Black 4 Step Problem Solving Astronomy and Large Numbers People have always been fascinated by the moon, the planets, and the stars. Hundreds of stories have been written to try and explain these lights in the sky. Different cultures in different times developed varied explanations for these celestial bodies, but almost all people through the ages believed two things. One, that the moon and the sun were about the same size; and two, that the moon, the planets, and the stars were very close to the earth. Then mathematics changed everything!! Over 2000 years ago a brilliant Greek mathematician named Eratosthenes used fairly simple mathematics to determine the circumference of the earth. This was one of the world's most valuable discoveries because once we knew the circumference of the earth, trigonometry could be used to find the distance to the moon, the sun and other heavenly bodies. Several years after Eratosthenes's discovery, two other Greek mathematicians used trigonometry to find that the moon was approximately 250,000 miles from the earth. This provided dramatic proof that the moon, the sun and the stars weren't just miles above us as previously thought, but were hundreds of thousands, and. possibly even millions of miles away. Humankind suddenly realized that everything around us was not what it appeared. 1
Mathematics was the key to our present understanding of the earth and the universe. As we continue to try and unlock the mysteries of space, mathematics will be one of our most important tools. The fastest traveler in our universe is light. Light travels 186,000 miles per second, which is fast enough to circle the earth over 7 times in one second. 2
You can tell how, far away a thunderstorm is by using this information about the speed of light and sound. When you see lightning, the thunder occurs at the same time, but because sound is much slower than light, it will take several seconds for the sound to reach your ears (unless the storm is directly overhead). If thunder sounds 12.5 seconds after the lighting, can only tell how far away the storm is? 3
We know that light is the fastest traveler in the universe, but even with light's extraordinary speed, it still takes many years for the light from the stars to reach our eyes. The closest star to us, besides the sun, is Alpha Centauri. Astronomers once believed that Alpha Centauri was a single star, but now it is known that it is a triple star. This triple star is approximately 23,462,784,000,000 miles from the earth. Distances in space are so large that astronomers find it much easier to use light-years as a, measurement of distance. A light-year is the distance light travels in a year. Instead of saying that Alpha Centauri is 23,462,784,000,000 miles away, astronomers say that it is 4 light-years away. Another term that astronomers use to measure large distances in space is a parsec. Each parsec is equal to 3.26 light-years. 4
Sometimes when we are dealing with large distances in space, our numbers become too large for a calculator. We need to learn how to multiply these large numbers on our calculator because we certainly do not want to do the math using paper and pencil!! When you multiply numbers that are too large for the calculator, you must remove all the zeros at the end of the numbers, multiply, and then return the zeros to your answer. Lets look at the example concerning the distance light travels in a week: 186,000 x 604,800 becomes 186 x 6048. 5
186 x 6048 = 1,124,928 186 x 6048 = 112,492,800,000 Solve the following problems on your calculator by removing zeros: A. 55,000 x 96,000 = B. 186,000 x 36,000 = C. 4005 x 92,000,000 = When you are solving problems about distances in space, you will be dealing with very large numbers. The names of these numbers are shown below. Billion Trillion. Quadrillion.. Quintillion Sextillion.. Septillion.. Octillion. Nonillion. Decillion. Undecillion... Duodecillion Tredecillion Quattuordecillion Quindecillion. Sexdecillion Septendecillion... Octodecillion Novemdecillion Vigintillion Googol... 9 zeros 12 zeros 15 zeros 18 zeros 21 zeros 24 zeros 27 zeros 30 zeros 33 zeros 36 zeros 39 zeros 42 zeros 45 zeros 48 zeros 51 zeros 54 zeros 57 zeros 60 zeros 63 zeros 100 zeros Googoplex.. a googol of zeros 6
Unit 1 Number Sense and Algebraic Thinking Mathematicians made a very interesting observation about circles that has proven to be very useful to astronomers and scientists. They found that you can find the circumference of any circle by multiplying the diameter of the circle by pi. 7