Question

You find yourself on a desert island and all you have is a copy of your textbook, Fundamentals of Renewable Energy Processes and a watch. The sky is very cloudy, so you can not see the stars. You determine that the time between sunset and sunrise is 10:05:10. You know the date is Dec 30, 2019. With this information is possible to figure out the latitude. Find it. Is this North or South? Use solar times for all calculations.

Answer 1

day length = 10.05.10

so converting them in hours

$1\, sec =\frac{1}{3600}\, hours$

1 min = - hours 60

$10.05.10 = 10\, hours + 5(\frac{1}{60})\, hours + 10(\frac{1}{3600})\, hours = 10.08611 \, hours$

$day \, length =\frac{2}{15}[\cos^{-1}(-\tan \phi \cdot \tan \delta )]$

$\delta = 23.45\sin \left [ \frac{360}{365}(284+n) \right ]$

n = number of days

n = January + February + March + April + May + June + July + August + September + October + November + December(till 30th Dec)

n = 31 + 28 + 31 + 30 + 31 +30 +31 + 31 + 30 +31 + 30 + 30 = 364 days

$\delta = 23.45\sin \left [ \frac{360}{365}(284+364) \right ]$

$\delta = -23.085 \,\, degrees$

$\phi = \, latitude \, in\, \, degrees$

10.08611ーー(cos-1 (-tan(d) * tan(-23.085))) 15

o = 30, 1 84°

As the phi is positive so we shall be in the NORTH

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