Every once in a while, the Moon moves into the Earth's shadow. You

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1 CHALLENGE: Lunar Eclipse! (Draft Only) How far and how big is the Moon? A lunar eclipse on Januar 2000 offers the chance to find out for yourself... and have doing it! GOALS: Every once in a while, the Moon moves into the Earth's shadow. You can observe this dramatic and majestic event from your backyard, street, or rooftop. And if you record the event using the MicroObservatory telescope, you'll be able to figure out how far and how large the Moon is. You'll find there's more to the Moon than meets the eye! Students should be able to: Model the Earth/Moon/Sun relationship. Apply simple geometry and arithmetic to determine size and distance of Moon. Estimate, deal with provisional knowledge, and examine assumptions. 'SCOPE IT OUT! IMPORTANT NOTE: For this event, please take NO MORE THAN 2 images between 10PM and midnight. This will ensure that all users have a chance to document the eclipse. Taking the Images: Remember, the Moon is bright so you'll have to use the gray filter. And use a short exposure time: 0.1 second. As the Moon slips into darkness, use the SAME exposure time: 0.1 second.

2 STUDENT'S PRIOR BELIEFS ABOUT THE MOON: Research has shown that many -- and perhaps MOST -- students believe that the phases of the Moon are caused by the shadow of the Earth falling on the Moon. In fact, this belief increases in frequency as students age from 9 to 14. (For a brief summary of research in this area, see "Rosalind Driver et al, "Making Sense of Secondary Science." Routledge, New York, 1994.) An eclipse is a great opportunity to: discuss with students their conceptions about the Moon's phases; to revisit the sun/moon/earth model; and to explore the difference between the Moon's phases and a lunar eclipse. GEARING UP: Want to get a discussion going with your students? Here are some great puzzlers about the eclipse: What is a lunar eclipse? Does a total eclipse of the Moon always occur when it's a full Moon? Why? (Use two balls to model the Earth/Moon and a light source that casts a shadow.) Does the eclipse become total at the same instant for everyone who can see the Moon -- even if they are two thousand miles apart? Why? The plane of the Moon's orbit is tilted slightly (about 6 degrees) relative to the plane of the Earth's orbit about the Sun. If both orbits were in exactly the same plane, how would this affect the number of lunar (and solar) eclipses per year on Earth? HEADS UP! Try watching the eclipse from your backyard, sidewalk, or rooftop. Here are some puzzlers: Why does the Moon appear reddish as the eclipse progresses? Notice the boundary on the Moon between light and shadow. During the eclipse, is this boundary as sharp as it is during a phase of the Moon? Is this true for both the telescope image and your naked eye (see below)? What's going on?

3 CREATE A DIGITAL MOVIE OF THE ECLIPSE: You can create your own movie of the eclipse. Just combine your image of the eclipse with images from other classrooms around the country. Or send us your image and we'll make a composite movie from all users' images. When you make your movie, consider this: Which is more accurate: The shadow moves across the face of the Moon? Or, the shadow is stationary, and the Moon moves across the shadow? Or is neither view completely accurate? INTERPRETING YOUR IMAGES: Take a good look at the eclipse images. When the Moon is half-eclipsed (half in shadow), does it look identical to a normal half-moon? What's the difference and why? During the eclipse, is the line between light and shadow as sharp as it is during a normal phase of the Moon? Is this true for both the telescope image and your naked eye? What's going on? Why can't you see the Moon's craters very well in any of your images of the eclipse? (Hint: Where is the sun relative to the illuminated part of the Moon? Next time you take vacation snapshots, be sure to consider the position of the sun, if you want to bring out the details of your scene. Photographers avoid shooting when the sun is directly overhead!) MEASURING THE UNIVERSE: DON'T LOOK IT UP... LOOK UP! Using your image of the eclipse, you can actually estimate the size and distance of the Moon! To do this, you'll need to know the size of the Earth. You'll also need to know the how the size of the Earth's shadow compares with the size of the Earth itself. Under what conditions would they be the same size? When is an object's shadow larger or smaller than the object itself? If the sun is larger than the Earth, the Earth's shadow gets smaller than the Earth:

4 ESTIMATING THE SIZE OF THE MOON: First you're going to compare the size of the Moon with the size of the Earth's shadow that it passes through. Then you'll have to decide how large the Earth's shadow really is, compared to the size of the Earth! Part I. Print out an image of your eclipsed Moon with Earth shadow. Now measure the diameter of the Moon on your image. The Moon's diameter is inches in my image. Now measure the diameter of the Earth's shadow in this image. A simple way to do this is shown on the insert. The Earth's shadow measures inches in my image. How many times larger than the Moon is the Earth's shadow? Earth's shadow is times larger than the Moon. IF the Earth's shadow seen in this image is the same size as the Earth (8000 miles diameter), how large would the Moon be? IF the shadow is same size as Earth, the Moon would be miles in diameter. (We'll come back to examine this assumption.)

5 PART II.: How big IS the Earth's shadow, at the distance of the Moon? DISCUSSION: In this discussion, we're going to ASSUME that the sun is larger than the Earth, and much further away than the Moon. In From the Ground Up!, we haven't shown that this assumption is true. But we CAN see if it leads to a consistent view of the Earth/Sun/Moon system. Let's use just one bit of information: During a SOLAR eclipse (when the Moon blocks out the sun), the eclipse is total only over a narrow path on the Earth. That's why, to see a solar eclipse, you have to go to just the right spot on Earth at just the right time. The photo at right shows the moon's shadow on the Earth during the solar eclipse of The shadow is about a hundred miles wide. In the following figure, if the Sun is very far away, then lines A and B are nearly parallel. If A and B are nearly parallel, then then shadowy TRIANGLES in these figures are similar triangles. Using simple geometry, you can see that the Earth's shadow is reduced by the same amount as the Moon's shadow is reduced, (over the same Earth-moon distance). Fig. NOT to scale. If the sun is VERY far from the Earth and Moon, then lines A and B are ALMOST parallel to each other.

6 Since the Moon's shadow is ALMOST one Moon diameter narrower than the Moon, then the Earth's shadow will be ALMOST one Moon diameter narrower than the Earth. Return to your measurements of the Moon and the Earth's shadow in part I. How will you modify the diameter of the shadow that you measured (in inches), to make it equal to the diameter of the Earth, at this scale? Answer: Since the shadow you have measured is SMALLER than the Earth by about one moon diameter, then if you ADD a moon diameter (in inches), you'll have the size of the Earth at this scale. Based on this correction, how large is the Moon relative to the Earth? If the Earth's corrected shadow is 8000 miles wide, then the Moon is miles wide. HOW FAR IS THE MOON? If you know how wide an object is, you can figure out how distant it is, provided you know how many degrees wide the object is in the sky. The FURTHER an object, the SMALLER the angle it makes in the sky. Use your eclipse image and the fact that the SCALE of a MicroObservatory image is 5 arc-seconds per pixel (zoomed-out mode). (Recall that 60 arc-seconds is one minute of arc, and 60 arc-minutes is one degree.) First measure your image: The Moon is pixels in diameter in my image. The Moon is therefore arc-seconds in diameter, which is degrees. Recall from "From the Ground Up!: Size and Scale Activity X" that an object that measures 1 degree wide is about 57 times further away than it is wide. A narrower image is proportionally further away. Then how far away is the Moon, IF it's diameter is the value you estimated in part I? The distance of the Moon is = (width of moon) x (57)/ (number of degrees wide) = miles

7 MAKING SENSE. You've just determined that the Moon is much smaller than the Earth. What's the significance of this size? If the Moon is much smaller than Earth, then how does its gravity compare to Earth's? Is the Moon massive enough to keep an atmosphere from evaporating into space? [See "From the Ground Up! Challenge X]. If the Moon is much smaller than Earth, could it have originated from Earth? [Discussion of origin of the Moon.] IN BOUNDS! Okay, you've got a number for the distance to the Moon. Is it REASONABLE? And how confident are you in this number? Take a look at the numbers you've used in your calculations. How precise are those numbers? Which ones would you want to know more accurately to have greater confidence in your result? Quality of input data Where are the sources of error in your calculations? For example, Possible sources of error Can you estimate a lower bound and an upper bound for the distance to the Moon, based on the data you've used? Based on my investigation, the Moon is No less than miles away. No more than miles away. us your results (you can attach images to the ). We'll publish them on the From the Ground Up! website.