Measuring the smiling morn

[sawyl]

I've finally got round to quantifying the changes in day length — something I often find myself pondering whilst on my early morning run, especially at this time of year when it seems to change so rapidly, but which ceases to interest me once I get home. After deciding to do something about it, I ran a couple of equations through Grapher to generate a curve showing day length:

Then it was a simple matter to determine the differential and convert the units from hours to minutes:

Now that I've worked out the numbers and confirmed my observations about the darkening mornings, I need never worry about any of this ever again. Hurrah!

Comments

[(Anonymous)]

you haven't labelled your axes. tsk tsk. and where's the raw data.

[drspleen.livejournal.com]

oops. that was me.

[sawyl.livejournal.com]

Ok, you asked for it. Here are the equations I used. I started off by converting the latitude into radians:

I then calculated the solar declination using the julian day, x, as my variable:

Then I calculated the daylength based on the sunrise time:

All of which makes the differential:

As to the lack of labels, I can only appologise — I couldn't work out how to get Grapher to label to axes and the documentation is, to say the least, sketchy.