Continuing from the last post with a slight pre-occupation with the nature and passing of time at this point in the calendar (i.e. start of a new year) ... some of the more interesting things I have learned during my teacher career have occurred due to my own students' natural curiosity. Really good questions driven by a young person's innate desire to know something is a great platform for learning - not only for the student but also for the teacher. And some of the most intriguing questions have to do with time and it's measurement. Why are there 365 days in a year?  25 hours in a day?  60 seconds in a minute?  Why do we need a leap year?  What is a leap second?

These last two questions lead to realizing that our man-made attempts to measure time in a regular and constant fashion is only accomplished by using some "correction" factors. The position (tilt) and motion of the earth is not 'regular' resulting in the fact that "clock" time (constant and regular) is not the same as "sun" time (position of the sun in the sky). Our measurement of time is based on the regular movement of the earth around the sun - but it's not precisely regular for two reasons: (1) the earth's equator is tilted at an angle of about 26 degrees in relation to the plane containing the earth's orbit about the sun, and (2) the earth's orbit about the sun is an ellipse rather than a circle. The length of a day is the time it takes for the sun to return to the highest point in the sky. But this will vary during a year due to the two reasons mentioned. Our clock time is determined by taking into account the effect that the earth's tilt (obliquity) and the unequal motion of the earth in relation to the sun (elliptical orbit) has on the time it takes between consecutive occurrences of the sun being at the highest point in the sky. The graph of each of these effects where day of the year versus # of minutes deviating from 24 hours is a sinusoid (transformation of a sine curve).  Although a bit oversimplified, essentially the sum of these two effects (obliquity & elliptical orbit) - thus the sum of the two graphs - gives us our clock time. This relationship is usually referred to as the Equation of Time (quite a serious sound to that phrase).

The graph above illustrates how the Equation of Time is determined by the sum of two sine curves.  I'm quite certain that this topic could be prove to be an appropriate area of investigation for a student to write an Exploration for the Internal Assessment component - probably most appopriate for the SL course.

see the page on the UK's National Maritime Museum on the Equation of Time