Using a period of 5.4 days, calculate the phases of the Delta Cephei measurements. Then you can plot magnitude versus phase. You should find that the magnitudes at the same phase will be about the same -- not exactly the same, though, because of the measurement errors that inevitably creep in. The accuracy of the plots is higher when the dates are expressed in terms of fractional days.
Try recomputing phases using different periods, say, 4.0 days or whatever you want. Prepare new phase diagrams. How does they compare to the first one?
Based on the past behavior of the Delta Cephei, the maximum brightness occurs on the following dates for the upcoming months. These dates are for the Pacific time zone; the date in other locations occasionally differs by one day.
Dates of Maximum Brightness
of Delta Cephei
|Sep. 29||Oct. 31||Dec. 2||Jan. 4, 1996|
|Oct. 4||Nov. 6||Dec. 8||Jan. 9|
|Oct. 10||Nov. 11||Dec. 13||Jan. 14|
|Oct. 15||Nov. 16||Dec. 19||Jan. 20|
|Oct. 21||Nov. 22||Dec. 24||Jan. 25|
|Oct. 26||Nov. 27||Dec. 29||Jan. 30|
Extra creditIf you're looking for a way to challenge advanced students, have them express their data in terms of "Julian date,'' an astronomical calendar system described in almanacs (such as The World Almanac) and books for advanced amateurs (such as The Observer's Handbook). The integer part of a Julian date represents the number of days elapsed since noon on Jan. 1, 4713 B.C. The fractional part represents the Universal Time. One quirk of the system is that a Julian day begins at noon, rather than midnight. The Julian date for midnight Jan. 1, 1995 is 244 9718.5; for midnight Jan. 1, 1996 the Julian date is 244 0083.5.
If students express their data in terms of Julian date, they can send them to the American Association of Variable Star Observers in Cambridge, Mass. (email: firstname.lastname@example.org). The maximum brightness of Delta Cephei occurs at the Julian dates 2449722.05 + 5.366269 N, where N is an integer.
The following table lists the measurements of Delta Cephei made by one amateur astronomer in autumn 1990. Your students can use these data for practice.
Measurements of Delta Cephei, Autumn 1990
|Calendar Date (Pacific time zone)||Julian Date||Magnitude|
|Nov. 1 (Oct. 32)||2448197.51||4.0|
Nov. 5 (Oct. 36)
|Nov. 6 (Oct. 37)||2448202.51||4.1|
Source: American Association of Variable Star Observers
This activity is a simplified version of one that appeared in Hands-On Astrophysics, a series of activities prepared by the American Association of Variable Star Observers with support from the National Science Foundation.
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