Astronomy 105 Observational Astronomy Fall 2021 Lab A Tentative Schedule WEEK DATES LAB LAB TOPIC TEXT 1 Aug 29 – Sep 2 N/A Syllabus Review N/A 2 Sep 5 - 9 A Scientific Calculations & Measurement On - Line Handout 3 Sep 12 – 16 B Kepler’s Laws On - Line Handout 4 Sep 19 - 23 C Star Charts On - Line Handout 5 Sep 26 - 30 D Solar Spectrum On - Line Handout 6 Oct 3 - 7 E Telescopes On - Line Handout 7 Oct 10 - 14 F The Period - Luminosity Relation On - Line Handout 8 Oct 17 - 21 G The HR Diagram and Colors of Stars On - Line Handout 9 Oct 24 - 28 H Size and Shape of the Galaxy On - Line Handout 10 Oct 31 – Nov 4 I Galaxy Classification On - Line Handout 11 Nov 7 - 11 L Origin of the Elements On - Line Handout 12 Nov 14 - 18 N/A No Class - Mid - Term Exam N/A 13 Nov 21 – 25 N/A No Class (Holiday) N/A 14 Nov 28 – Dec 2 J Introduction to Photometry 1 On - Line Handout 15 Dec 5 – 9 K Introduction to Photometry 2 On - Line Handout 16 Dec 12 - 16 N/A No Class (Finals Week) Lab J&K Due N/A Astro 105 Fall 2022 Lab A – Measurements and Powers of Ten OBJECTIVES: • After completing this exercise, the student should be able to: • 1. Make calculations using scientific notation • 2. Round off numbers to the correct number of significant digits. • 3. Estimate errors associated with a data set' • 4. Graph data and represent it with a visually estimated best fit line or curve. STUDENT MATERIALS • The student is expected to have the following items: ruler (cm and inches), and a calculator STUDENT REQUIREMENTS • This lab can be done individually or with lab partners. Each student is expected to at least share the workload. • After completing this exercise, tum in data sheet, with your name on it. Astro 105 Fall 2022 Lab A – Measurements and Powers of Ten Introduction • During the analyses of data, astronomers must frequently deal with extremely large and small numbers and perform mathematical calculations with these numbers. • This lab will help you learn how to make these types of calculations, how to analyze data, and how to graph an associated data set. You will also learn to estimate errors. Astro 105 Fall 2022 Lab A – Measurements and Powers of Ten This lab consists of five parts: 1) Practice making calculations using powers of ten – multiplication and division. 2) Writing numbers in scientific notation and determining the number of significant digits 3) Making a series of measurements and determining the errors associated with these measurements 4) Calculating the log of a series of numbers 5) Graphing two sets of data on a piece of graph paper Astro 105 Fall 2022 Lab A – Background A . Calculations Using Powers of Ten • In the lab, you will need to multiply and divide numbers written in scientific notation. This may seem difficult but it is actually simple. Suppose you want to multiply 2000 by 300; you could write 2000 x 300 = 600000. • We note that 2000 = 2 x 1000 = 2 x 10 3 and 300 = 3 x 100 = 3 x 10 2 • In scientific notation it would look like: • (2.0x10 3 ) x (3.0x10 2 ) = (2.0x3.0) x (10 3 x10 2 ) = 6.0 x 10 (2+3) = 6.0x10 5 • In other words, you multiplied number parts together first ( the 2.0 and the 3.0 ) then for multiplication , you add the exponent parts together. Astro 105 Fall 2022 Exponents, Powers of Ten – Scientific Notation Some common powers of ten you should know: • 10 2 = 100 = one hundred • 10 3 = 1000 = one thousand • 10 4 = 10,000 = ten thousand • 10 5 = 100,000 = one hundred thousand • 10 6 = 1,000,000 = one million • 10 9 = 1,000,000,000 = one billion • 10 12 = 1,000,000,000,000 = one trillion • We will regularly run into much bigger numbers (1.98 x 10 30 ) Astro 105 Fall 2022 Lab A – Background A . Calculations Using Powers of Ten • Division of powers of ten is similar, except you subtract the exponent part. For example: • 600000 / 300 = 6000 / 3 = 2000 • In scientific notation, this becomes • 6.0 x 10 5 / 3.0 x 10 2 = 2.0 x 10 (5 - 2) = 2.0 x 10 3 • You first divide the number part, then subtract the exponents. Astro 105 Fall 2022 Lab A – Background A . Calculations Using Powers of Ten • Raising a number in scientific notation to an exponent. • (2 x 10 2 ) 3 • First raise the number part (2.0) to the exponent = (2) 3 = 2 x 2 x 2 = 8 • Then raise the exponent to the exponent (you multiply the exponents together: • (10 2 ) 3 = 10 (2x3) = 10 6 • So, (2 x 10 2 ) 3 = 8 x 10 6 • Raising powers of ten to exponent involves multiply the exponents together Astro 105 Fall 2022 Lab A – Measurements and Powers of Ten B . Significant Figures • For this lab course, you will need to write the correct number of significant digits for calculations. • What you need to remember is that the mathematical results cannot be any more precise than the least precise value used in the calculation. • For example: 3. 14 x 6.9321 = 21. 76 • Note that the result has only two digits past the decimal point, because one of the factors (3.14) has only two digits past the decimal point. • Note: significant figures is not quite the same as rounding Astro 105 Fall 2022 Lab A – Measurements and Powers of Ten C . Data Collection • A main source of uncertainty in scientific numbers involves collecting data. E rrors related to the collection process, naturally creep in, and are not considered mistakes . In other words, each piece of data does not have infinite precision and is limited to how well the measuring instrument can be read . This is another example of how scientists use words differently • Errors ≠ Mistakes • This part of the lab has the student take multiple simple measurements (measuring the dimensions of your lab table) and then comparing each measurement with the average, and deciding how many significant digits the measurements, and the resulting calculation has. Astro 105 Fall 2022 Lab A - Exponents - Logarithms D. Logarithms • In this section you will use the log function on your calculator to determine the log of various numbers. • All you need to do in punch in the number and hit the log button. • On some calculators you need to hit log first, then type in the number. • For example: Find log (3): Type in 3, then hit log = 0.477 • Also: 5 Log (30.1/10) = 5 x Log (3.01) = 5 x 0.478 = 2.4 Astro 105 Fall 2022 Lab A – Measurements and Powers of Ten E . Graphing Data • Most of you have probably seen graphing numbers or coordinates with an X and Y axis in your math or other classes. When you did this, you calculated, and marked the positions of points on the graph and then drew straight or curved lines through those points. You will do the same for this part of the lab. • In order to visualize data or see trends, Astronomers and other scientists plot data in much the same way. • Note that the individual data points never exactly line up, because of measurement errors. Astro 105 Fall 2022 Lab A – Measurements and Powers of Ten E . Graphing Data • You have two sets of data to graph. Use graph paper provided, it already has the axis labeled. Don’t “connect the dots” but draw a smooth line or curve through the data. Connecting the dots is the wrong answer for this problem Astro 105 Fall 2022 Lab A – Measurements and Powers of Ten E . Graphing Data Astro 105 Fall 2022 Right Answer Wrong Answer Once again, on the graphs DO NOT CONNECT THE DOTS Draw a smooth line that fits most of the dots Astro 105 Fall 2022 Questions? Astro 105 Fall 2022