ModellingSunriseAndSunsetTimes

Modelling Sunrise and Sunset Times

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

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: $f(x)={a}\sin(bx+c)+d$

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.).

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.

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

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