating. 4
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 N Pole Zenith l l=latitude To the Sun =Declination of Sun Parallel to equator Equator and Celestial Equator The angle alters the amount of solar radation we get per unit area S 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 L With Perspective For Columbus at Noon Either equinox (sun at declination =0 o ) it is l = =40 o (flux/flux if sun at zenith)=0.77 zenith l =60 o sun 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 solar heating in winter flux in winter ~ solar heating in summer flux in summer daylight in winter daylight in summer 0.45 ~ 0.96 9.1 14.9 ~ 0.29 L L >L This is all due to the 23.5 o tilt between the equator and the ecliptic. 2000 Dec 21: Winter Solstice 2001 Mar 20: Vernal Equinox Winter Spring Summer Autumn sun 2001 June 21: Summer Solstice 2001 Sept 22: Autumnal Equinox Summer Autumn Winter Spring Rick Pogge L 5
The Earth-Sun Distance Seasons are not due to the shape of the Earth s orbit! 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 June 21 Sun s altitude at noon: 73.5º Insolation: 960 W/m 2 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) December 21 Sun s altitude at noon: 26.5º Insolation: 450 W/m 2 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) 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 Eclipses 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 6
The Moon s orbit is tilted out of the ecliptic by 5 o Possibilities at a new Moon 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 Line of nodes aligned with Earth-Sun line solar eclipse occurs Angle of up to 5 degrees Line of nodes not aligned with Earth-Sun line no eclipse occurs Line of nodes not aligned with Earth-Sun line no eclipse occurs Sun Moon Earth NOT TO SCALE WOULD NOT FIT ON PAGE! 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 Wait a minute! Why is the eclipse year shorter than the sidereal year? 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 (the next few slides are only of interest if you want to dig a bit deeper ) Noon Not to Scale 7
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 Line of nodes at start 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) Not to Scale no precession 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 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 Line of nodes Half an eclipse year later 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 D M (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 moon total partial penumbral 8
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. Lunar Eclipses pictures 2 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 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 penumbra umbra Earth 9
Solar Eclipse From Space Animation of April 8 2024 Eclipse (Rick Pogge) Total Solar Eclipse Moon Near Pericenter (umbra exists) 1999 from the Russian space station Mir The Umbra Totality never lasts more than 7 ½ minutes. Annular Solar Eclipse Moon Near Apocenter (no umbra) Partial Eclipse in the penumbra O. Staiger Solar Corona Total Solar Eclipse Paths 10
Annular Solar Eclipse Paths 11