Index-a Don't Forget To Hit <ESC> before going to a different page. Let's play a game of 30 questions. No, not that old standard of 20 questions, but one with an extra 10 questions added in and one that uses numeric answers (from 1 to 30). If you get stumped, go on to the next one. Perhaps the answer you need will be one of those left over when you complete all the questions you're sure of. Each answer is a number. The answers are the numbers 1-30. Each number appears only once. (Obviously) the questions are not in the right order.. 1. Aside from an extra 385 yards, how many miles is a marathon race? 2. If 27 solid cubes are formed into one big 3x3x3 cube how many individual cubes, at most, are visible from any single angle? 3. In the movie Spinal Tap what number is: "Well, it is one louder.."? 4.

'Via Dolorosa' is the (how many) Stations of the Cross, the Christian ritual tracing the key stages of the death of Jesus, beginning with his condemnation and ending with his being laid in the tomb? 5. How many dots are on a (standard 1-6) die? 6. The Russian 'Crimea Highway' trunk road from Moscow to the Crimea in Ukraine is the M (what)? 7. What number, between two hyphens, is used by journalists, etc., to mark the end of a newspaper or broadcast story? 8. How many unique dominoes are in a standard 'double six' set? 9. What number turned on its side (rotated 90 degrees) is the symbol for infinity? 10. The Marvel Comics superhero team led by Mr Fantastic was the Fanstastic (what)? 11. What is the larger number of the binary system? 12. Japanese haiku poems loosely comprise how many syllables? 13. The Tropics of Cancer and Capricorn are respectively (what number)-and-half degrees north and south of the Equator? 14. What number is Hurricane on the Beaufort Scale? 15.

Greek deka, and Latin decem, are what number? 16. Conventionally how many books are in the Bible's New Testament? 17. How many legs (or arms) are most usually on a starfish? 18. A lunar month is an average (how many) days plus 12 hours, 44 minutes and 3 seconds? 19. 'Roaring' refers to what pluralised number in describing a 1900s decade of western world prosperity? 20. Traditionally what number of years anniversary is symbolized by silver? 21. What is generally stated to be the number of major joints in the human body? 22. What number is the French coded slang 'vingt-deux!', which warns that police are coming? 23. What is the only number that equals twice the sum of its digits (digit means numerical symbol)? 24. The early/mid-1900s American vaudeville comedy act was called the (how many) Stooges? 25. Any line of three numbers in the 'magic square' (a 3 x 3 grid of the numbers 1-9) adds up to what? 26.

What is the international SPI resin/polymer identification coding system number (typically shown within a recycling triangle symbol) for polystyrene? 27. Traditionally the diameter of the 45rpm gramophone record is (how many) inches? 28. Pure gold is (how many)-carat? 29. The expression 'On cloud (what)' refers to being blissfully happy? 30. Each player begins with (how many) pieces in a game of chess? Daniel David "Danny" Kirwan (born 13 May 1950) is a British musician whose greatest success came with his role as guitarist, singer and songwriter with the blues-rock band Fleetwood Mac between 1968 and 1972. Kirwan's first recorded work with the band was on the huge instrumental hit single "Albatross". Green later stated that, "I would never have done "Albatross" if it wasn't for Danny. I would never have had a number one hit record." The B-side of the single was Kirwan's first published tune, the instrumental "Jigsaw Puzzle Blues".

This was an old clarinet piece, written by Joe Venuti and Adrian Rollini, and recorded by the Joe Venuti / Eddie Lang Blue Five in 1933. Kirwan had adapted the piece for himself and Green to play on guitar, but Green remembered, "I couldn't do it properly... My style wasn't all that satisfactory to Danny, but his style wasn't all that satisfactory to me." So Kirwan played all the guitar parts himself. . Exactly how long is a lunar month? | Old Farmer's Almanac Exactly how long is a lunar month? Share: Question: Exactly how long is a lunar month? Answer: The Moon’s synodic period (the length of a lunar month) is 29.53059 days – or 29 days, 12 hours, 44 minutes, and 2.8 seconds. Lunar Month / OPTcorp.com | OPT Telescopes Lunar Month This entry was posted on October 20, 2008 by The Team at OPT. In lunar calendars, a lunar month is the time between two identical syzygies (new moons or full moons). There are many variations.

In Middle-Eastern and European traditions, the month starts when the young crescent Moon becomes first visible at evening after conjunction with the Sun 1 or 2 days before that evening (e.g. in the Islamic calendar). In ancient Egypt the lunar month began on the day when the moon could no longer be seen just before sunrise. Others use a reckoned moon (e.g. the Hebrew calendar), or use a tabular scheme (Ecclesiastical lunar calendar). Yet others run from full moon to full moon. Calendars count integer days, so months may be 29 or 30 days in length, in some regular or irregular sequence. But all lunar months approximate the mean length of the synodic month of approximately 29.53059 days (29 days, 12 hours, 44 minutes and 3 seconds). There are several different ways of expressing the lunar month. The Moon's orbital period in a non-rotating frame of reference (which on average is equal to its rotation period) is about 27.32 days (27 days, 7 hours, 43 minutes, 11.6 seconds).

This is known as a sidereal month and is measured by observing how long it takes the Moon to pass a fixed star on the celestial sphere. A synodic month is 29.53 days (29 days, 12 hours, 44 minutes, 2.8 seconds) and is measured from New Moon to New Moon. A New Moon is defined to occur when the Moon has the same ecliptic longitude as the Sun, as seen from the center of the Earth : i.e. when the Sun, Moon and Earth are almost on one line. A synodic month is longer than a sidereal month because the Earth-Moon system is orbiting the Sun in the same direction as the Moon is orbiting the Earth. Therefore, the Sun appears to move with respect to the stars , and it takes about 2.2 days longer for the Moon to return to the apparent position of the Sun. The synodic month is the most common way of expressing the lunar cycle. An anomalistic month is the Moon's orbital period measured from perigee to perigee - the point in the Moon's orbit when it is closest to Earth. An anomalistic month is about 27.55 days on average.

The tropical month is the time for the Moon to return to the same ecliptic longitude, i.e. measured from the equinox ; it is slightly shorter than the sidereal month because of precession of the equinoxes. The draconic month or nodal month is the period in which the Moon returns to the same node of its orbit; the nodes are the two points where the Moon's orbit crosses the plane of the Earth's orbit. Its duration is about 27.21 days on average. This entry was posted in Uncategorized on October 20, 2008 by The Team at OPT. ← Previous Post Next Post → Leave a Reply Does a Premature Birth Change Your Sun-Sign? Does a Premature Birth Change Your Sun-Sign? by Elbert Wade, PMAFA - Professional Certified Consultant Astrologer Copyright � 2014 - 2016 - Elbert Wade - Worldwide Rights Reserved Astrologer Elbert Wade often gets questions from site visitors about how a premature birth (less than 9 months) might change someone's Sun-Sign. And this, of course, is very important from an astrological perspective.

Let's attempt to shed some light -- but not to completely settle this matter since that would be impossible in every individual case. Question 1: First and very important, were you (or someone else) really born prematurely? Consider these facts. The normal human gestation period is nine LUNAR months, not nine calendar months. (Gestation begins when the fertilized zygote implants in the female uterus and ends with the actual birth.) Question 2: How many days equal a calendar month? Answer: Calendar months (depending on the year) range from 28 (29 in leap years -- see below) to 30 or 31 days. (Months in normal years equate to 30.41666666 days (30.4+); in Leap years the result is 30.5 days.) Thirty days hath September, Which has 28 days time; Leap years, February has 29. Question 3: How many days are in a LUNAR month? Answer: No matter which year, a Lunar month is 29 days plus 12 hours and 44 minutes (essentially 29 and 1/2 days).

That is the amount of time it takes for the Moon to pass through each of its eight phases -- New Moon, New Crescent, First Quarter, New Gibbous, Full Moon, Old Gibbous, Last Quarter, and Old Crescent, which may or may not (most likely) be totally in the same calendar month. (This lunar process is known as a synodic month.) Question 4: How many 24-hour days are required for a normal human full gestation ? Answer: The average (meaning some slighty less, some slightly more) length of human gestation is 280 days, or 40 weeks, from the first day of the woman's last menstrual period. (Question: Where is this date actually recorded by every female of child-bearing age?) COMMENT: It is worth noting that often older family members/friends may "calculate" the birth date using calendar rather than Lunar months, or might use flawed math -- or perhaps some "folklore" means. Friends/family members may take great joy in telling the expectant mother the birth date -- and too often they are wrong. This may cause the expectant mother great concern and consequently cause her to believe the baby is premature -- when it is not.

CONCLUSION (?): With so many possible variables, it might be difficult to know -- without calculating a birth chart for the date, correct time and place of birth -- which is the actual Sun-Sign, but if the birth is just a few hours/or less than a day (depending on time zone) after the Sun moves to a new sign, your (or their) Sun-Sign might not be changed -- at least in a large percentage of premature births -- which in fact may not actually be premature. ADDITIONAL COMMENT: If the birth was, without any doubt whatsoever, actually premature then the Sun-Sign would be changed but ONLY from the one others -- not you -- anticipated. And whether or not it is the one you would have chosen you must accept and live with it for your entire lifetime. It's always best to love whatever your Sun-Sign and strive to better understand both its potential positives and negatives early to learn how to make the most of whatever Sun-Sign it may be. (An in-depth natal horoscope reading can help with this.) BOTTOM LINE: The Sun-Sign is ALWAYS determined by the actual date of birth and the hour (time) and place -- never by the "normal" or "expected" date of birth.

Astrologically (and medically), birth time is defined as that moment when the infant first inhales oxygen, thereby making the transition from a liquid to a gaseous (air) environment. Fact: Nobody can claim any Sun-Sign until they actually are born by whatever means -- natural, c-section, induced or whatever else. Seriously consider this: How can anything be changed before it exists in fact or actually happens? FOOTNOTE: Also consider that in some cases the claim of a "premature" birth is an attempt to cover for an out-of-wedlock pregnancy perhaps leading to a legal marriage ("shot-gun"?) at some time (weeks or months) after the fact. (Typically this might apply to the first-born -- or only offspring -- in a belated legal marriage.) Check For Leap Year -- Year: is Lunar month - definition of lunar month by The Free Dictionary Lunar month - definition of lunar month by The Free Dictionary Related to lunar month: lunar calendar lunar month n. The average time between successive new or full moons, equal to 29 days, 12 hours, 44 minutes. Also called synodic month.

lunar month (Units) another name for synodic month See month 6 month (mʌnθ) n. 1. any of the 12 parts, as January or May, into which the calendar year is divided. 2. the time from any day of one calendar month to the corresponding day of the next. 3. a period of four weeks or 30 days. 4. a. Also called solar month. one-twelfth of a solar year. b. Also called lunar month. the period of a complete revolution of the moon around the earth, as between successive new moons ( synodic month ), or between successive conjunctions with a star ( sidereal month ). 5. months, an indefinitely long period of time: I haven't seen him for months. Idioms: a month of Sundays, an indeterminately great length of time. [before 900; Middle English; Old English mōnath; c. Old Frisian mōnath, Old High German mānōd, (German Monat), Old Norse mānathr, Gothic mēnōths.

See moon ] ThesaurusAntonymsRelated WordsSynonymsLegend: Lunar month L Lunar month In lunar calendars , a lunar month is the time between two identical syzygies (new moons or full moons). There are many variations. In Middle-Eastern and European traditions, the month starts when the young crescent moon becomes first visible at evening after conjunction with the Sun 1 or 2 days before that evening (e.g. in the Islamic calendar). In ancient Egypt the lunar month began on the day when the moon could no longer be seen just before sunrise. Others use a reckoned moon (e.g. the Hebrew calendar), or use a tabular scheme (Ecclesiastical lunar calendar). Yet others run from full moon to full moon. Calendars count integer days, so months may be 29 or 30 days in length, in some regular or irregular sequence. But all lunar months approximate the mean length of the synodic month of approximately 29.53059 days (29 days, 12 hours , 44 minutes and 3 seconds ). There are several different ways of expressing the lunar month.

The Moon's orbital period in a non-rotating frame of reference (which on average is equal to its rotation period) is about 27.32 days (27 days, 7 hours, 43 minutes, 11.6 seconds). This is known as a sidereal month and is measured by observing how long it takes the Moon to pass a fixed star on the celestial sphere . A synodic month is 29.53 days (29 days, 12 hours, 44 minutes, 2.8 seconds) and is measured from New Moon to New Moon. A New Moon is defined to occur when the Moon has the same ecliptic longitude as the Sun, as seen from the center of the Earth: i.e. when the Sun, Moon and Earth are almost on one line. A synodic month is longer than a sidereal month because the Earth-Moon system is orbiting the Sun in the same direction as the Moon is orbiting the Earth. Therefore, the Sun appears to move with respect to the stars, and it takes about 2.2 days longer for the Moon to return to the apparent position of the Sun.

The synodic month is the most common way of expressing the lunar cycle. An anomalistic month is the Moon's orbital period measured from perigee to perigee - the point in the Moon's orbit when it is closest to Earth. An anomalistic month is about 27.55 days on average. The tropical month is the time for the Moon to return to the same ecliptic longitude, i.e. measured from the equinox ; it is slightly shorter than the sidereal month because of precession of the equinoxes . The draconic month or nodal month is the period in which the Moon returns to the same node of its orbit; the nodes are the two points where the Moon's orbit crosses the plane of the Earth's orbit. Its duration is about 27.21 days on average. Soil Temperatures on the Moon Soil Temperatures on the Moon Model Parameters Temperature vs Depth MODEL DESCRIPTION This is a very simple model of soil temperatures on the Moon’s Equator, intended to be used for teaching and learning about weather and climate. It’s just one-dimensional heat transfer through the soil forced by incoming solar radiation that heats the soil and outgoing thermal radiation that cools it at the surface.

The Moon is “tidally locked” to the Earth so that the time required to rotate once on its axis is exactly the same as the period of its orbit around the Earth (that is, the length of the Moon’s “day” is the same as the length of a Lunar “month:” 29 Earth days, 12 hours, 44 minutes). The Moon has no atmosphere, and the “tilt” of its axis relative to the orbital plane of the Earth-Moon system around the Sun is negligible. Therefore the calculation of insolation at the Lunar surface is much simpler than the one you did for the Earth in problem 1 above. Assuming that the tilt of the Moon’s axis is zero, declination = 0. So at the Moon’s equator the cosine of the solar zenith angle is just equal to the cosine of the hour angle. Much simpler than the Earth!

On Earth the surface energy budget is given by Bonan’s equation 13.1: \[ \begin{aligned} \rho c \frac{\Delta T}{\Delta t}\Delta z = (S\downarrow - S\uparrow + L\downarrow - L\uparrow) - H - \lambda E = G \end{aligned} \] On the left-hand side, \(\rho\) is the density of the soil (kg m-3), \(c\) is the heat capacity of the soil (J m-3 K-1), \(\Delta T\) is the change in soil temperature (Kelvin) over a time step (\(\Delta t\), seconds) for each soil layer whose thickness is \(\Delta z\) (meters). On the right-hand side the four terms inside the parentheses are the fluxes of shortwave radiation down and up, and longwave radiation down and up. \(H\) is the turbulent flux of sensible heat, \(\lambda\) is the latent heat of evaporation of water, \(E\) is the rate of evaporation of water from the surface, and \(G\) is the change in ground heat storage.

All terms in this equation have the units of W m-2. The Moon’s surface energy budget is much simpler! There’s no water to evaporate and no turbulent air to carry sensible heat. There’s a little bit of longwave radiation emitted by the Earth that heats the Moon’s surface, but on the far side (which we never see) this is zero so we can neglect this. All of the upward flux of shortwave radiation is just the incoming solar radiation times the Moon’s albedo. To calculate upward longwave emission we can assume the surface emits as a blackbody. So the Moon’s surface energy budget is \[ \begin{aligned} \rho c \frac{\Delta T}{\Delta t}\Delta z = S\downarrow (1-albedo) - \sigma T_S^4 \end{aligned} \] In visible wavelengths, the Moon is surprisingly dark, with an albedo of just 7% (like asphalt!). Across the whole Solar spectrum it’s a little brighter, so please use the broadband albedo of 11%. To calculate the temperature, divide the Lunar “soil” into 15 layers.

Make the top layer thinnest (0.02 m = 2 cm), and then make each layer underneath 1.5 times as thick as the one above. This will get you 15 lunar soil temperatures down to about 17.5 meters depth. The downward flux of heat at the top of each layer is proportional to the difference in temperature between adjacent layers according to Bonan’s equation 9.1: \[ \begin{aligned} \rho c \frac{\Delta T}{\Delta t}\Delta z = -k \frac{\Delta T}{\Delta z} \end{aligned} \] The proportionality constant \(k\) is called the “thermal conductivity.” The negative sign is there because the layers are counted down from the surface but the heat flux is defined as positive upward, away from the surface. Changes in soil temperature are determined by the difference in the heat flux into and out of each layer.

This is called the “heat flux divergence,” given by Bonan’s equation 9.2: \[ \begin{aligned} F \uparrow = -k \frac{\Delta T}{\Delta z} = -(F_Z - F_{z+\Delta z}) \end{aligned} \] There’s a nice worked example of this on Bonan page 133. The book also gives typical values of heat capacity and thermal conductivity for different kinds of soil. The Lunar “soil” is actually made up of mineral grains blasted to smithereens by billions of years of impact bombardment. Unlike Earth soils, the pore space is not filled with water or air. It’s just vacuum, so the heat flow through the lunar soil is much slower than on Earth, depending on conductance and thermal radiation between adjacent grains! According to Colozza (1991) , the volumetric heat capacity of lunar regolith is about 4.4 million J m-3 K-1. Use this value for \(ρc\) in the equation above. The thermal conductivity of lunar “soil” is only about 0.025 W m-1 K-1.

This is about 100 times less conductive than soils on Earth! To calculate the changes in temperature with depth and time you’ll need to add solar radiation to the surface, subtract upward longwave, and step the heat flux equations forward in time. You’ll find that if you use a time step that’s too long, the numerical solution will become unstable and you’ll get crazy values (for example negative temperatures Kelvin). I find I can get away with a time step of a few hours. The program that does the calculation is very simple, and the code that controls this website is surprisingly simple too! It is all written in the programming language R . You can read all about it on the “Website Code” tab to the right.

How this website works (including all the code!) This website is controlled using the R package “ shiny .” There are four important components: The lunar soil temperature model itself ( moon.R ) A program that plots timeseries of the radiation, fluxes, and temps ( plot.moon.R ) A program that plots soil temperatures as a funciton of depth and time ( plot.soilT.image.R ) The user interface ( ui.R ) that controls the sliders and passes inputs to the model The “server” ( server.R ) that responds to user interface events in the web browser Scroll down or click links in the list above to read all about it!

This is the module that calculates soil temperatures on the Moon moon.R: moon <- function(time.step=3600, albedo=0.08){ # Calculate temperatures in lunar soil ("regolith") for 10 lunar days # resulting from diurnal cycles of solar heating and longwave cooling # Assume no tilt of lunar axis, ignore seasonal changes in Moon-Sun distance # A lunar day (or month!) is 29 Earth days plus 12.75 hours hours.per.lunar.day <- 24 * 29 + 12.75 # Simulate 10 lunar days n.lunar.days <- 10 # Figure out how many time steps to take to do n lunar days n.steps <- n.lunar.days * hours.per.lunar.day * 3600 / time.step # Parameters heat.capacity <- 4.4e6 # (J/m3 per Kelvin, from Colozza 1991, pages 2-3) thermal.conductivity <- 0.025 # (W/m per Kelvin, also from Colozza 1991) sigma <- 5.67e-8 # (W/m2/K4, Stefan-B

oltzmann coefficient) solar.constant <- 1367.

# Watts/m2 # Set depths and thicknesses of each soil layer n.layers <- 15 dz <- rep(NA, n.layers) # layer thickness (meters) depth <- dz dz[1] <- 0.02 # Top layer is thinnest (2 cm) depth[1] <- dz[1] / 2 layer.mult <- 1.5 for (L in 2:n.layers) { dz[L] <- dz[L-1] * layer.mult depth[L] <- sum(dz[1:(L-1)]) + dz[L] / 2 } # Set up arrays for later plotting empty <- rep(NA, n.steps-1) R.net <- empty SW.down <- empty SW.up <- empty LW.down <- empty LW.up <- empty lunar.date <- empty # Initial soil temperature soilT <- matrix(NA, nrow=n.layers, ncol=n.steps) # array to hold soil temps (Kelvin) soilT[ , 1] <- 273.

# Initial soil temps = 298 K = 25 C # Array to hold heat fluxes flux <- matrix(NA, nrow=n.layers+1, ncol=n.steps-1) # array to hold heat fluxes (W/m2) flux[ ,1] <- NA # upward flux at top of layer L # Set elapsed time to zero at beginning of simulation elapsed <- 0. # Time step the model for (i in 1:(n.steps-1)) { # Calculate date and time (lunar solar time = LST) elapsed <- elapsed + time.step hours <- elapsed / 3600.

lunar.date[i] <- hours/hours.per.lunar.day day <- floor(lunar.date[i]) LST <- hours - (hours.per.lunar.day * day) # Calculate position of Sun in Lunar sky hour.angle <- -pi + (LST / hours.per.lunar.day) * 2 * pi cos.z <- max(cos(hour.angle), 0.) # Calculate SW gain using Bonan (Chapter 4) SW.down[i] <- solar.constant * cos.z SW.up[i] <- SW.down[i] * albedo # Calculate LW using sky temp = 5 Kelvin LW.down[i] <- sigma * 5^4 # Upward longwave from surface assumes blackbody (emissivity = 1) LW.up[i] <- sigma * soilT[1,i] ^ 4 # Net radiation R.net[i] <- SW.down[i] - SW.up[i] + LW.down[i] - LW.up[i] # Soil temperature # Compute upward flux at top of each layer flux[1,i] <- -R.net[i] # top flux boundary condition for (L in 2:n.layers){ flux[L,i] <- -thermal.conductivity * (soilT[L-1,i] - soilT[L,i]) / ((

dz[L-1]+dz[L])/2) } flux[n.layers+1,i] <- 0.

# bottom flux boundary condition # Compute new temperatures for each layer for (L in 1:n.layers) { soilT[L,i+1] <- soilT[L,i] - (flux[L,i] - flux[L+1,i]) * time.step / (heat.capacity * dz[L]) } } return(list(SW.down=SW.down, SW.up=SW.up, LW.down=LW.down, LW.up=LW.up, R.net=R.net, flux=flux, soilT=soilT[,1:(n.steps-1)], lunar.date=lunar.date, depth=depth)) } This is module that plots the timeseries of the radiation, fluxes, and temperatures plot.moon.R: plot.moon <- function(output){ # ladder plot of radiation, turbulent fluxes, and temperatures # Format is a "grid" of three timeseries panels stacked vertically on one page # Set plot margins bottomMargin <- 4 leftMargin <- 5 topMargin <- 1 rightMargin <- .5 orig.par <- par(no.readonly=TRUE) # Remember changable parameters to reset later par(mfcol=c(3,1), mar=c(bottomMargin,leftMargin,topMargin,rightMargin),oma=c(0,2.,1.,0)) attach(output

) #======================================= # Top panel shows radiation components plot.min<- min(c(SW.down-SW.up, LW.down-LW.up, R.net)) plot.max <- max(c(SW.down-SW.up, LW.down-LW.up, R.net)) plot(lunar.date, SW.down-SW.up, typ='l', col='yellow', lwd=2, ylim=c(plot.min, plot.max), main='Radiation', ylab=expression(W ~~ m^-2), xlab='', cex.main=1.3, cex.lab=1.3, cex.axis=1.3) lines(lunar.date, LW.down-LW.up, col='red',lwd=2) lines(lunar.date, R.net, col='black',lwd=2) legend('topright', c('SW','LW','Net'), col=c('darkgoldenrod2','red','black'), lwd=c(2,2,2)) #======================================= # Middle panel shows fluxes plot.min<- min(flux) plot.max <- max(flux) colors <- c('darkred','darkorange2','darkgoldenrod2','green','blue') plot(lunar.date, flux[1,], typ='l',

 col='red', lwd=2, ylim=c(-100,100), main='Heat Fluxes', ylab=expression(W ~~ m^-2), xlab='', cex.main=1.3, cex.lab=1.3, cex.axis=1.3) for (L in 2:5) { lines(lunar.date, flux[L,], col=colors[L],lwd=1) } #======================================= # Bottom panel shows temperatures plot.min <- min(soilT) plot.max <- max(soilT) plot(lunar.date, soilT[1,], typ='l', col='red', lwd=2, ylim=c(plot.min, plot.max), main='Temperatures', ylab='Kelvin', xlab='Lunar Month', cex.main=1.3, cex.lab=1.3, cex.axis=1.3) for (L in 2:5) { lines(lunar.date, soilT[L,], col=colors[L],lwd=1) } detach(output) par(orig.par) } This is module that plots the temperatures as a function of depth and time plot.soilT.image.R: plot.soilT

.image <- function(output){ # Make a color-filled contour plot of lunar soil temperature by depth and time library(fields) # Need this to make the image.plot # Draw an image using colors to represent the insolation image.plot(output$lunar.date,100*output$depth,t(output$soilT), ylim=c(50,0), xlab='Lunar Days', ylab='Depth (cm)', main='Lunar Soil Temperature (Kelvin)', cex.main=1.5, cex.axis=1.2, cex.lab=1.3) } This is the user interface that actually controls this website ui.R: library(shiny) library(markdown) # Define UI for calculation of lunar temperatures shinyUI(pageWithSidebar( # Application title headerPanel("Soil Temperatures on the Moon"), # Sidebar with sliders that control various available options sidebarPanel( img(src='normal_A11Aldrin.jpg'), h4('Model Parameters'), sliderInput("albedo", "Albedo (percent)", min = 5, max = 30, value = 11, step=1), sliderInput("time.step", "Time Step (hours):", min = 0.5, max = 1

2, value = 1, step=0.5) ), # Main panel consists of a tabset displays model output or model description mainPanel( tabsetPanel( tabPanel("Fluxes", h3("Component Fluxes and Temperatures"), plotOutput("fluxes"), tags$style(type="text/css", ".tab-content { overflow: visible; }")), tabPanel("Depths", h3("Temperature vs Depth"), plotOutput("soil"), tags$style(type="text/css", ".tab-content { overflow: visible; }")), tabPanel("Description", includeHTML('doc/model.description.html')), tabPanel("Website Code", includeMarkdown('doc/website.code.md')) ) ) )) Here is the server module that responds to user interface events server.R: library(shiny) # Source required R scripts source('model/moon.R') source('model/plot.moon.R') source('model/plot.soilT.image.R') shinyServer(function(input, output) { # time-depth plot of soil temperatures output$soil <- renderPlot( plot.soilT.image(moon(albedo=input$albedo/100, time.step=input$time.step*3600)) ) # Stacked timeseries of component fluxes

 and temperatures output$fluxes <- renderPlot( plot.moon(moon(albedo=input$albedo/100, time.step=input$time.step*3600)) ) } ) Explanation 384 385 Notice that the period from Nisan 1 to Tishri 1 is always the same: 177 days, regardless of the type of year.

By the application of certain rules discussed below it is possible to accommodate all the requirements of the Jewish calendar with a sequence of years having only these six lengths. Note that in a regular year Adar may be called "Adar I" or simply "Adar" whereas in a leap year the two Adars are called "Adar I" and "Adar II". The process of establishing the calendar for a particular year consists of the following steps: a) determine if the year is a leap year, b) find the day of the Molad (new moon) of Tishri for that year, c) adjust its Rosh Hashanah date according to the rules explained below, d) similarly, determine the Rosh Hashanah date of the next year, e) determine the length of the year (and hence its type) to fill the duration between the two Rosh Hashanah days. A set of rules has been established for determining how to position the day of Rosh Hashanah, given the day of the Molad. Determining if a year is a leap year is done by simply calculating its position in the 19-year cycle which began in the year 1.

As was mentioned above, the duration between lunar cycles is 29 days, 12 hours, 44 minutes and 3 1/3 seconds. If the time of one Molad is known, the time of successive or previous ones can be determined by adding or subtracting multiples of this interval. From this process it is calculated that the first new moon of the year 1 took place on Sunday evening at 11 minutes, 20 seconds after 11 PM. The time of the Tishri Molad for any year can be determined by performing the previous calculation. But, since the lunar cycle repeats every 19 years, shortcuts can be taken. For example, it is only necessary to add 2 days, 16 hours, 33 minutes and 3 1/3 seconds to a particular new moon to find the day of the new moon exactly one 19-year-cycle later. Or 2 days, 23 hours, 5 minutes and 33 1/3 seconds have to be added to a particular new moon to find the new moon exactly 100 cycles (1900 years) later.

Now the following rules are applied: Tishri 1 (Rosh Hashanah) will be on the day of the Molad except when falling into one of the four exceptions below (which is more often than not), in which case it is then delayed by one day. Rule 1: When the new moon occurs on Wednesday, Friday, or Sunday, or Rule 2: When the new moon occurs at noon (18 hours after the start of the day at sunset) or later, or Rule 3: When the new moon of an ordinary year occurs on Tuesday at 11 minutes and 20 seconds after 3 am or later, or Rule 4: When, at the termination of a leap year, the new moon occurs on Monday at 32 minutes and 43 1/3 seconds after 9 am or later. When Rules 2, 3, or 4 apply, if delaying Rosh Hashanah by one day causes it to fall within Rule 1, it is delayed a second day. Explanation of the Four Rules The first rule causes the two holidays mentioned above to fall only on the permissible days.

The second rule is an astronomical adjustment which considers the relationship between the observation of the new moon and the actual time of the lunar conjunction. Since the moon is in conjunction with the sun when it is "new", its first crescent is most readily observed just after sunset on the evening of the conjunction, but the actual conjunction may have occurred many hours before. The duration between the true conjunction and the observation of this first crescent is a complex calculation which takes into account the season, the lunar latitude and the geographical latitude and longitude of the place of observation. The second rule is an adjustment for the factors relating to the observation of the first crescent moon from the city of Jerusalem. The third rule accommodates the limitation imposed by having only the six possible year-lengths given above. If the new moon occurred on the stated time (or later) the Rosh Hashanah new moon of the following year would occur on Saturday at noon (or later).

This can be seen by adding 4 days, 8 hours, 48 minutes and 40 seconds (the time that must be added to a new moon to find the new moon exactly 12 lunar months later) to 2 days, 3 hours, 11 minutes and 20 seconds. This would call for the application of the first two rules and the postponement of the Rosh Hashanah from Saturday to Monday. This, in turn, would require a year length of 356 days (50 weeks plus 6 days), which is not accommodated. So the Rosh Hashanah is postponed to Thursday (Rule 1 applies) and the year is 354 days long. The fourth rule is also necessary to accommodate the year length limitations but occurs very infrequently. If one subtracts the time necessary to calculate the new moon exactly 13 lunar months earlier (5 days, 21 hours, 32 minutes and 43 1/3 seconds) one finds that the new moon at the start of the year occurred at 12 noon on Tuesday. Under Rules 1 and 2 it would have been postponed until Thursday.

This, in turn, would have required a 382-day leap year (54 weeks plus 4 days), which is not accommodated. So Rosh Hashanah is postponed to Tuesday and the year is 383 days long. Selecting the Year Type At this point, the Rosh Hashanah day calculation is made for the next year. The starting day and ending day of the year are then known as well as whether it must be a leap year. The year type is chosen from the six possibilities according to the length required. A simple way to chose the type is to use the table showing the number of days added from one New Year's Day to the next. Days Added to Year for Various Year Types Year Type 385 0 The type is now easily determined by examining the day of the week on which the year begins and ends. The application of Rules 3 and 4 above have assured us that these are the only types necessary to accommodate all situations. The year is now completely defined and the corresponding Gregorian dates must be found. Correlation to the Gregorian Calendar The correlation to the Gregorian calendar is very unsophisticated.

Simply stated: there is no direct relationship between the Jewish and Gregorian calendars. They both are related to the solar cycle but according to totally different rules. Every date, in the course of the 19-year cycle can fall within a range of thirty days. The only way to determine corresponding Gregorian dates is to: 1) Have a known correspondence as a reference point. (Saturday, September 30, 1989, corresponds to Tishri 1, 5750.) 2) Count how many days in one calendar system exist between the reference date and the desired date. 3) Count the same number of days from the reference in the second calendar system. The calculations can take advantage of certain patterns to reduce their complexity. Charts and tables have been drawn up to help or a computer can be programmed to do the calculations. It is interesting to note that the Christian holiday of Easter and all the holidays tied to it also retain a relation to the lunar cycle. In the year 325, the date of Easter was set by the Council of Nicaea to be the first Sunday after the first full moon occurring on or after the vernal equinox.

Because the calculations of the full moon and vernal equinox were too complex, the calculation was simplified to assume that the vernal equinox is always on March 21. Easter and Passover usually come within a week of each other, but in some Jewish leap years Passover occurs a whole month after Easter. Anniversaries Anniversaries can present a special problem for the Jewish calendar because there are often days that occur in one year which are absent in another. In the Gregorian calendar there is only one special case to consider, February 29th. People born or married on that date can simply decide to celebrate on February 28th or March 1st for years that are not leap years. But the Jewish calendar has an entire leap month as well as two months which can vary in length, so special rules have been established. The anniversary of the death of a close relative (called a Yahrzeit) is of particularly importance and has unique rules associated with it. 1) The anniversary of a date which was the 30th of Heshvan or Kislev in a year in which that month has 29 days is observed on the 1st of the next month.

There is an exception for the observance of a Yahrzeit, namely: if, in the first year after the death, the anniversary month has 29 days then the Yahrzeit is observed on the 29th of that month and continues to be observed on the 29th for all years in which the anniversary month has only 29 days. 2) The anniversary of a date in Adar of an ordinary year is observed on the same date in Adar II of a leap year except for a Yahrzeit which is observed on the same date in Adar I of a leap year. 3) The anniversary of a date in Adar I of a leap year is observed on the same date in Adar of an ordinary year. If the original date was the 30th of Adar I of a leap year then, in an ordinary year, the anniversary is observed on the 1st of Nisan. There is an exception for the observance of a Yahrzeit. A Yahrzeit is observed on the 29th of Adar in an ordinary year. 4) The anniversary of a date in Adar II is observed on the same date of Adar of an ordinary year.

Weekly Readings The five books of the Old Testament (Torah) are divided into 54 weekly portions which are read, one each Sabbath, throughout the year. Only the last portion, Ve-Zot-ha-Berakhah, is not read on the Sabbath but on Simchat Torah. The new cycle begins on the Sabbath after Simchat Torah. Each weekly portion has an accompanying reading from one of the Prophets (Haftarah). These are all listed below. Torah Reading and the Prophets 1. Bereshit, Gen 1:1-6:8 Isa 42:5-43:11 2. No'ah, Gen 6:9-11:32 Isa 54:1-55:5 3. Lekh Lekha, Gen 12:1-17:27 Isa 40:27-41:16 4. Va-Yera, Gen 18:1-22:24 II Kings 4:1-37 5.

Hayyei Sarah, Gen 23:1-25:18 I Kings 1:1-31 6. Toledot, Gen 25:19-28:9 Mal 1:1-2:7 7. Va-Yeze, Gen 28:10-32:3 Hos 12:13-14:10 8. Va-Yishlah, Gen 32:4-36:43 Hos 11:7-12:12 9. Va-Yeshev, Gen 37:1-40:23 Amos 2:6-3:8 10. Mi-Kez, Gen 41:1-44:17 I Kings 3:15-4:1 11. Va-Yiggash, Gen 44:18-47:27 Ezek 37:15-28 12. Va-Yehi, Gen 47:28-50:26 I Kings 2:1-12 13.

Shemot, Ex 1:1-6:1 Isa 27:6-28:13, 29:22-23 14. Va-Era, Ex 6:2-9:35 Ezek 28:25-29:21 15. Bo, Ex 10:1-13:16 Jer 46:13-28 16. Be-Shallah, Ex 13:17-17:16 Judge 4:4-5:31 17. Yitro, Ex 18:1-20:23 Isa 6:1-7:6,9:5 18. Mishpatim, Ex 21:1-24:18 Jer 34:8-22, 33:25-26 19. Terumah, Ex 25:1-27:19 I Kings 5:26-6:13 20.

Tezavveh, Ex 27:20-30:10 Ezek 43:10-27 21. Ki Tissa, Ex 30:11-34:35 I Kings 18:1-39 22. Va-Yakhel, Ex 35:1-38:20 I Kings 7:40-50 23. Pekudei, Ex 38:21-40:38 I Kings 7:51-8:21 24. Va-Yikra, Lev 1:1-5:26 Isa 43:21-44:23 25. Zav, Lev 6:1-8:36 Jer 7:21-8:3, 9:22-23 26. Shemini, Lev 9:1-11:47 II Sam 6:1-7:17 27.

Tazri'a, Lev 12:1-13:.59 II Kings 4:42-5:19 28. Mezora, Lev 14:1-15:23 II Kings 7:3-20 29. Aharei Mot, Lev 16:1-18:30 Ezek 22:1-19 30. Kedoshim, Lev 19:1-20:27 Amos 9:7-15 31. Emor, Lev 21:1-24:23 Ezek 44:15-31 32. Be-Har, Lev 25:1-26:2 Jer 32:6-27 33. Be-Hukkotai, Lev 26:3-27:34 Jer 16:19-17:14 34. Be-Midbar, Num 1:1-4:20 Hos 2:1-22 35.

Naso, Num 4:21-7:89 Judge 13:2-25 36. Be-Ha'alotkha, Num 8:1-12:16 Zech 2:14-4:7 37. Shela Lekha, Num 13:1-15:41 Josh 2:1-24 38. Korah, Num 16:1-18:32 I Sam 11:14-12:22 39. Hukkat, Num 19:1-22:1 Judge 11:1-33 40. Balak, Num 22:2-25:9 Micah 5:6-6:8 41. Pinhas, Num 25:10-30:1 I Kings 18:46-19:21 42. Mattot, Num 30:2-32:42 Jer 1:1-2:3 43.

Masei, Num 33:1-36:13 Jer 2:4-28, 3:4 44. Devarim, Deut 1:1-3:22 Isa 1:1-27 45. Va-Ethannan, Deut 3:23-7:11 Isa 40:1-26 46. Ekev, Deut 7:12-11:25 Isa 49:14-51:3 47. Re'eh, Deut 11:26-16:17 Isa 54:11-55:5 48. Shofetim, Deut 16:18-21:9 Isa 51:12-52:12 49. Ki Teze, Deut 21:10-25:19 Isa 54:1-10 50. Ki Tavo, Deut 26:1-29:8 Isa 60:1-22 51.

Nizzavim, Deut 29:9-30:20 Isa 61:10-63:9 52. Va-Yelekh, Deut 31:1-30 Isa 55:6-56:8 53. Ha'azinu, Deut 32:1-52 II Sam 22:1-51 54. Ve-Zot ha-Berakhah, Deut 33:1-34:12 Josh 1:1-18 There are a sufficient number of portions to accommodate different readings on the longer years so it is necessary to double-up on some weeks in shorter years in order that all the portions be read. Also, there are special readings that are substituted on the holidays. These substitutions require a complex series of adjustments to be sure that all portions are read regardless of the year length. Special Haftarah readings are also said when celebrating a new moon. To further complicate the matter, not all congregations observe the same rules. JCAL for Windows shows the Torah and Haftarah reading that normally would apply to that week as well as the substitutions that are often made.

Note that JCAL for Windows shows the weekly readings normally read on Monday, Thursday and the Sabbath. It does not show special weekday or holiday readings that may occur during the week. The user is CAUTIONED to check these readings inasmuch as there will be variations from congregation to congregation. History of the Gregorian Calendar The calendar that we use today was first formulated in several inaccurate variations by the Romans. By the time of Julius Caesar, January was falling in autumn so he ordered his Greek mavin, Sosigenes, to make reforms to the calendar. He added 90 days to the year 46 BC to correct for the seasonal drift and adjusted the lengths of the months, as we know them to be today. On the assumption that the solar year is 365 1/4 days long he introduced the leap year by adding one day to February every four years. This is known as the Julian calendar. The use of the leap year was an improvement but not entirely accurate. The true solar year is 365 days, 5 hours, 48 minutes, and 46 seconds.

One 366-day year every four years equates to an average year of 365 days, 6 hours. Every year an error of 11 minutes, 14 seconds was added (about one day in 128 years). In the year 730 the Venerable Bede, an Anglo Saxon monk, announced that the year was in error by more than 11 minutes but, alas, they paid no attention to him and nothing was done for another 800 years. By the 16th century it was estimated that the accumulated error was ten days. So in the year 1582 Pope Gregory XIII revised the calendar by declaring that the day following October 4th would be October 15th, suppressing ten days. To eliminate the continuing error of one day in 128 years he ordained that centesimal years (years ending in hundreds) should not be leap years unless they are divisible by 400.

(1700, 1800 and 1900 were not leap years but 2000 is.) This reduces the year length by three days every 400 years or one day every 133 1/3 years. This Gregorian calendar is the one we use today. The Gregorian reform compensates by three days (72 hours) every 400 years. The actual excess accumulated is 74 hours, 53 minutes and 20 seconds. The error of 2 hours, 53 minutes and 20 seconds every 400 years accumulates to one day in 3323 years. Oh well, nobody's perfect. The Gregorian calendar was adopted at once by France, Italy, Spain, Portugal and Luxembourg. Within two years most German Catholic states, parts of Switzerland and The Netherlands adopted the new calendar. The rest of The Netherlands, along with Denmark and the German Protestant states followed in 1699-1700. The British Government imposed the Gregorian calendar on all its possessions, including the American colonies in 1752.

By this time an error of more than one additional day had accumulated so the British decreed that the day following September 2, 1752 should be called September 14, a correction of 11 days. All dates preceding were designated O.S., for Old Style. In addition, New Years Day was moved to January 1 from March 25. (Under the Old Style, for example, March 24, 1700 was followed by March 25, 1701). George Washington's birthday, which was February 11, 1731, O.S. became February 22, 1732. Non-European countries were slower to adopt the Gregorian calendar: Japan in 1873, Egypt in 1875, China in 1912 and Turkey in 1917. In 1918 the revolutionary government in Russia decreed that January 31, Old Style, would be followed by February 14, New Style, though the Orthodox Church has retained the Julian calendar as have other Middle Eastern Christian sects.

Timeline of interesting calendar facts History Web Site Timeline of interesting calendar facts Length of the tropical year, defined as the average interval between vernal equinoxes. This calendar year was the objective of the Gregorian calendar reform, which finalized the calendar as we use it today. 365 days, 5 hours, 49 minutes (365.2424 Universal days) Lengthening of the vernal equinox year over the last two millennia (0.0001 universal days per year) Variation of this length in the next few millennia Lunar month in 2000 C.E. 29 days, 12 hours, 44 minutes, 2.9 seconds The earliest known date 4236 B.C.E., the founding of the Egyptian calendar Ancient Egyptian calendar year Date Emperor Huangdi invented the Chinese calendar (legend) 354 days (lunar year) with days added at intervals to keep the Chinese lunar calendar aligned with the seasons Early Greek year 354 days, with days added Jewish Year 354 days, with days added Early Roman year 304 days, amended in 700 C.E.

to 355 days The year according to Julius Caesar (The Julian calendar) Date Caesar changed Roman year to Julian calendar Time the old Roman calendar was misaligned with the solar year as designated by Caesar Total length of 45 B.C.E., known as the "Year of Confusion," after adding 80 days Date Sanhedrin president Hillel II codified the Jewish calendar The year as amended by Pope Gregory XIII (Gregorian calendar year) 365 days, 5 hours, 49 minutes, 12 seconds Date Pope Gregory reformed the calendar 1582 Length of time the Julian calendar overestimates our calendar year per year, as determined by Pope Gregory Days Pope Gregory removed to correct the calendar's drift Dates Gregory eliminated by Papal bull to realign his calendar with the solar year Dates most Catholic countries accepted the Gregorian calendar Date Protestant Germany accepted the Gregorian calendar partial acceptance in 1700, full acceptance in 1775 Date Great Britain (and the American colonies) accepted the Gregorian calendar Date Benjamin Franklin first proposed Daylight Saving Time 1784 Days eliminated by the British Parliament to realign the old calendar (Julian) with the Gregorian calendar Date Japan

 accepted the Gregorian calendar Date Russia accepted the Gregorian calendar 1917 (and again in 1940) Date China accepted the Gregorian calendar 1949 Date the Eastern Orthodox Church last voted to reject the Gregorian calendar and retain the Julian calendar Length of time the Gregorian calendar is off from the average vernal equinox year about 12 seconds per year Length of time the Gregorian calendar has become misaligned with the vernal equinox over the 414 years since Gregory's reform in 1582 1 hour and 20 minutes When the Gregorian calendar will become twelve calendar hours ahead of the astronomer's mean tropical year 4th or 5th millennium C.E.

When the Gregorian calendar will become twelve calendar hours ahead of the mean vernal-equinox year beyond the 7th millennium C.E. Date Atomic Time replaced Earth Time as the world's official scientific time standard Current official definition of the second time it takes for 9,192,631,770 oscillations of the Cesium atom at zero magnetic field The mean vernal equinox year expressed in oscillations of atomic cesium at the year 2000 Notes: ï¿½ Slowing of the vernal equinox year The length of the year has increased slightly over the millennia for a variety of reasons. These include: the gradual slowing of the Earth's rotation, slow changes in the Earth's orbit due to other planets and the moon, as well as regular effects due to precession of the Earth's axis of rotation every 26,000 years. ï¿½ Measures of the year There is a subtle but important difference in two primary measures of the year, used by our calendar and by astronomers.

The year mentioned above is the length of the tropical year defined as the mean interval between vernal equinoxes (1582-2000 C.E.) : 365 days, 5 hours, 49 minutes (365.2424 Universal days). Another measure of the year often used is the astronomer's mean tropical year, defined as 365 days, 5 hours, 48 minutes, 45 seconds. ï¿½ Atomic time The measurement of time is currently determined by an international consortium based in France which averages the time from approximately 220 atomic clocks in over two dozen countries. The atomic clock is the only object that both tells time and generates a precise time scale. Historically, the calculation of time has been based on the position of the earth relative to the sun using noon, when the sun is highest in the sky, as a marker.

The length of the second, which corresponds to the length of time required for 9,192,631,770 cycles of the Cesium atom at zero magnetic field, was determined near the end of the 19th century; this second is thus equivalent to the second defined by the fraction 1/31 556 925.97 47 of the year 1900. In 1967, the official second was set as equal to an average second of Earth's rotation time; the calculation of the average is necessary due to the fact that the earth rotates at a slightly irregular rate. Today, time is determined by counting official seconds. This is subject to slight measurement inaccuracies; thus, the international community calculates a stable time by averaging accumulated seconds from several clocks worldwide. Next, this figure is compared to a few highly accurate laboratory measurements of the second. Every month, the official world time is adjusted by a few nanoseconds. Politically, time is a cooperative venture; and, by making time an international endeavor, the international community benefits from the combined resources of many laboratories.

Question: A lunar month is an average (how many) days plus 12 hours, 44 minutes and 3 seconds?
Answer: 29