oce (version 1.1-1)

moonAngle: Lunar Angle as Function of Space and Time

Description

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.

Usage

moonAngle(t, longitude = 0, latitude = 0, useRefraction = TRUE)

Arguments

t

time, a POSIXt object (converted to timezone "UTC", if it is not already in that timezone), a character or numeric value that corresponds to such a time.

longitude

observer longitude in degrees east

latitude

observer latitude in degrees north

useRefraction

boolean, set to TRUE to apply a correction for atmospheric refraction. (Ignored at present.)

Value

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.

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Alternate formulations

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.

References

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.

See Also

The equivalent function for the sun is sunAngle.

Other things related to astronomy: eclipticalToEquatorial, equatorialToLocalHorizontal, julianCenturyAnomaly, julianDay, siderealTime, sunAngle

Examples

# NOT RUN {
library(oce)
par(mfrow=c(3,2))
y <- 2012
m <- 4
days <- 1:3
## Halifax sunrise/sunset (see e.g. https://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)
}

# }