How do you calculate angle of incidence given latitude and time of the month? Please use anything other than snell's formula.
For example: latitude 60 degrees North on June 21st.
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Suppose first the Earth is not tilted on its orbit around the Sun. The rays of Sun will arrive perpendicular at any point on the Earth Ecuador, and the angle of incidence of Sun light at a given point will be just the latitude of the point. This will happen no matter the time of the year. See the first figure below.
`/_i = latitude`
Now suppose the Earth is tilt on its axis with the angle 23.45 degree. See the second figure. At the moment of year when you have the longest day in northern hemisphere (21 June, position 1) the angle of incidence at the Ecuador will be -23.45 degree (because of the tilt angle). Thus in this day on a given point on the Earth the angle of incidence will be
`/_i = latitude - 23.45`
Now suppose the Earth starts to rotate around the Sun. The angle of incidence will start to change with the day of the year as a cosinusoidal function of the angle that Earth is making on its trajectory around the sun.
where the time `t` is measured in days elapsed from 21 June (the longest day in northern hemisphere).
Therefore at latitude 60 degree North on June 21, the angle of incidence will be `(60-23.45)*cos(0) =36.55 deg`
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