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Lab Title: Studying Solar and Lunar Eclipses Using Voyager II

Equipment:

Macintosh computer and the Voyager II planetarium program fromCarina Software.

Purpose:

To learn about the differences between solar and lunar eclipses.

Requirements:

This lab is to be performed individually (or in groups of no morethan two if there are not enough computers). If you must work in pairs,take turns manipulating the computer and taking the data. You shouldswitch off from time to time so everyone gets a chance to use the computer.

Although you may use the computer and the program with yourpartner to collect data, all calculations, graphing, and any narratives inyour lab report must be your own original work!

At the end of the lab write-up, you will find a Project Report form onwhich to do all of your work. Hand in only the Project Report form(including any additional sheets of paper if you need to) along with anycomputer printouts requested in the lab write-up. Do NOT hand in the labwrite-up itself!

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Introduction:

COVER UP: SOLAR ECLIPSE CONDITIONS

As the Moon revolves about the Earth, it sometimes passes betweenthe Earth and the Sun. When this happens a solar eclipse results. As youcan see from the Figure 1, a necessary condition for a solar eclipse is that theMoon be in a new phase. But although the Moon goes through the newphase once each month, there is not a solar eclipse each month. This impliesthat the Moon does not usually pass directly between the Earth and Sun atnew moon.

Penumbra

Umbra

Cross Sectionof the

Moon's Shadow

Earth

Sun

Eclipse Path

Figure 1. Solar Eclipse Geometry

Usually at new Moon, the Moon passes either above or below the Sun.Hence, the Moon being in a new phase is a necessary but not a sufficientcondition for a solar eclipse. The other required condition for a total solareclipse is that the Moon must pass directly between the Earth and Sun,which can happen only if the Moon is in the ecliptic plane. The reason thatthe Moon is not always in the ecliptic is that the Moon's orbital plane isinclined to the ecliptic plane by about 5 degrees.

Just as the Earth's shadow has two parts, so does the shadow of theMoon. The inner, darker region is called the umbra and the outer, lighterregion is called the penumbra.

Figure 2 shows the possible types and duration of solar eclipses.Notice that the Moon's shadow covers a relatively small area on the Earth'ssurface. Only those few people who are in the shadow region will actuallysee a solar eclipse. Individuals in the penumbra will see a partial solareclipse while those in the umbra will view a total solar eclipse. The

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Moon's shadow sweeps across the Earth's surface from west to east, and asolar eclipse is seen at different times by people at different locations. Thepath traveled by the Moon's umbra is known as the solar eclipse path.

B. Shortest DurationA. Longest Duration

C. Annular Eclipse

Figure 2. Solar Eclipse Types and Duration

Because the Moon revolves about the Earth in an elliptical orbit, itsdistance from the Earth varies. When the Moon is close to the Earth itsapparent size is larger than when it is far from the Earth. If a solar eclipseoccurs when the Moon is close, its apparent size will be somewhat largerthan that of the Sun, the solar eclipse path will be wider, and the duration ofthe solar eclipse will be longer (Figure 2, A). The maximum possibleduration of totality is around 8 minutes. The reverse is true when the Moonis far from the Earth (Figure 2, B). From time to time the Moon can be sofar away that its apparent size is less than the Sun's. When this happens, theMoon does not completely cover up the Sun, and a ring (annulus) of sunlightremains visible around the Moon. This type of solar eclipse is called anannular eclipse (Figure 2, C).

The outermost part of the Sun's atmosphere, the corona, is a veryfaint, tenuous gas that is difficult to observe with ground-based telescopesexcept during a total solar eclipse. For this reason, astronomers havehistorically gone to great lengths and great distances to observe solareclipses. Now that orbiting instruments have made it possible to produceartificial solar eclipses with some ease, the scientific importance of naturalsolar eclipses is not quite as great. However, the esthetic aspects of solareclipses still make them one of the most striking and exciting ofastronomical events.

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Procedure:

Your instructor will inform you about which computers on campuscurrently have the program installed on their hard drives. Position themouse cursor arrow over the icon (picture) of the Mac's hard disk anddouble click on the mouse button. A list of the contents of the hard disk willappear. Move the mouse cursor over the Astronomy 30 folder's icon andagain double click the mouse button to reveal the contents. Clicking themouse button twice when the cursor arrow is on the picture of the Voyagerfolder will open the folder and reveal a picture (icon) of the program itselfcalled Voyager II in the file list. Position the mouse cursor over theVoyager II icon and double click to run the program.

SET LOCATION AND TIME

Set your location to the nearest major city to your school:

❏ Control ➧ Set Location ➧ Location Lists...Scroll to City in Major Cities dialog windowHighlight city and Double Click or press return

❏ Control ➧ Define Horizon...Select Use Standard Horizon

For now, you do not have to change the date and time. Use whatever valuesVoyager has entered.

PREDICTING SOLAR ECLIPSES

If the angular separation between two celestial objects is small andthey therefore appear close together in the sky, they are said to be inconjunction. To determine the dates and times of solar eclipses you willsearch for conjunctions between the Moon and Sun.

❏ Chart ➧ Chart Coordinates ➧ Local Horizon❏ Chart ➧ Chart Coordinates ➧ 180° Projection❏ to 180°❏ Time Step 2 minutes in the Control Panel❏ Click to view Planet Panel

On the left side of the Planet Panel is an area containing 16 littlesymbol boxes. From left to right in the first row, these symbols representthe Sun, Mercury, Venus, and Earth. Under these are the symbols for Mars,

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Jupiter, Saturn, and Uranus. The next-to-the-last row has Neptune, Pluto,the Moon, and the Earth's (or the Moon's) shadow. Notice that the planets'symbol boxes are ordered according to their distance from the Sun.

When these symbol boxes are black, the corresponding objects can beviewed. Note that above, only the Sun and Moon symbol boxes are turned on(black), so only the Sun and Moon will be visible and the planets will not bevisible. You can turn off objects by clicking on each symbol one at a time or byholding down the mouse button and dragging across the symbols so that thecursor acts like an eraser. Clicking once on a turned off (white) symbol boxwill turn it on (black).

When you double click on a symbol box, that object is centered onthe screen. Double click on the Sun symbol to center the Sun. You will findthat when you center an object, that object's symbol appears in the Lockbox. Click the Lock box and it turns black meaning that object will alwaysremain centered on the screen. The Lock box containing the Sun's symbolis also black and hence the Sun will always remain centered on the screen.When the Lock box is not black, an object will not remain centered.

❏ Turn off all planets❏ Turn ON only Moon and Sun❏ Center (Double click) Sun❏ Lock Sun❏ Options ➧ Conjunction Search...❏ Conjunction Search dialog window

Select Sun and MoonSearch From This YearSearch To Next YearSeparation 0.50 degreesClick Search

As the search proceeds, the date and time of each conjunction (possiblesolar eclipse) is displayed. Note that the separation angle you entered in theConjunction Search dialog window is an upper limit so that the list will containall conjunctions with a separation angle less than or equal to this number.

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The type and visibility of a solar eclipse may be different at differentlocations on the Earth. If your search did not find any total or partial solareclipses that were above your local horizon, it might be that there werenone in the specified time interval. Try a longer time interval from this yearonward. Keep extending the ending year search date until you find onethat IS visible above your local horizon!

An asterisk (*) next to a conjunction date indicates that one or bothobjects are below the horizon at your particular location when theconjunction takes place. If this is the case, all or some of the solar eclipsewill NOT be visible from your location. If you wish to stop the searchbefore it is completed you can click the Cancel button. Double click on thelisted conjunction to display the sky with the objects centered on the screen.You can also highlight the listed conjunction and click the Set Time button.

When your search is completed, to 5° and look at a few of thepossible solar eclipse dates (conjunctions) that are above the horizon atyour location and use the advance time (+) and/or the reverse time (–)

arrows in the Control Panel to watch the motion of theMoon near its new phase. To stop the motion, click once anywhere else inthe Sky Chart window. To determine more accurately when a solar eclipsebegins and ends, you may want to shorten the Time Step to 1 minute.

Project Result 1: Hand in a printout showing the next solar eclipseoccurring nearest today's date (from today ONWARD) that is visible above thehorizon at your location and answer the related questions. But, before youmake a printout select:

❏ File ➧ Print Options...Select Use Black Stars with White SkyClick OK or press return

To print the Voyager screen, choose:

❏ File ➧ Print Sky Chart...Click OK or press return

Note that since you are using a white sky, the new Moon will appear white andthe Sun will appear black on your printout! Clearly label the Sun and the Moon.

Project Result 2: Search for all solar eclipses beginning this year overthe next 20 years with a separation of 0.50° or less during this time interval.Divide the total number (including those below your local horizon) of theseSun-Moon conjunctions (solar eclipses) you found by 20 to find an estimatefor the average yearly frequency of all types of solar eclipses.

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THE SOLAR ECLIPSE OF JULY 1991

A relatively long solar eclipse visible from the northern hemispheretook place in July 1991. The eclipse path passed over one of the largestobservatories in the world, situated on top of an extinct volcano. To viewthis solar eclipse from this site, Mauna Kea, Hawaii:

❏ Control ➧ Set Location ➧ Location Lists...Scroll to Mauna Kea in the Major Cities dialog windowHighlight city and Double Click or press return

❏ Control ➧ Set Time ➧ Local Mean Time...❏ Set Local Mean Time dialog window

7/11/1991 AD6:20 AMDaylight Saving Time OFFClick OK or press return

❏ Time Step 5 minutes❏ Field ➧ Center on Planet ➧ Sun❏ Click to display Planet Panel❏ Sun and Moon ON❏ Center Sun❏ Lock Sun❏ Chart ➧ Chart Coordinates ➧ Local Horizon❏ Chart ➧ Chart Coordinates ➧ 180° Projection❏ to 5°

Project Result 3: Use the advance time (+) and/or the reverse time (–) arrows

in the Control Panel to watch the eclipse. To determine moreaccurately when the eclipse begins and ends, you may want to shorten the TimeStep to 1 minute. Hand in a white sky printout showing the solar eclipse as theMoon passes in front of the Sun as viewed from Mauna Kea, Hawaii and answerthe related questions. Clearly label the Sun and the Moon on your printout.

Project Result 4: The type and visibility of a solar eclipse may be different atdifferent locations on the Earth. Repeat for La Paz, Mexico which is located onthe southernmost tip of the Baja peninsula. Clearly label the Sun and the Moon.

Project Result 5: The type and visibility of a solar eclipse may be different atdifferent locations on the Earth. Repeat for San Francisco, California. Clearlylabel the Sun and the Moon.

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FROM THE MOON'S POINT OF VIEW

With Voyager you can view a solar eclipse from the Moon and see thesolar eclipse path as the Moon's shadow sweeps across the Earth's surface.

❏ Control ➧ Observe from Planet... ➧ Moon❏ Control ➧ Set Time ➧ Universal Time...❏ Set Universal Time dialog window

7/11/1991 AD17:00 hoursClick OK or press return

❏ Time Step 2 minutes❏ Earth On❏ Moon's Shadow On (the symbol just to the right of the Moon's symbol)❏ Double click Earth to Center❏ Lock Earth

❏ to 2°

Project Result 6: Use the advance time (+) and/or the reverse time (–)

arrows in the Control Panel to watch the Moon's shadow moveacross the Earth. To determine more accurately when the shadow crosses aparticular location, you may want to shorten the Time Step. Complete thesketch for the direction of motion of the small dark umbra of the Moon'sshadow and note the approximate Universal Times that the shadow crossesMauna Kea, Hawaii and then La Paz, Mexico.

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SHADOWING THE MOON: LUNAR ECLIPSE CONDITIONS

When the Moon is in a full phase, it sometimes passes through theEarth's shadow. When this happens, a lunar eclipse occurs (see Figure 3).But although the Moon goes through the full phase once each month, there isnot a lunar eclipse each month. Generally, the Moon passes either above orbelow the shadow. Hence, the Moon being in a full phase is a necessary butnot a sufficient condition for a lunar eclipse.

Penumbra

Umbra

Cross Sectionof the

Earth's Shadow

Sun

Figure 3. Lunar Eclipse Geometry

The other required condition is, of course, that the Moon must passthrough the Earth's shadow, which can happen only if the Moon is in orclose to the Earth's orbital plane. This plane, called the ecliptic derives itsname from the requirement that the Moon be near the plane for a lunareclipse to occur. The reason that the Moon is not always in the ecliptic isthat the Moon's orbital plane is inclined to the ecliptic plane by about 5degrees.

The Earth's shadow has two parts. The inner, darker region is calledthe umbra and the outer, lighter region is called the penumbra. Neither theumbra nor the penumbra is completely dark because the Earth's atmospherescatters sunlight into the shadow. During a lunar eclipse, the Moon darkensand becomes redder, but does not completely disappear.

Figure 4 shows the possible types of lunar eclipses. When the Moonis in the penumbra, only a very small darkening occurs, so penumbral lunareclipses are difficult to detect with the naked eye. It is partial and totalumbral lunar eclipses that are most easily seen.

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Partial Umbral Eclipse

Total Umbral Eclipse

Total Penumbral Eclipse

No Eclipse

Partial Penumbral Eclipse

Figure 4. Types of Lunar Eclipses

SET LOCATION AND TIME

Set your location to the nearest major city to your school:

❏ Control ➧ Return to EarthControl ➧ Set Location ➧ Location Lists...Scroll to City in Major Cities dialog windowHighlight city and Double Click or press return

For now, you do not have to change the date and time. Use whatever valuesVoyager has entered.

PREDICTING LUNAR ECLIPSES

To determine the dates and times of lunar eclipses, you will search forconjunctions between the Moon and the shadow of the Earth.

❏ Chart ➧ Chart Coordinates ➧ Local Horizon❏ Chart ➧ Chart Coordinates ➧ 180° Projection❏ to 180°❏ Time Step 4 minutes in the Control Panel❏ Click for Planet Panel

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❏ Moon ON❏ Earth's Shadow ON❏ Center (Double click) Earth's Shadow❏ Lock Earth's Shadow

❏ Options ➧ Conjunction Search...❏ Conjunction Search dialog window

Select Moon and Earth's ShadowSearch From This YearSearch To Next YearSeparation 1.0 degreesClick Search

As the search proceeds, the date, time, and angular separation of eachconjunction are displayed. The type and visibility of a lunar eclipse may bedifferent at different locations on the Earth. If your search did not find anytotal or partial umbral lunar eclipses that were above your local horizon, itmight be that there were none in the specified time interval. Try a longertime interval from this year onward. Keep extending the ending yearsearch date until you find one that IS visible above your local horizon!

An asterisk (*) next to a conjunction indicates that one or both objectsare below the horizon at your location when the conjunction takes place. Ifthis is the case, all or some of the lunar eclipse will not be visible from yourlocation. If you wish to stop the search before it is completed, you can clickthe Cancel button. Double click on the listed conjunction to display the skywith the objects centered on the screen. You can also highlight the listedconjunction and click the Set Time button.

When your search is completed, to 10° and look at a few of thepossible lunar eclipse dates (conjunctions) that are above the horizon atyour location and use the advance time (+) and/or the reverse time (–)

arrows in the Control Panel to watch the motion of theMoon near its full phase. To stop the motion, click once anywhere else inthe Sky Chart window. To determine more accurately when the Moonenters and leaves different parts of the Earth's shadow, you may want toshorten the Time Step to 1 minute.

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Project Result 7: Hand in a printout showing the next lunar eclipseoccurring nearest today's date (from today ONWARD) that is visible abovethe horizon at your location and answer the related questions. Be sure tomake a White Sky printout as you did in Project Result 1. Note that sinceyou are using a white sky, the full Moon will appear black and the eclipsedMoon will appear white on your printout! Clearly label the Moon and boththe umbra and the penumbra of the Earth's shadow.

Project Result 8: Search for all lunar eclipses beginning this year overthe next 20 years with a separation of 1.0° or less during this time interval.Divide the total number (including those below your local horizon) of theseconjunctions (lunar eclipses) you found by 20 to find an estimate for theaverage yearly frequency of all types of lunar eclipses.

FROM THE MOON'S POINT OF VIEW, AGAIN

With Voyager you can also view a lunar eclipse from the Moon and watchthe Earth pass in front of the Sun.

❏ Control ➧ Observe from Planet... ➧ Moon❏ Control ➧ Set Time ➧ Universal Time...❏ Set Universal Time dialog window

12/21/1991 AD7:30 hoursClick OK or press return

❏ Time Step 2 minutes❏ Earth On❏ Sun On❏ Center (Double click) Sun❏ Lock Sun❏ to 5°

Project Result 9: Use the advance time (+) and/or the reverse time (–)

arrows in the Control Panel to watch the Earth move acrossthe Sun. To determine more accurately when the eclipse begins and ends, youmay want to shorten the Time Step. Hand in a printout showing the lunareclipse just before the Earth passes in front of the Sun as viewed from theMoon and answer the related questions. Be sure to make a White Skyprintout as you did in Project Result 1. Note that since you are using a whitesky, the Sun will appear black on your printout! Clearly label the Earth andthe Sun.

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Studying Solar and Lunar Eclipses

Name: Lab Partners:

Date:

PROJECT RESULTS

1. Printout showing the next solar eclipse nearest to today's date(from TODAY ONWARD) that is above your local horizon. Clearly labelthe Sun and the Moon.

A. Solar eclipse data (Local Time and Date)

City Longitude (W, E)Latitude (N, S)

Date

Type of solar eclipse ________________

Start of solar eclipse (AM, PM)Middle of solar eclipse (AM, PM)End of solar eclipse (AM, PM)

B. About how long did the solar eclipse last? ___________ If the solar eclipse was total, estimate the duration of totality, that is, the time that the Sun was totally covered by the Moon. __________________

2. Solar eclipse frequency

A. Time interval of search = ______________ years

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B. Separation angle = __________ degrees

C. Total number of all solar eclipses for the next 20 years = _______

D. Average yearly frequency of solar eclipses = ____________ per year.

3. Printout of the July 1991 solar eclipse as viewed from Mauna Kea, Hawaii

A. Solar eclipse data (Local Time and Date)

City Longitude (W, E)Latitude (N, S)

Date

Type of solar eclipse ________________

Start of solar eclipse (AM, PM)Middle of solar eclipse (AM, PM)End of solar eclipse (AM, PM)

B. About how long did the solar eclipse last in Mauna Kea from beginning to end? __________ If the solar eclipse was total, estimate the duration of totality, that is, the time that the Sun was totally covered by the Moon. _____

C. Draw an arrow on your printout showing the apparent path of the Moon before, during, and after the solar eclipse as viewed from this location.

4. Printout of the July 1991 solar eclipse as viewed from La Paz, Mexico

A. Solar eclipse data (Local Time and Date)

City Longitude (W, E)Latitude (N, S)

Date Type of solar eclipse ________________

Start of solar eclipse (AM, PM)Middle of solar eclipse (AM, PM)End of solar eclipse (AM, PM)

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B. About how long did the solar eclipse last in La Paz from beginningto end? __________ If the solar eclipse was total, estimate the duration of totality, that is, the time that the Sun was totally coveredby the Moon. __________________

C. What are the angular sizes of the Sun and the Moon during the total solar eclipse in La Paz? (Clicking in the center of each object will bring up a Data Window with information that will help you.)

Angular size of Moon = _____________ arc minutes (')

Angular size of Sun = _______________ arc minutes (')

D. If the solar eclipse in La Paz had instead been an annular eclipse, how would the two angular sizes shown above have compared? Which one of the angular sizes would have changed? Why?

5. Printout of the July 1991 solar eclipse as viewed from San Francisco

A. Solar eclipse data (Local Time and Date)

City Longitude (W, E)Latitude (N, S)

Date

Type of solar eclipse ________________Start of solar eclipse (AM, PM)Middle of solar eclipse (AM, PM)End of solar eclipse (AM, PM)

B. About how long did the solar eclipse last in San Francisco from beginning to end? __________ If the solar eclipse was total, estimate the duration of totality, that is, the time that the Sun was totally covered by the Moon. __________________

C. Describe the differences between the view of the July 1991 solar eclipse from San Francisco and the view from Mauna Kea, Hawaii.

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6. July 1991 solar eclipse as seen from the Moon

A. Sketch the path and direction of motion of the small dark umbra of the Moon's shadow on the map below. Show the eclipse path and indicate with an arrow the direction of motion of the Moon's umbral shadow on the picture of the Earth's surface:

B. Illumination of the Earth ___________ %

Phase of the Earth ___________

C. Universal Time that the umbra of the Moon's shadow crosses

Mauna Kea, Hawaii _____________ UT

La Paz, Mexico ________________ UT

D. Knowing that the distance from Mauna Kea to La Paz is 2970 miles, use the time difference between Mauna Kea and La Paz from part C to calculate approximately how fast (in miles per hour) that the shadow of the Moon moves across the Earth's surface. Show your work below.

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7. Printout showing the next lunar eclipse nearest to today's date(from TODAY ONWARD) that is above your local horizon. Clearly labelthe Moon and both the umbra and the penumbra of the Earth's shadow.

A. Lunar eclipse data (Local Time and Date)

City Longitude (W, E)Latitude (N, S)

Date

Type of lunar eclipse

Moon entered:Penumbra at (AM, PM)Umbra at (AM, PM)

Mid lunar eclipse time (AM, PM)

Moon left:Umbra at (AM, PM)Penumbra at (AM, PM)

B. About how long was part or all of the Moon in the Earth's shadow regions?

C. About how long was part or all of the Moon in the smaller umbra?

D. Recalling that the apparent angular diameter of the Moon is about0.5 degrees, use your printout of this lunar eclipse to estimate the angular diameter of the umbra and of the penumbra in degrees. Show your technique and work directly on the printout using a metric ruler to make the necessary measurements.

Angular diameter of umbra _____________ degrees

Angular diameter of penumbra __________ degrees

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E. The Moon moves eastward about one-half a degree per hour. If the Moon passed directly through the center of the Earth's shadow, how long would the Moon remain completely within the umbra? Show your work below.

Time in umbra _____________

How long would the Moon remain completely within the penumbra?

Time in penumbra __________

8. Lunar eclipse frequency

A. Time interval of search = ______________ years

B. Separation angle = __________ degrees

C. Total number of all lunar eclipses for the next 20 years = _______

D. Average yearly frequency of lunar eclipses = ____________ per year.

E. Divide your result for question 8D by your result for question 2D to seehow the average yearly frequency of lunar eclipses compares to the average yearly frequency of solar eclipses.

F. Which type of eclipse happens more often? _________________

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9. Printout of the December 1991 lunar eclipse as viewed from the Moon. Clearly label the Earth and the Sun.

A. Use your printout of this lunar eclipse to estimate the angular diameter of the Earth when viewed from the Moon using the fact that the angular diameter of the Sun is about 0.5° (= 30 arc minutes). Show your technique and work directly on the printout.

Angular diameter of Earth _____________ degrees

B. Illumination of the Earth ___________ %

Phase of the Earth ___________

C. Universal Time that the Earth

First starts to pass in front of the Sun _____________ UT

Completes its trip across the face of the Sun _____________ UT

D. Carefully study the relative sizes of the Sun and the Earth during the eclipse. Can there be an annular lunar eclipse? Why or why not?

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Conclusions and Comments

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Name: __________________

Lab Partner: __________________

Pre-lab Exercises: Studying Solar and Lunar Eclipses Using Voyager II

1. Carefully define each of the following terms:

(a) Penumbral shadow

(b) Umbral shadow

(c) Ecliptic

(d) Line of Nodes

(e) Annular eclipse

2. (a) Describe the apparent motion of the Earth through the lunar sky asviewed from a point on the surface of the Moon that is facing the Earth.(Remember that the Moon always presents the same side toward the Earthbecause it's gravitationally locked into a 1:1 spin-orbit resonance.)

(b) Would you always see the same side of the Earth from the Moon? Whyor why not?

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3. Does the Earth go through phases when viewed from the surface of theMoon? Why or why not?

4. Viewed from Mare Imbrium on the surface of the Moon, the Earth:(i) rises and sets every 24 hours,(ii) is always below the horizon,(iii) is always at the same place in the sky but goes through monthly phases,(iv) rises and sets every 29.5 days.

Which of the above choices are true? Why?

5. The Sun is actually 400 times larger in diameter than the Moon but in aremarkable cosmic coincidence it happens that the Sun is also 400 timesfarther away from the Earth than the Moon. As a consequence, the Sun andthe Moon appear to be the same size in the sky when viewed from the Earth!

(a) The diameter of the Earth is 12,800 km and the diameter of the Moon is3400 km. How many times larger is the Earth than the Moon?

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(b) Use a drawing compass and a metric ruler to make three circles belowshowing the correct relative sizes of the Sun, the Moon, and the Earth asviewed from different vantage points.

Make the Sun (as viewed from either the Earth or the Moon) a circle ofdiameter 2 cm (about the size of a nickel):

The Moon as viewed from the Earth:

The Earth as viewed from the Moon: