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General Astronomy Using Excel for Lab Analysis

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Introduction Being able to use a spreadsheet to help in analysis of any laboratory work is a very useful skill. You can use it to tabulate your data, perform (repetitive) computations and do a variety of data analysis procedures –These include, but are not limited to Graphics Statistics Correlations

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These notes will lead you through the process of setting up a spreadsheet to analyze one of the computer labs assigned for this class. We will assume that the lab has been done and the data is now available We will be using the Microsoft Excel © spreadsheet, but most spreadsheet programs will operating in a similar fashion. Introduction

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Starting up… Start your spreadsheet program by double-clicking its icon

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The program should appear looking something like this:

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Let's start by clicking the cell labeled by the intersection of column 'A' and row '1': Then typing a heading

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Next add a set of labels for the table. It should look like the table shown in the lab: Notice that we've boldfaced the header; used 'symbol' format to get the Greek letters, and put some boxes about the headings

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To insert a symbol, click the Symbol on the Ribbon (top portion). A box will appear and you can click the symbol you want. Also we need some constants, so we will insert 4 blank rows to add things like the speed of light, c, and the laboratory wavelengths:

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Now, type in the values obtained during the lab

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Adding formulas Now, we have to add the formulas to do all the calculations. We will only use the 1 st row. Once we get that one right we can copy (or using spreadsheet-speak: replicate) to the other rows. A formula starts with an '=' sign in the cell. You use a combination of typing and the mouse to build it – generally the keyboard to type operations such as multiply (*) and the mouse to select other cells in the formula. For example in cell H10, we will calculate the difference between the measured value, in cell F10 and the lab value in cell C4. Click cell H10, type a '=' then click cell F10, type a '-' then click cell C4 You should see the following in the white area above the column labels: =F10-C4 [Note: we are making a mistake here. The formula itself is OK. However there is a slight subtlety that can cause problems later, but at this point we want to do that to show what will happen.]

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You can see the result, 88.3 in the cell. Now do the same thing for cell I10. It should look like: =G10-C5

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Now, use the mouse to select both H10 and I10, then use the 'copy' (or Control-C). Then, click on cell H11, and 'paste' (Control-V)

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Look at H11 and I11. Something is very wrong! If you select the H11, the formula says: =F11-C5 That's incorrect. That is λ K (measured) - λ H (Lab) It should be, =F11-C4

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Using the '$' operator The problem was caused during the copy-paste. Spreadsheets are setup to automatically adjust the rows and columns - When we pasted into H11 from H10 all rows in the formula were incremented by 1. We need to tell the program that it should not change the C4 to a C5. This is done with the '$' mark. Placing this before a row value (or a column value) freezes the value. So the formulas in H10 and I10 should look like: =F10-C$4 =G10-C$5 Then when we copy-paste the values in H11 and I11 will look like =F11-C$4 =G11-C$4

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In fact, now we can copy H10 and G10 and using the mouse, select H11 through H14 and paste. Now, that looks good - and we did the arithmetic for all the rows of data with a couple of keystrokes

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Now we can write the formula for VK. Notice that we freeze both the column and the row. Next we'll select J10 and copy; select K10 and paste. Then select both J10 and K10 and paste into J11 through J14

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That was easy. Notice the formula in the selected cell, K14, has automatically incremented the needed cells, but kept the reference to the speed of light in cell C3. Now, select L10. The formula is =AVERAGE(J10:K10). Then select it and copy-paste (replicate) it down the rows

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A really easy way to do repetitive calculations. Now the hard one, the formula for Distance will be: (in D10) =10^((C10-B10+5)/5) Or, "10 to the ((m-M+5)/5" The formula in E10 is simply: =D10/1000000

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All of the basic arithmetic has now been done. (With a bit of formatting to make the decimal places look OK). Now we can add the analysis portion.

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We need to save some room for the images, so let's hide a few rows. Use the mouse to 'paint' rows 2 through 6; Then right-click the mouse. A popup panel will appear. Select 'hide'. Notice the rows "jump" from 1 to 7. You can bring them back by doing the same selection, but choosing 'unhide' from the popup

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On the ribbon (the top portion of the screen), select Insert, then Scatter, then click the image with points, but no lines.

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Right-clicking the chart, then selecting 'Select Data' followed by 'Add' brings up an Edit Series popup. Use the mouse to enter data into the x and y boxes. Then hit OK for this Edit Series and for the Select Data boxes. Then double-click the chart, and – on the ribbon – click 'layout 3'. You may have to again select Change Chart Type and select the points only image.

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Right-clicking the Trendline and then selecting Format Trendline brings up a popup. Select 'Set Intercept = 0.0' and 'Display Equation…' The slope of the trendline, in this case 68.79, is the Hubble Constant, H We can copy that to a convenient column

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Now we can just add the remaining computations. Using the fact that 1 pc = 3.09 x 10 13 Km

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EASY! Formulas: Cell K19: =I19*I18*1000000 Cell I20: =I19*I17 Cell I21: =K19/I20/31500000 Cell K21:=I21/1E9

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