Lecture 5 Chapter 1. Topics for today. Phases of the Moon. Angular Measure and Parallax. Solar and Lunar Eclipses

Transcription

1 Lecture 5 Chapter 1 Topics for today Phases of the Moon Angular Measure and Parallax Solar and Lunar Eclipses

2 ! Day, year, seasons Our Calendar! How about months?

3 Phases of the Moon

4 Why do we see phases?! The Moon emits no light of its own! shines by reflecting light from the Sun! The half of the Moon phasing the Sun is always lit! We see a combination of lit and dark areas

5 Phases of the Moon! The Moon and Earth are tidally locked! Moon keeps the same side towards Earth at all times. Rotation period = Orbital period!"#$#%&'"()#*$+,"#$'(-).#/(-0#1)#('.&'#2('#/(-#3(#$+*$/"#"&&#4&'#2$5&# "#64&#7-"3#8&#"+(*+/#"%1))1)9#$'(-).#:;'(3$<)9#()#4&'#$=1">?#

6 Difference between solar (24 h) and sidereal (23 h 56 m) day

7 Synodic month = time from one new Moon to the next

8 Sidereal month = time for one full rotation with respect to the stars = 27.3 days Synodic month = time from one new Moon to the next = 29.5 days

9 Note: there is a problem with the previous diagram In reality, the radius of the Moon s orbit is 60 x that of the Earth s radius All places on Earth see almost the same new Moon

10 Full Moon

11 Phases of the Moon

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13 Note: We are viewing Earth from the North - orbital motion is anticlockwise Also: the radius of Earth is very small (1/60) compared with the radius of the Moon s orbit all places on Earth see almost the same phase of the Moon Motion of the Moon around Earth is anticlockwise We are looking at the North pole of Earth and the Sun is on the right of diagram

14 Waxing = getting bigger or brighter Phases of the Moon

15 Phases of the Moon

16 Note: Earth, Sun, and Moon do not lie on one line Phases of the Moon

17 Waning = getting smaller or dimmer Phases of the Moon

18 Is the orientation of the crescent correct? - no Phases of the Moon

19 Phases of the Moon

20 Remember Angular Sizes?!"#$%&'()*+,(-( 123)*0&%(4*+,(.*)/&"0,(

21 Angular Size! Angular size of an object depends on two things! The physical size of the object! The distance to the object!"#$%&'()*+,(-( 123)*0&%(4*+,(.*)/&"0,(

22 ! The Moon and the Sun, coincidentally, have nearly the same angular size

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24 More Precisely 1-1: Angular Measure Full circle contains 360 (degrees) Each degree contains 60! (arc-minutes) Each arc-minute contains 60!! (arc-seconds) Angular size of an object depends on its actual size and distance from viewer

25 Practical Measurements

26 !"#$%&'()*+,(-( 123)*0&%(4*+,( Text.*)/&"0,( A dime at a distance of one mile subtends an angle of one arc sec

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28 Distance AB Circumference = Parallax angle degrees

29 Parallax can be used to measure distances using trigonometry

30 1.6 The Measurement of Distance Parallax: Similar to triangulation, but look at apparent motion of object against distant background from two vantage points

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33 Measurement of Earth s radius (Eratosthanes) Baseline of 800 km Two observations at the same time but separated by 800 km

34 Distance AB Circumference = Parallax angle degrees 800 km = x Pi x Radius of Earth 360 R = 800 (km) x x 3.14 x 7.2 = 6370 km good to a few %

35 Eclipses! The Earth & Moon cast shadows.! When either passes through the other s shadow, we have an eclipse.! Why don t we have an eclipse every full & new Moon?

36 ! Moon s orbit tilted 5 to ecliptic plane! Crosses ecliptic plane only at the two nodes! Eclipse possible only when full/new occur near nodes

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42 The Moon Moves Over the Sun

43 The Sun is Nearly Covered

44 The Moon is not a perfect sphere The Diamond Ring

45 Total Solar Eclipse

46 Angular Size of Sun and Moon! The Sun and Moon have very different physical sizes! Radius of Sun is 7x10 5 km! Radius of Moon is 1.7x10 3 km (7x10 5 /1.7x10 3 ) = (7/1.7)x10 (5-3) = 4.1x10 2 ~ 400! Sun is ~ 400 times bigger than the Moon!!! How can they appear to be nearly the same size during an eclipse?

47 What is the ratio of the distances of the Moon and Sun from Earth? Sun distance = ^8 km = 150 million km Moon distance = 384,000 km Ratio = 390 Sun radius = 696,000 km Moon radius = 1738 km Ratio = 400

48 Small variations in distance due to eccentric orbits! Why does an annular eclipse look different? Question!"#$%&'()*+,(-( 123)*0&%(4*+,(.*)/&"0,(

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50 Moon more distant from Earth An Annular Solar Eclipse

51 Future total eclipses

52 Lunar Eclipse!!"#$%&'()*+&,*$-**.&$%*&/0.&".1&$%*& 2((.&!&2((.&'()*+&$%#(03%&$%*&!"#$%4+& +%"1(-&

53 The Lunar Eclipse! We see a total lunar eclipse when the Moon moves through the Earth s inner shadow (umbra)! We see a partial lunar eclipse when the Moon moves through the Earth s outer shadow (penumbra)! Where do you need to be to observer a Lunar eclipse?

54 The Lunar Eclipse! We see a total lunar eclipse when the Moon moves through the Earth s inner shadow (umbra)! We see a partial lunar eclipse when the Moon moves through the Earth s outer shadow (penumbra)! Lunar eclipses are visible anywhere on the night-time side of the Earth

55 Moon appears red during eclipse

56 A Lunar Eclipse

57 When & How Often?! Lunar eclipses occur at FULL Moon PHASE! Lunar eclipses do not occur every month because the Moon s orbital plane is tilted with respect to the ecliptic! Lunar eclipses occur 2-5 times per year while solar eclipses occur every ~ 1.5 year and are only visible from a very small region