LAB #1

1 Name: _________________________________ Partner(s): _____________________________ _____________________________ AST 111: Lab #1 Introduction to Solar System Astronomy Objectives  To become familiar with the proper usage of scientific notation and common astronomical units  To use ratios and small objects to model the scale of the solar system References  Conceptual Astrophysics (1 st edition), Sirola Materials  Calculator  Tape measures (metric)  Softball  Marbles  Pinheads Introduction Astronomy, including solar system astronomy, is the science of the very big (and perhaps surprisingly, sometimes the science of the very small). Because of this, people often have trouble imagining the size and scale of astronomical objects and systems. Astronomers approach these difficulties in a variety of ways. We will show how to express “extreme” numbers in more user -friendly manners and to use more appropriate units of measurement. It also helps many students to see just how various large numbers relate to each other – as an example, we will create a scale model of the solar system by using a softball to represent the Sun. Activity #1: Scientific Notation Very large or very small numbers may be represented in a compact form known as scientific notation. Scientific notation uses our decimal (i.e. base 10) numbering system to make large and/or small numbers more manageable. Consider a few examples:

2 The mass of the planet Earth, in kilograms 1 , is 5,970,000,000,000,000,000,000,000. If we had to write this number out every time we needed it, we would quickly get wrist cramps! More importantly, it impedes rather than furthers understanding – even professional astronomers struggle to make sense of numbers this large. Let’s use scientific notation to better interpret this number. First, notice that we have written the decimal point at the end of the number. This usually isn’t done, but here we want it to stand out. Move the decimal point until it is behind the first non-zero digit of the number. In this case, that number is 5. Next, count up the number of columns the decimal point moved; here, the decimal point moved 24 places. Now we can restate the number in scientific notation: 24 10 97 . 5  The “24” is called the exponent. If we write out 10 24 in long form, we would see that it is equal to 1,000,000,000,000,000,000,000,000, or a 1 followed by 24 zeroes. Scientific notation has recast the number as 24 10 97 . 5  , or “five point nine seven times ten to the twenty- fourth power”. A lso, as an important aside, note we only kept the non-zero digits in front – 5.97, not 5.970 or 5.9700 etc. The zeroes in the long-form number are merely spacers; they represent columns of ten, not actual numbers. In general, we need only keep the first three or four digits of a number. The above was an example of a very large number. What about a very small number? For example, the mass of an electron, again in kilograms, is 0.000 000 000 000 000 000 000 000 000 000 911 which is a tiny number indeed! Le t’s apply scientific notation to this number. Move the decimal point behind the first non-zero digit as we did earlier. For this example, the decimal point moves 31 places and the first non-zero digit is 9. Because the number is less than one – or, equivalently, the decimal point moved to the right instead of the left – the exponent is negative. Our new representation of the number is now 31 10 11 . 9   It is clear that we have gained a great deal in clarity and understanding by rewriting these numbers in scientific notation. 1 A kilogram is equivalent to 2.2 pounds on the surface of the Earth. The comparison is complicated because kilograms are units of mass (the amount of “stuff” an object has) and pounds are units of weight, which depends on mass and gravity both.

3 Below in Table 1-1 are examples of numbers you might encounter in astronomy. For a number given in long form, write its equivalent in scientific notation. For a number given in scientific notation, write its equivalent in long form. Table 1-1. Numbers in Long Form and Scientific Notation. Activity #2: Units of Measurement Even when numbers can be expressed in the more compact form of scientific notation, they still may not mean much to a reader. The distance from the Earth to the Sun is a good example: km 000 , 700 , 149 km 10 497 . 1 8   Rounding off, the Earth is about 150 million kilometers (or 93 million miles) from the Sun. To put this in perspective, consider a car owner who puts 15,000 km (or 9300 miles) on the car’s odometer each year. How many years would it take to drive 150 million kilometers? Write your answer below. 150 million km / (15,000 km per year) = __________ years One way to deal with unwieldy numbers is to change how the numbers are expressed – in other words, to change the units. The most important unit in solar system astronomy is the Astronomical Unit , or the AU , defined as the average distance of the Earth from the Sun: km 10 497 . 1 AU 1 8   This allows astronomers to make better sense of the scale of the solar system. Instead of Earth being about 150 million kilometers from the Sun, we can say the Earth is 1 AU from the Sun. The planet Mars is 228 million kilometers from the Sun – or 1.52 AU from the Sun… and so on. 1.097 X 10 7 Number in Long Form Number in Scientific Notation 297,000 5.67 X 10 -8 0.000 000 000 066 7 2.898 X 10 7