moonAngle {oce} | R Documentation |
Lunar angle as function of space and time.
moonAngle(t, longitude=0, latitude=0, useRefraction=TRUE)
t |
time, a POSIXt object (must be in timezone UTC), or a numeric value that corresponds to such a time. |
longitude |
observer longitude in degrees east |
latitude |
observer latitude in degrees north |
useRefraction |
boolean, set to |
The calculations are based on formulae provided by Meeus [1982],
primarily in chapters 6, 18, and 30. The first step is to compute sidereal
time as formulated in Meeus [1982] chapter 7, which in turn uses Julian day
computed according to as formulae in Meeus [1982] chapter 3. Using these
quantities, formulae in Meeus [1982] chapter 30 are then used to compute
geocentric longitude (lambda, in the Meeus notation),
geocentric latitude (beta), and parallax. Then the
obliquity
of the ecliptic is computed with Meeus [1982] equation
18.4. Equatorial coordinates (right ascension and declination) are
computed with equations 8.3 and 8.4 from Meeus [1982], using
eclipticalToEquatorial
. The hour angle (H) is
computed using the unnumbered equation preceding Meeus's [1982] equation
8.1. Finally, Meeus [1982] equations 8.5 and 8.6 are used to calculate the
local azimuth and altitude of the moon, using
equatorialToLocalHorizontal
.
A list containing the following.
time |
time |
azimuth |
moon azimuth, in degrees eastward of north, from 0 to 360. Note: this is not the convention used by Meeus, who uses degrees westward of South. (See diagram below.) |
altitude |
moon altitude, in degrees from -90 to 90. (See diagram below.) |
rightAscension |
right ascension, in degrees |
declination |
declination, in degrees |
lambda |
geocentric longitude, in degrees |
beta |
geocentric latitude, in degrees |
diameter |
lunar diameter, in degrees. |
distance |
earth-moon distance, in kilometers) |
illuminatedFraction |
fraction of moon's visible disk that is illuminated |
phase |
phase of the moon, defined in equation 32.3 of Meeus [1982]. The fractional part of which is 0 for new moon, 1/4 for first quarter, 1/2 for full moon, and 3/4 for last quarter. |
Formulae provide by Meeus [1982] are used for
all calculations here. Meeus [1991] provides formulae that are similar,
but that differ in the 5th or 6th digits. For example, the formula for
ephemeris time in Meeus [1991] differs from that in Meeus [1992] at the
5th digit, and almost all of the approximately 200 coefficients in the
relevant formulae also differ in the 5th and 6th digits. Discussion of
the changing formulations is best left to members of the astronomical
community. For the present purpose, it may be sufficient to note that
moonAngle
, based on Meeus [1982], reproduces the values provided in
example 45.a of Meeus [1991] to 4 significant digits, e.g. with all angles
matching to under 2 minutes of arc.
Dan Kelley, based on formulae in Meeus [1982].
Meeus, Jean, 1982. Astronomical formulae for calculators. Willmann-Bell. Richmond VA, USA. 201 pages.
Meeus, Jean, 1991. Astronomical algorithms. Willmann-Bell, Richmond VA, USA. 429 pages.
The equivalent function for the sun is sunAngle
.
library(oce) par(mfrow=c(3,2)) y <- 2012 m <- 4 days <- 1:3 ## Halifax sunrise/sunset (see e.g. http://www.timeanddate.com/worldclock) rises <- ISOdatetime(y, m, days,c(13,15,16), c(55, 04, 16),0,tz="UTC") + 3 * 3600 # ADT sets <- ISOdatetime(y, m,days,c(3,4,4), c(42, 15, 45),0,tz="UTC") + 3 * 3600 azrises <- c(69, 75, 82) azsets <- c(293, 288, 281) latitude <- 44.65 longitude <- -63.6 for (i in 1:3) { t <- ISOdatetime(y, m, days[i],0,0,0,tz="UTC") + seq(0, 24*3600, 3600/4) ma <- moonAngle(t, longitude, latitude) oce.plot.ts(t, ma$altitude, type='l', mar=c(2, 3, 1, 1), cex=1/2, ylab="Altitude") abline(h=0) points(rises[i], 0, col='red', pch=3, lwd=2, cex=1.5) points(sets[i], 0, col='blue', pch=3, lwd=2, cex=1.5) oce.plot.ts(t, ma$azimuth, type='l', mar=c(2, 3, 1, 1), cex=1/2, ylab="Azimuth") points(rises[i], -180+azrises[i], col='red', pch=3, lwd=2, cex=1.5) points(sets[i], -180+azsets[i], col='blue', pch=3, lwd=2, cex=1.5) }