# δ Cephei: Worksheet #2

 Fall 2010 ASTR 110L, Sec. 1 Name: ________________

 Date/Time Days Phase Magnitude Obs. 1. ____________ ____________ ____________ ____________ ____ 2. ____________ ____________ ____________ ____________ ____ 3. ____________ ____________ ____________ ____________ ____ 4. ____________ ____________ ____________ ____________ ____ 5. ____________ ____________ ____________ ____________ ____ 6. ____________ ____________ ____________ ____________ ____ 7. ____________ ____________ ____________ ____________ ____ 8. ____________ ____________ ____________ ____________ ____ 9. ____________ ____________ ____________ ____________ ____ 10. ____________ ____________ ____________ ____________ ____ 11. ____________ ____________ ____________ ____________ ____ 12. ____________ ____________ ____________ ____________ ____ 13. ____________ ____________ ____________ ____________ ____ 14. ____________ ____________ ____________ ____________ ____

### Instructions

First, collect the data. We have observed δ Cephei on five nights (28-Sep, 05-Oct, 12-Oct, 19-Oct, & 16-Nov); weather permitting, we may observe it again tonight. Copy the dates, times, and average magnitudes for each night from δ Cephei Worksheet #1 to the table above. Eight more observations (made by Mike Nassir and Josh Barnes) will be provided in class; there will be two observations on pink paper, another two on purple paper, and four individual observations on white paper. Make sure the dates of the observations on white paper are all different. Copy the dates, times, magnitudes, and observer's initials to the table above (the initials go in the Obs. column.

Second, plot magnitude versus date on the top graph provided with this handout. Plot each magnitude and date as accurately as you can, taking account of the time the observations were made. Don't expect to see any obvious pattern in this graph; the star has gone through many cycles this semester, and our observations catch the star at random points in its cycle.

Third, for each observation, calculate the number of days since 01-Sep at 0:00 HST. Express your answer to the nearest tenth of a day, and write this number in the Days column.

• Example: The observation on 05-Oct at 21:00 HST was made 29 + 5 + (21÷24) = 34.875 days after 01-Sep at 0:00 HST, so write 34.9 in the Days column.

Fourth, for each observation, divide the number of days since 01-Sep at 0:00 HST by the period of δ Cephei, which is 5.37 days, and keep only the part after the decimal point. Write this number in the Phase column, rounding it to two significant figures.

• Example: For the observation on 05-Oct, we have 34.9 ÷ 5.37 = 6.49907, so write 0.50 in the Phase column.

Fifth, plot magnitude versus phase on the bottom graph provided with this handout. Plot each point twice; once with the phase you just computed, and again after adding 1 to the phase.

As you plot these points, you should gradually see a regular pattern of variation emerge; this is the ``light curve'' of δ Cephei. (The pattern will appear to repeat, since each point is plotted twice). Why does this graph display a regular pattern, while the first one did not? The answer has to do with the fact that a star like δ Cephei varies in a regular and predictable way, repeating the same behavior again and again. Because of this, we can make observations over a long period, calculate where in the star's cycle each observation falls, and put them together to see how the star varies over the course of its cycle.

 Joshua E. Barnes      (barnes at ifa.hawaii.edu) Updated: 24 November 2010 http://www.ifa.hawaii.edu/~barnes/ast110l_f10/delta_cephei_ws2.html