The sun is 1.39 X 10 6 km in linear diameter and 1.50 X 10 8 km from Earth. You can repeat this calculation for the angular diameter of the sun. The moon’s orbit is slightly elliptical, so it can sometimes look a bit larger or smaller, but its angular diameter is always close to 0.5°. If you divide by 60, you get 31 minutes of arc or, dividing by 60 again, about 0.5°. To solve for angular diameter, you can multiply both sides by 206,265 and find that the angular diameter is 1870 seconds of arc. What is its angular diameter? The moon’s linear diameter and distance are both given in the same units, kilometers, so you can put them directly into the small-angle formula: angular diameter The moon has a linear diameter of 3476 km and a distance from Earth of about 384,000 km. You can use this formula to find any one of these three quantities if you know the other two here you are interested in finding the angular diameter of the moon. In the small-angle formula, you should always express angular diameter in seconds of arc and always use the same units for distance and linear diameter: angular diameter The small-angle formulagives you a way to figure out the angular diameter of any object, whether it is a pizza, the moon, or a galaxy. Clearly, the farther away an object is, the smaller its angular diameter. The angular diameter of an object is the angle formed by lines extending toward you from opposite sides of the object and meeting at your eye ( Figure 3-6). The linear diameter of the moon is 3476 km. You use linear diameter when you order a 16-inch pizza-the pizza is 16 inches in diameter. Linear diameter is simply the distance between an object’s opposite sides. This is the key to understanding solar eclipses. You learned about the angular diameter of an object in Chapter 2 now you need to think carefully about how the size and distance of an object like the moon determine its angular diameter.
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That lucky coincidence allows you to see total solar eclipses. Our moon has the same angular diameter as our sun, so it can cover the sun almost exactly. These spectacular sights are possible because we on Earth are very lucky. During a particular solar eclipse, people in one place on Earth may see a total eclipse, while people only a few hundred kilometers away see a partial eclipse. If the moon covers only part of the sun, the eclipse is a partial solar eclipse. If the moon covers the disk of the sun completely, the eclipse is a total solar eclipse. A SOLAR ECLIPSE OCCURS when the moon moves between Earth and the sun.