Download or view DurinsDay.frink in plain text format
// Calculate Durin's Day, from The Hobbit.
//
// "The first day of the dwarves' New Year, said Thorin, is as all should
// know the first day of the last moon of Autumn on the threshold of Winter.
// We still call it Durin's Day when the last moon of Autumn and the sun are
// in the sky together. But this will not help us much, I fear, for it passes
// our skill in these days to guess when such a time will come again."
//
// Many of these definitions are vague, and we use some conventions to put
// the dates earlier than a strict astronomical reading might yield. The
// astronomical figures are rigorous, but the clarity of Thorin's definition
// is in some question.
use sun.frink
// How many years should be checked?
years = 25
// How chatty should we be?
verbose[] :=
{
// true: report everything
// false: report New Year's Days and Durin's Days
return true
}
y = parseInt[input["Enter year: ",2000]]
limit = y + years
// GPS-surveyed position for east side of MIT's Infinite corridor, Cambridge,
// Massachusetts.
lat = 42.36002 degrees North
long = 71.09332 degrees West
// NWS for Denver, CO
//lat = 39.78 degrees North
//long = 104.88 degrees West
// Greenwich, England
//lat = DMS[51,28,38] North
//long = 0 degrees West
// Loop until we find a New Year's Day with:
// a sunrise or sunset when the moon is entirely above the horizon
// AND the separation between sun and moon is at least 7.5 degrees,
// which has been proven to be minimal for seeing a crescent.
// See http://www.skyandtelescope.com/observing/objects/projects/3308686.html
// and http://www.earthsky.org/faq/young-moon-visibility
do
{
found = false
dawn = false
nyd = NewYearsDay[y]
print[" New Year's Day occurs on "]
if (verbose[])
println["$nyd."]
else
println[(nyd -> ###yyyy-MM-dd###) + "."]
if (verbose[])
printSunMoonPos[nyd, lat, long]
sunrise = sunrise[nyd, lat, long]
sunset = sunset[nyd, lat, long]
if (verbose[])
println[" Sunrise is at $sunrise"]
[moonalt, sep] = printSunMoonPos[sunrise, lat, long]
if (moonalt > moonRadiusAngle[sunrise]) and (sep > 7.5 degrees)
{
found = true
dawn = true
}
if (verbose[])
println[" Sunset is at $sunset"]
[moonalt, sep] = printSunMoonPos[sunset, lat, long]
if (moonalt > moonRadiusAngle[sunset]) and (sep > 7.5 degrees)
{
found = true
dawn = false
}
if (! found) and (verbose[])
{
println[" This is not Durin's Day."]
println[]
}
if (found)
{
print["Durin's day occurs at "]
if (dawn)
print["dawn"]
else
print["dusk"]
println[" on " + (nyd -> ### MMMM d, yyyy ###) + "."]
if (verbose[])
println[]
}
y = y + 1
} while (y < limit)
// Print the position of sun and moon at a specified time.
printSunMoonPos[nyd, lat, long] :=
{
[sunaz, sunalt] = refractedSunAzimuthAltitude[nyd, lat, long]
[moonaz, moonalt] = refractedMoonAzimuthAltitude[nyd, lat, long]
sep = sunMoonAngularSeparation[nyd, lat, long]
if (verbose[])
{
illum = moonIlluminatedFraction[nyd]
illum1 = moonIlluminatedFraction[nyd + 1 minute]
if (illum1 > illum)
indicator = "waxing"
else
indicator = "waning"
println[" At this time, the altitude of the moon is: " +
format[moonalt, "degrees" , 5]]
println[" Angular separation: " + format[sep,"degrees",3]]
println[" Moon illuminated fraction: " +
format[illum, percent, 3] + "% ($indicator)"]
println[]
}
return [moonalt, sep]
}
// Find New Year's Day, the first day of the last month before the
// cross-quarter day between the autumn equinox and winter solstice.
NewYearsDay[y] :=
{
autumn = autumnEquinox[y]
winter = winterSolstice[y]
endautumn = autumn + (winter-autumn)/2
// Find the last new moon of "autumn."
nextmoon = endautumn
do
{
newmoon = newMoon[nextmoon]
nextmoon = newmoon - lunarmonth
} while newmoon > endautumn
// Return the new moon
return newmoon
}
Download or view DurinsDay.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen was born 19966 days, 15 hours, 42 minutes ago.