Movatterモバイル変換

The following table calculates the exposed part b in relation to the whole circle. The formulas mention 3 parameters, which signify:

Note: The expression "observer" in the remarks refers to a hypothetical observer located on the center of the planet's "disc".

Angle between observer and sun's zenith:

Thanks to Andrew Green for spotting an error which was introducedwhile translating from HTML to XLM in formulas#m_eq_1(1) and#m_eq_9(9).

Latitude of observer:

Angle between solar disc and sun's zenith:

Distance from observer to sun's zenith:

Distance from observer to the center of the sun's circle:

Exposed radius part between sun's zenith and sun's circle:

Adjust range:

Angle between center of sun's disc and sunrise or sunset point on the solar circle (not the planet's disc), resp.:

Exposed fraction of the sun's circle (0=never...1 = whole day):

To get the number of hours the sun shines at the givenDay at the given LatitudeLat,b needs to be multiplied by 24.

Function Graphs

Notice, that depending on what your plotting software accepts (deg/rad), you might need to modify theb formula slightly. For example would you useARCCOS(1-m)/(2*PI())*360/180 inMicrosoft Excel, which simplifies toARCCOS(1-m)/PI().

Thanks to reader justanote for this observation.

Above formulas for the Length of Dayb produce the following graphs over a whole year, shown for the latitudes at 0deg, 10deg ... 90deg North:

/img/lod_fig02.jpg

The twilight angle (sun below horizon), as per above definition:

Thickness of the planet's disc:

The anglev is identical with the Latitude. This is true along the whole radius of the solar circle, particularly also where the distance between the solar circle and the surface of the planet disc ish:

Knowing the anglev, the radius fractioni (an extention of the radius fractionm) can be calculated:

The whole radius fractionm+i defines the point, at which the planet disc's lower surface is crossed by the solar circle. The valuem is the same as calculated above. Note, however, that its uncorrected value must be used:

Adjust range: 0...2 is the valid range (see comments in the formula table of the preceding section).Note, that them part (before adjustment) is the same as in the previous section, but range adjustment may not happen before the addition of thei term.

Angle between center of sun's disc and lower twilight point on thesolar circle (not the planet's disc):

Exposed fraction of the sun's circle (0=never...1=whole day).The arc describes the daytime plus both twilight zones (b+2e):