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Unformatted text preview: 12/24/11 Astronom Notes 2 - Motions of the Sun and the Moon Motion of the Sun
What's cove re d he re :
How does the Sun appear to move over the course of a year?
What defines the seasons?
What causes the seasons?
What is really going on - does the Earth move or does the Sun move?
What is the zodiac, and does it help you predict the future? (NO!!!!)
What are the phases of the Moon?
What causes tides?
What are eclipses?
Once people figured out how the stars moved - or thought they did - they could turn their attention to the next object - the Sun.
Unfortunately, its motion isn't easy to understand. The Sun's path varies over the course of the year. Sometimes it rises in the
northeast, and sometimes it rises in the southeast. Only on two days does it rise directly in the East and set directly in the West.
These special dates are known as the Equino e s . To give you their full names, they are the Ve rnal Equino , which is around
March 21, and the Autumnal Equino , which is around September 21. You may recognize these dates as the beginnings of
the seasons of Spring and Autumn. These dates - the Equinoxes - have nothing to do with the weather; they have to do with the
location of the Sun relative to the Celestial Equator.
Now for the rest of the year, the Sun's path and its rising and setting locations vary. As seen from Iowa, during the winter the
Sun rises in the southeast and sets in the southwest. In the summer it rises in the northeast and sets in the northwest. There are
two days when the rising and setting locations are at their most extreme (furthest north or furthest south). These days are also
the dates that the Sun travels a path that is also an extreme - very long and high above the horizon or very short and low to the
horizon. These are the days known as the Winte r Sols tice , which occurs around December 21 (shortest day), while the other
is called, oddly enough, the Summe r Sols tice , and it occurs around June 21. Of course, you know these days as the beginning
of Winter and Summer. Like the dates of Equinoxes, they have really nothing to do with the weather, but with the position of
the Sun relative to the Celestial Equator.
One thing you have to remember about the Sun is that it makes it very difficult to see anything else in the sky when it is out even though the stars and planets are out there, the brightness of the Sun is so overwhelming that you don't have much of a
chance of see them until the Sun sets. Which stars would be visible? Which constellations would be visible if we could turn off
the Sun? That depends upon what time of the year you look. If you were to turn the Sun down so that you could see the stars
at the same time that you could see the Sun, you would notice that the Sun appears to move slowly toward the East from one
day to the next - it moves about 1 each day. In about a month it has moved 30 to the East relative to the stars; in four months,
it will be about 120 east of where it started; and after one year, it will have gone about 360 . That means it is back where it
started from, since there are 360 in a circle! This also explains why we see different constellations in different seasons. As the
Sun moves slowly in front of various constellations, those constellations are no longer visible since they are too close to the Sun,
but constellations far from them are visible, since they will be visible when the Sun has set or before it rises. Since the Sun
appears to move relative to these stars, it will gradually cover up other stars, and other stars that were previously not visible will
again be viewable as the Sun gets further away from them.
Actually, the folks in the old days could figure out where the Sun would be relative to the stars by looking at the stars which
were visible when the Sun set. They knew which constellations the Sun covered up and when they were covered up (which
time of the year they were or were not visible). If you were to map out the path of the Sun relative to the stars, you would see it
as a curved line on the Celestial Sphere. Take a look at Figure 1 to see the path relative to the Celestial Equator. This image is
of a flattened out Celestial Sphere, and the dates mark the locations of the Sun relative to the stars over the course of the year. www.uni.edu/morgans/astro/course/Notes/section1/new2.html 1/12 12/24/11 Astronom Notes 2 - Motions of the Sun and the Moon Fi g re 1. The a h f he S , he ec i ic, h
The ca i
f he S
he e i e a d eai e
he bac g
d a a d he Ce e ia E a (dec=0).
ice i i dica ed. S e dec i a i
a e a e a i dica ed. As is apparent, the path of the Sun is curved relative to the Celestial Equator. There are times during the year when it is north of
the Celestial Equator and other times when it is south of it. The declination of the Sun varies throughout the year. (Of course, its
R. A. changes as well, becoming slowly larger each day as the Sun moves eastward relative to the stars, but we'll pay more
attention to the declination). On the days of the Equinoxes, the Sun is right on the Celestial Equator, so it has a declination of 0 ,
and on the Solstices, it has the most extreme value for its declination, 23.5 N on the date of the Summer Solstice and 23.5 S
on the Winter Solstice. The Solstice dates mark when the Sun is at its greatest distance from the Celestial Equator.
The path the Sun appears to make amongst the stars is known as the e clip ic. Just like the Celestial Equator, it would make a
large circle on the Celestial Sphere. In fact the ecliptic is a big circle that is tilted 23.5 relative to the circle made by the
Celestial equator. This is shown in Figure 2.
Fi g re 2. The ca i f he Ec i ic he Ce e ia S he e. Why is it like this? Why does the Sun travel on its own unusual path? Here is where I
get to shatter all of your delusions - there is no Santa Claus! Oh, wait, that wasn't the
delusion I was supposed to shatter. No, the concept I get to confuse you with is
concerning all these motions I have described so far.
The stars do no move across the sky in approximately 24 hours.
The Sun does no move across the sky in approximately 24 hours.
The Sun does no travel amongst the stars and moves slowly eastward each
If they aren't moving, what is? WE ARE! Almost all the motions of the sky are due
to motions of the Earth. The main motion is the ro a ion of the Earth. We spin
around once in approximately 24 hours - that is why we see the stars and Sun appear
to move in about 24 hours. What about the Sun moving eastward relative to the stars over the course of the year? Again, we
are doing it - we are moving around the Sun, and it takes one year for us to get back to where we started. This motion results
in our seeing the Sun in front of stars of different constellations over the course of the year. Figure 3 illustrates this concept. I'm
not saying that nothing in the Universe moves except for the Earth - it's just that the Earth's motion is so large, so close, and so
obvious to our senses that it has the greatest influence on how we see the sky. As you'll see, practically everything in the
Universe moves. www.uni.edu/morgans/astro/course/Notes/section1/new2.html 2/12 12/24/11 Astronom Notes 2 - Motions of the Sun and the Moon Fi g re 3. The apparent mot ion of t he Sun amongst
t he st ars is due t o t he mot ion of t he Eart h around
t he Sun and our changing v iewpoint . The st ars t hat
we would see behind t he Sun in Januar would be
dif f erent f rom t he st ars we would see behind t he
Sun in Februar , March, and ev er ot her mont h,
since we are changing t he locat ion f rom which we
v iew t he Sun.
If our motion about the Sun makes it look like the Sun is in front of different stars over the course of the year, why is the
apparent path of the Sun, the ecliptic, tilted relative to the Celestial Equator? Again, our bad - we're the ones that are tilted. If
you hold your head to the side and walk around all day like that, and if you don't know you have your head tilted, you might
think that the entire world is at an angle.
Since the Earth is tilted, there are times when the tilt has the Sun located north of the Celestial Equator and other times when the
Sun is located south of the Celestial Equator. If the Earth were not tilted then the Sun would be always located on the Celestial
Equator - which would be pretty boring. The angle of the tilt, 23.5 , is an important number (remember seeing it in values for
the Sun's declination?). Just stay tuned, you'll see it again.
The Earth is tilted over; is that such a big deal? You're darn right it is, because without this tilt, there would be no seasons. As
the Earth goes around the Sun, the tilt of the Earth causes different parts of the Earth to receive different amounts of sunlight.
During the months of May, June and July, the northern hemisphere of the Earth is tilted more toward the Earth than the southern
hemisphere. That gives the northern hemisphere a greater amount of heat and results in higher temperatures and more sunburns.
The opposite is true during November, December and January, when the Northern hemisphere is tilted away from the Sun.
Check out Figure 4 to see the situation.
Fi g re 4. The t ilt of t he Eart h and it s mot ion around t he Sun mak e it
appear as if t he Sun is going f urt her t o t he nort h (nort h of t he Celest ial
Equat or) or sout h (sout h of t he Celest ial Equat or) ov er t he course of a
Here is an animated image showing how the surface of the Earth gets
different amounts of sunlight depending upon the time of year and the latitude. Each image is taken about one week apart at the
same time of day, and since the curved surface of the Earth is flattened down in the image the lighting pattern is rather strangely
shaped. You should pay careful attention to the date of each image and how some parts of the Earth are in total darkness some
times during the course of the year (the polar regions). If you want to see how the sunlight falls on the surface of the Earth over
the course of a single day, just click here. In this case, the images are about one hour apart.
On the Summer and the Winter Solstice (around June 21 and December 21 respectively), the Sun reaches its most northern
and southern declinations. People who live at a latitude of 23.5 north and south of the equator will have the Sun at their zenith
at noon only on that day of the year (June 21 or December 21 depending upon whether they live at 23.5 north or south). You
may have noticed these latitudes marked on maps because of their special relation to the Sun - these are the T opic . They are
the T opic of Cap ico n, located at 23.5 S, when the Sun is at the zenith on about December 21, and the T opic of Cance ,
found at a latitude of 23.5 N, where the Sun is found at the zenith on about June 21.
These two lines also limit the locations where the Sun is visible at the zenith. Only between the latitudes of 23.5 N and 23.5 S
would you ever have the Sun directly overhead. Since the declination system is an extension of the latitude system, the Sun's
declination can only have values within that range as well, between 23.5 N and 23.5 S.
Here is an animation of the Sun relative to the stars. Each image is seven days apart so that you are seeing how far the Sun
moves in a week's time relative to the stars. You'll see that it moves toward the left (East), and sometimes it goes further to the
south and sometimes it goes further to the north. These are the stars and constellations that the Sun would appear to be in front
of at some time during the year, if we could see the stars located behind the Sun in the daytime. You may notice that many of
www.uni.edu/morgans/astro/course/Notes/section1/new2.html 3/12 12/24/11 Astronom Notes 2 - Motions of the Sun and the Moon ;
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The tilt of the Earth doesn't change much (currently at 23.5 ), but the direction that the pole points changes. The North pole
star (Polaris) will not be there all the time - in a few hundred years the current north star will be just another star in the northern
sky, since it will not be located at the North Celestial Pole. In the past, other stars would have been called the Pole star, since
they were closer to the North Celestial Pole than Polaris was. During your life time, Polaris will be the North Star, since the
wobbling is pretty slow. One precession takes about 26,000 years. Figure 5 shows a simplified view of the precession of the
Fi g re 5. The direct ion t hat t he Eart h's pole point s changes slowl so t hat in t he f ar
f ut ure it will be point ing t o st ars such as Alderamin, Vega, Thuban, and ev ent uall
again Polaris. Length of a Da - Solar vers us Sidereal
How long does it take the Earth to spin around exactly once? We could figure that out by
timing how long it takes something in the sky to get back to its original position from one
day to the next. If we time the motion of the Sun, we see that it takes almost exactly 24 hours for the Sun to get back to where
it started from one day to the next. I guess that answers it, right? Before we jump the gun, let's time another object - a bright
star, for example. How long does it take a star to get back to the same place in the sky from one day to the next? Does it take
24 hours for one complete rotation? No it doesn't. It takes 23 hours and 56 minutes. Big deal; that's almost 24 hours; there is
only a four minute difference; does it really matter? You bet your banana skin it matters!The basic upshot is stars rise or set four
minutes earlier each day. If a star rises tonight at 8 P.M., it will rise at 7:56 the next night, then 7:52 the night after, and then
7:48 the next night. A week after the first rise time, it will rise 4 x 7 = 28 minutes earlier (7:32). In one week, a star will be rising
about half an hour earlier - that's a pretty big difference, so don't ignore those four minutes.
Why is there a four minute difference? Which of these values tells us what the rotation period of the Earth is? Remember, it is
the spinning of the Earth that causes the observed motions of the Sun and the stars over the course of the day (or night) - but
there are two different time spans here - which one corresponds to the rotation period of the Earth?
Believe it or not, it is the stars, not the Sun, that determine the amount of time for one rotation of the Earth. While all clocks on
the Earth are based on the 24 hour time scale of the Solar Da , it is the more subtle Side re al Da (or "star" day) that tells us
how fast the Earth is spinning. It takes the Earth 23 hours and 56 minutes to complete one rotation.
Why is there a difference between a Solar day and a Sidereal day? The cause is the motion of the Earth, in this case our orbital
motion around the Sun. To illustrate what's going on, follow the stick in Figure 6. It starts out one day pointing directly at the
Sun (at noon) and at a very distant star (a star way off to the right).
Fi g re 6. The t ime it t ak es f or a posit ion on t he Eart h t o line up wit h a dist ant st ar (wa of f t o
t he right ) is 23 hours and 56 minut es. Howev er, t he Sun will not be lined up wit h t he posit ion
on t he Eart h, and an addit ional f our minut es are needed.
After 23 hours and 56 minutes, the Earth will have not only made one complete rotation, but will have
also moved in its orbit. The stick will no longer be pointing toward the Sun, but it will again be pointing toward the star - this
tells us that the Earth has made exactly (no more, no less) one rotation. The time on our watches is 11:56 AM - NOT NOON!
- since it is 23 hours and 56 minutes from the previous day. If you want to see the stick pointing again at the Sun, you must wait
four more minutes for the Earth to spin a little bit further around. When that happens, the time will again be noon.
You might be a bit amazed at how I was able to easily draw up the motions of the Earth and such so quickly, but how did I
know which way it was going? There is a rule about how things in the solar system move and you can use it to draw similar
diagrams. All major motions in the solar system are in a COUNTER-CLOCK WISE direction when observed from above
the North Pole. This includes the motions associated with the Earth, the Moon, the orbital motions of the planets, and most of
www.uni.edu/morgans/astro/course/Notes/section1/new2.html 5/12 12/24/11 Astronom Notes 2 - Motions of the Sun and the Moon their rotation motions as well. There are of course some exceptions, but they aren't that common. If you have to quickly draw
any solar system motions, you'll know which way the stuff is moving - again, there are a few exceptions and I'll tell you what
they are if necessary. The M
After figuring out how the stars and the Sun move, it is time to tackle the next object - the Moon. The motion of the Moon is
more complex; it doesn't follow exactly the ecliptic or the celestial equator, but does make a path around the Earth that is
similar to each of those paths. What sets the Moon apart from the other objects is the fact that its appearance changes - it goes
through phases. The phases of the Moon take 29.5 days to go through an entire cycle.
The phases occur in a very predictable sequence. Here is the order of the phases - New (when you can't see
the Moon - it's all dark), Waxing Crescent, First Quarter (when you see the right half lit), Waxing Gibbous,
Full (when you see the entire lit surface), Waning Gibbous, Third Quarter - also called Last Quarter (when
you see the left side lit up), Waning Crescent, and back to where we started, New. A picture of the phases is
shown in Figure 7. It takes about one week to go from one major phase to the next - by major phase I mean
New, the Quarters and Full. If the Moon is New today, it will be a First Quarter Moon in about one week, and a full Moon
two weeks from today. The fact that it takes about 29.5 days to go through the cycle is the reason there are about 30 days in a
month, since many ancient societies used the Moon as a time keeper. Fi g re 7. The phases of t he Moon as seen f rom Iowa when t he Moon is high in t he sk (on our meridian).
What causes the phases? To figure that out, you need to look at the interaction of the light source (Sun) and the alignment of the
Moon with the Earth. The Moon will have a certain phase depending upon two things 1. The location of the Moon in its orbit about the Earth
2. The location of the Sun relative to the Earth and the Moon at that time
Don't forget about these two things.
The Quarter Moons occur when the Sun and the Moon are 90 degrees apart in the sky as viewed from the Earth. The New
and Full phases occur during times when the Earth, Moon and Sun are in a straight line. Figure 8 is a composite of the various
phases and the location of the Moon in the sky. Remember, it takes about a week for the Moon to go from one major phase to
the next, so that the view you see during one evening isn't too much different from the view you see the next night. You may
have seen the Moon when it is close to the Full phase and it may appear to you to be Full for several days, while technically it is
only Full at the time it is in a line with the Earth and the Sun. Also, the way that the Moon is illuminated gives us the view we see
- when most of the lit surface is turned away from the Earth, we see only a small crescent; when most of the surface is turned
toward the Earth, we see the gibbous phase Moon.
Here is a little java program showing just one phase at a time. You can see how the Moon looks to you in the sky depending
upon where it is located in its orbit about the Earth. www.uni.edu/morgans/astro/course/Notes/section1/new2.html 6/12 12/24/11 Astronom Notes 2 - Motions of the Sun and the Moon Fi g re 8. The phases of t he Moon shown at t heir
locat ions relat iv e t o t he posit ion of t he Eart h and
t he Sun (of f t o t he right ). The phase of t he Moon is
det ermined b it s locat ion relat iv e t o t he Eart h and
Sun. The right side of t he Moon is t he onl part t hat
is illuminat ed, since t he Sun is of f t o t he right . The
phase t hat we see depends upon how much of t hat
side of t he Moon is v isible f rom t he Eart h, which
depends upon where t he Moon is in it s orbit about
t he Eart h.
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when it is high ov erhead (6 P.M.).
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M 50 , M , ' . Fi g re 10. The Moon mak es one complet e orbit of t he Eart h in 27.3
da s, but it will not be again Full unt il a t ot al of 29.5 da s has passed.
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same amount of t ime it t ak es t o mak e one rot at ion. If it
didn't rot at e, we'd hav e t he sit uat ion on t he lef t , where
dif f erent sides of t he Moon would be v isible f rom t he Eart h
as it goes around t he Eart h. One side of t he Moon is
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12. F E , Fi g re 12. The Moon's pull on t he wat er and t he Eart h produces bulges on t he t wo sides of t he Eart h. The degree of
t he pull is shown b t he arrows, wit h t he side nearer t he Moon hav ing t he largest pull, and t he side f urt her hav ing t he
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9/12 12/24/11 Astronom Notes 2 - Motions of the Sun and the Moon Fi g re 13. The il of he Moon' o bi mean ha mo of he ime i i n' lined p f o an eclip e o occ .
I he Moon en i el da k d ing a l na eclip e? No, o can ill ee i , ho gh i i dimmed and of en colo ed. Wh ? The
Ea h ha an a mo phe e hich end o bend ligh a o nd he Ea h, and hi fall pon he Moon. The ligh doe ge
di colo ed, ho gh; of en a ed, o ange o b o n colo i een. Thi eall ca ed he heck o of folk in he old da
he didn' kno
ha a going on, hich a mo of he ime.
Fi g re 14. A m l iple e po e image of a l na eclip e. When he eclip e f i
a o he b igh ne of he Moon i
o g ea ha onl ho e po e a e ed. The mb a, hich i he da k e pa of he hado , doe n' appea o
ha e an colo in he e image . Onl a mid-eclip e i he Moon da k ened eno gh o ha he colo of he mb a i
i ible. Eclip e pho og aph cop igh 2000 b F ed E penak co e of
.M Eclip e.com.
The e a e o egion of he hado , he umbra and pe numbra. The e co e pond o he da ke pa of he hado and he
no comple el da k pa e pec i el . The e a e ho n in Fig e 15. If o e e on he Moon, and looked back o a d he
Ea h (and he S n), o o ld ee he S n blocked o if o e e in he mb a, hile if o e e in he pen mb a, ome pa
of he S n'
face o ld ill be i ible o o .
Fi g re 15. The hado , mb a and pen mb a, ca b he Ea h d ing a l na eclip e. The Moon i e pe iencing a
o al l na eclip e he e ince i i in he mb a - he da k e hado .
L na eclip e can be full - he Moon pa e comple el h o gh he Ea h' mb al hado , partial - i pa e onl h o gh
pa of he mb al hado , o pe numbral - i onl pa e h o gh he pen mb a. The be a e of co e he f ll eclip e , hich
can la fo ho a he Moon a e e he en i e leng h of he mb al hado , hile he lea e ci ing a e he pen mb al
eclip e , hich a e eall diffic l o ee ince he nligh ha fall on he Moon'
face i o b igh o begin i h. He e i a
able of l na eclip e ha ill be occ ing o e he ne fe ea - ome of hich a e i ible f om Io a. He e i an anima ion
ho ing ho he Decembe 2010 l na eclip e ill look f om Io a. The loca ion of he mb a and pen mb a hado a e
indica ed. The loca ion of he Ea h' hado appea o a ligh l in he anima ion, ince he Ea h i mo ing a ell a he
Fi g re 16. The hado , mb a and pen mb a, ca b he Ea h d ing a l na eclip e a e een a ci cle he e. The
ha he Ea h ca look lik e ci cle , ince i i a phe e. The Moon' pa h i ho n f o he h ee dif f e en
pe of l na eclip e . The op pa h i f o a pen mb al eclip e, he e he Moon ne e pa e in o he mb a, b i
onl in he pen mb al hado . The cen al pa h ho a o al l na eclip e, he e he Moon pa e en i el h o gh
he mb al hado . The bo om pa h i f o a pa ial eclip e, he e onl a pa of he Moon' hado goe in o he
mb a. I i po ible o ha e pa ial pen mb al eclip e , b ho e a e o lame he a en' o h men ioning.
While no a pec ac la a ola eclip e , l na eclip e a e ill a he nea o ee - ho gh he a e be ie ed hen he e
a e no clo d in he k . The e a e all abo 2 l na eclip e each ea , ho gh he a e no al a i ible f om he US. To
ee he eclip e o ha e o ee he Moon a he ime of he eclip e, o man people can ee one. Of co e i i po ible o
p edic he da e and ime of eclip e . The ne "good" l na eclip e i ible f om he US ill occ on he nigh of Decembe
M ch mo e pec ac la a e ola eclip e . The e occ onl hen he Moon i Ne and loca ed on he eclip ic (i i on he
node). J b chance he Moon and he S n ha e abo he ame ang la i e - he a e bo h abo 1/2 deg ee in i e. The
i e of he hado - he mb a - i e mall, beca e he Moon can onl j ba el co e p he S n. Thi i ill a ed in
Fig e 17.
Fi g re 17. The hado ca b he Moon d ing a Sola eclip e. Onl a he poin on he Ea h he e he mb a
eache he f ace o ld o e pe ience a o al ola eclip e.
To e pe ience a total s olar e clips e , o m be loca ed in he na o mb al pa h of da kne . Thi i of en efe ed o a
he path of totalit . I i o na o (a mo onl abo 300 km ide), and he mo ion of he S n, Moon and Ea h a e a he
fa , ha o ill onl e pe ience a mo abo e en min e of o ali . D ing he momen befo e he o al eclip e, a io
www.uni.edu/morgans/astro/course/Notes/section1/new2.html 10/12 12/24/11 Astronom Notes 2 - Motions of the Sun and the Moon ; diamond ing e ffe c ,
, S, . Fi g re 18. The diamond ring ef f ect . Onl a f ract ion of t he surf ace of t he Sun is v isible here, but it is enough t o cast a
bright light t hrough t he v alle s along t he edge of t he Moon. Eclipse phot ograph cop right 2001 b Fred Espenak
court es of www.MrEclipse.com.
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Fi g re 19. Eclipse glasses, wit h special f ilt ers, are t he best wa t o v iew an eclipse saf el .
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Fi g re 20. A series of images showing a t ot al solar eclipse. The images are combined t oget her t o show t he eclipse in
dif f erent st ages, wit h t ot alit occurring in t he middle image. Eclipse phot ograph cop right 2001 b Fred Espenak
court es of www.MrEclipse.com.
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11/12 12/24/11 Astronom Notes 2 - Motions of the Sun and the Moon Ec i e a e a
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Fi g re 21. Pa h of o al ola eclip e a e ho n (on lef ) and ann la eclip e (on he igh ). If o click on he
image o 'll ee a la ge e ion of he map. Fo he o al eclip e map , an ob e e o ld ha e o be loca ed in he
da k pa h o e pe ience a o al ola eclip e. To ee he S n "
o nd" he Moon d ing an ann la eclip e, and
ob e e o ld ha e o be loca ed along he pa h ho n in he map on he igh. Eclip e map co e of F ed
E penak - NASA/Godda d Space Fligh Cen e . Fo mo e inf o ma ion on ola and l na eclip e , ee F ed E penak '
Eclip e Home Page: h p:// nea h.g f c.na a.go /eclip e/eclip e.h ml Now that ou've re ad this s e ction, ou s hould be able to ans we r the s e que s tions ....
O he Ve a E i
a ), ha i he dec i a i
f he S ? Whe e
he Ea h
ha e be ca ed ha e i a
e i h?
H d e he S
e e a i e he a ?
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Wh d e he S a ea
e e a i e he a ?
Wha ca e he ea
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Wha i he e e ce f ha e , he
d he be i ib e, i i g, e i g, a d h d e i cha ge f
Wha ca e ide ? Wha i he diffe e ce be ee a ea a d i g ide?
Wha c di i a e eeded f a a ec i e? A a ec i e? Wh d ' he ha e a f he i e? www.uni.edu/morgans/astro/course/Notes/section1/new2.html he 12/12 ...
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