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!! Modelling Sunrise and Sunset Times

The graph of the sunrise and sunset times in London (U.K.) throughout the year is shown on the site below:

The graphs of the sunrise and sunset times in London (U.K.) throughout the year are shown below:

IMG:SunriseTime.gif

IMG:SunsetTime.gif

Can you explain the kinks in the curve?

Accurate data for various locations can be found at http://www.timeanddate.com/worldclock/sunrise.html

By making a simple adjustment, the sunrise and sunset times for London (U.K.) (without kinks !!!) can be modelled using the sine function.

Consider the sine function: EQN:f(x)={a}\sin(bx+c)+d

The project is to choose the values of the coefficients !/ a, b, c !/ and /d/ to best model

the annual cycle of sunrise (or sunset) times in London (U.K.).

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Hints:

* On what dates are the vernal equinox and autumnal equinox?

* On what dates are summer solstice and winter solstice?

* Consider how the graph changes for Peterborough (U.K.) a city 75 miles North of London (U.K.)

* Find the functions that best models the sunrise and sunset times at Peterborough (UK).

* Consider how the graph changes for Bristol (U.K.), a city 107 miles West of London (U.K.)

* By looking at the data, test your predictions.

* Investigate how change of latitude alters the graph of the sunrise and sunset times.

* Investigate how change of longitude alters the graph of the sunrise and sunset times.

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This is one of the many Enrichment tasks on this site.