Figure 4.16. Overall layout of a spreadsheet for lightcurve period determination.

Figure 4.16. Overall layout of a spreadsheet for lightcurve period determination.

Enter all of your data into your spreadsheet as a table of observation time (t) and differential magnitude [f (t)]. Select an (arbitrary) value of P—based on your best guess from a geometrical analysis such as described above. Then for night #2 and subsequent, derotate the time of each observation by t ^ t — NP, using whatever value of N will make the data overlap in time with night #1. Plot the result, adjusting the level of night #2's data by a delta-comp if needed. Iterate through estimates of P and N until you find the "best-fit" estimate of the period, where the data from multiple nights overlaps nicely, and the curve is a plausible rotational lightcurve.

The overall structure of the spreadsheet is illustrated in Figure 4.16. The spreadsheet is built and used in seven steps. Steps 1 through 5 are devoted to creating the spreadsheet, and entering and formatting your data. Steps 6 and 7 are where the actual data analysis happens. You'll have to go through all seven steps for your first project, but once the spreadsheet has been created, you can enter new data and analyze it without having to repeat steps 1 through 6.

Step 1: Set up the headings, enter your raw data, and calculate the time of each observation As shown in Figure 4.17, your raw data is entered in columns A and C. Column A contains the Julian Date (JD) of each observation.* Column C contains the differential photometry (object minus comp star) in magnitudes. Column B

*If your observations span more than a few nights, it is wise to include light-time correction in the observations time, so that the "observation time'' represents the time that the light left the asteroid, rather than the time that it arrived at Earth. (See Appendix A for a discussion of "light-time" corrections, and of Julian Days.)

contains the formula that translates JD into "hours since the first data point.'' This is primarily a mathematical convenience, since it's easier to work with small numbers, and it's common (although not mandatory) to report lightcurve periods in "hours" rather than "days".

Step 2: Set Column D to contain the Tgt-Comp data from Session 1 Enter the equation that copies Session 1 data into column D, as shown in Figure 4.18.

Step 3: Calculate the "wrapped" time of Session 2 observations, and the associated "adjusted" Obj-Comp As shown in Figure 4.19, column E is where you enter the formula that "derotates" Session 2 data by an integer number of rotations of the asteroid. Cell F4 contains the number of rotations through which to perform the derotation (N2). Note that when you are doing the analysis in Step 7, you must only enter integer values for N2 into cell F4. Column F contains the formula that adjusts the differential magnitude up or down by delta-comp, to align sessions that used different comp stars. Cell F3 contains the delta-comp by which the differential photometry will be adjusted; delta-comp can be any number, and may be positive or negative.

In cell B2, create a named variable "P'', and enter any arbitrary value. This is your estimated period (in hours).

The Excel formula in cell D6 is: =C6

Copy this formula down column D. to the bottom of the data for Session 1.

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