January
February
March
April
May
June
July
August
September
October
November
December
Calculated Times
Sun Rise: –:–
Sun Set: –:–
Moon Rise: –:–
Moon Set: –:–
Moon Phase: —
Understanding Sun and Moon Rise/Set Calculations
Calculating the precise times for sunrise, sunset, moonrise, and moonset for a specific location and date is a complex astronomical task. It involves understanding celestial mechanics, Earth's rotation, and the apparent motion of the Sun and Moon against the backdrop of stars. These calculations are crucial for various fields, including astronomy, navigation, photography, agriculture, and even daily planning for outdoor activities.
The Science Behind the Times
The core of these calculations relies on determining the celestial sphere's coordinates for the Sun and Moon relative to the observer's location on Earth. Key factors include:
Observer's Location: Latitude and Longitude are fundamental. Latitude determines how high the celestial pole is above the horizon, affecting the apparent path of celestial bodies. Longitude determines the local time relative to a standard meridian (like Greenwich).
Date and Time: Earth's orbital position around the Sun changes daily (affecting solar declination), and its axial tilt causes seasons. The Moon's orbit around Earth is also complex and changes over time.
Earth's Rotation: The 24-hour rotation of the Earth is the primary driver of daily sunrise and sunset.
Celestial Coordinates: Calculations involve converting standard astronomical coordinates (like Right Ascension and Declination) into local apparent sidereal time and then into local solar time.
Atmospheric Refraction: The Earth's atmosphere bends sunlight, making the Sun appear higher in the sky than it geometrically is. This effect means sunrise is observed slightly before the Sun's geometric center clears the horizon, and sunset occurs slightly after it dips below.
Moon's Orbit: The Moon's path around the Earth is not perfectly circular and is influenced by the Sun's gravity, leading to variations in its rise and set times daily. The Moon also has its own declination, changing throughout its monthly orbit.
Simplified Astronomical Calculations
While precise astronomical algorithms can be very detailed, a common approach involves these steps:
Calculate Julian Day: Convert the given date (Year, Month, Day) into a Julian Day number, a continuous count of days since a specific epoch.
Calculate Sun's Position: Using the Julian Day, calculate the Sun's mean anomaly, eccentric anomaly, and finally its ecliptic longitude. This allows estimation of its Right Ascension and Declination.
Calculate Sun's Hour Angle: The hour angle at which the Sun is at the horizon (for sunrise/sunset) depends on the observer's latitude and the Sun's declination. For sunrise/sunset, the Sun's altitude is approximately -0.833 degrees (accounting for refraction and the Sun's apparent diameter).
Convert to Local Time: Use the calculated hour angle, observer's longitude, and the equation of time (the difference between mean solar time and apparent solar time) to find the local solar time of sunrise/sunset. This is then converted to standard time using the timezone offset.
Calculate Moon's Position: Similar to the Sun, but significantly more complex due to the Moon's faster orbit, varying distance, and perturbations. Astronomical libraries or more advanced algorithms are typically used for accurate lunar positions.
Calculate Moon's Hour Angle: Similar to the Sun, using the Moon's declination and the observer's latitude.
Convert to Local Time: Convert the Moon's hour angle to local time, accounting for its specific path and the observer's longitude and timezone.
Moon Phase: The moon phase is determined by the angle between the Sun, Earth, and Moon (the ecliptic longitude difference between the Sun and Moon).
The formula for the hour angle (H) at sunrise/sunset for a celestial body with declination (δ) at latitude (φ) when its altitude (a) is observed is:
For sunrise/sunset, 'a' is typically taken as -0.833 degrees. For the Moon, the calculation is similar but uses the Moon's declination, which varies significantly throughout its orbit.
Use Cases for This Calculator
Photography: Planning shoots during the "golden hour" (shortly after sunrise or before sunset) for optimal lighting.
Outdoor Activities: Scheduling hiking, camping, or other activities to maximize daylight or be aware of nightfall.
Astronomy: Amateur astronomers planning observation sessions, knowing when celestial objects will rise and set.
Navigation: Traditional celestial navigation and confirming times with modern GPS.
Agriculture: Understanding daily light cycles for crop management or livestock.
Events: Planning outdoor events, weddings, or festivals.
This calculator provides estimated times based on standard astronomical models. Atmospheric conditions and specific geographical obstructions (like mountains) can slightly alter the exact observed times.
// JavaScript for Sun and Moon Rise/Set Calculator
function calculateRiseSetTimes() {
var lat = parseFloat(document.getElementById("latitude").value);
var lon = parseFloat(document.getElementById("longitude").value);
var tzOffset = parseFloat(document.getElementById("timezone").value);
var year = parseInt(document.getElementById("year").value);
var month = parseInt(document.getElementById("month").value);
var day = parseInt(document.getElementById("day").value);
var errorMessages = document.getElementById("errorMessages");
errorMessages.innerHTML = "";
// — Input Validation —
if (isNaN(lat) || lat 90) {
errorMessages.innerHTML += "Please enter a valid latitude between -90 and 90 degrees.";
}
if (isNaN(lon) || lon 180) {
errorMessages.innerHTML += "Please enter a valid longitude between -180 and 180 degrees.";
}
if (isNaN(tzOffset)) {
errorMessages.innerHTML += "Please enter a valid timezone offset (e.g., -5, +1).";
}
if (isNaN(year) || year 9999) {
errorMessages.innerHTML += "Please enter a valid year.";
}
if (isNaN(month) || month 12) {
errorMessages.innerHTML += "Please select a valid month.";
}
if (isNaN(day) || day 31) {
errorMessages.innerHTML += "Please enter a valid day.";
}
// Basic check for day validity based on month (more complex leap year check omitted for simplicity but would be needed for full accuracy)
if (month === 2 && day > 29) {
errorMessages.innerHTML += "Day cannot be greater than 29 for February.";
} else if ([4, 6, 9, 11].includes(month) && day > 30) {
errorMessages.innerHTML += "Day cannot be greater than 30 for this month.";
}
if (errorMessages.innerHTML) {
// Clear previous results if there are errors
document.getElementById("sunRiseTime").innerHTML = '–:–';
document.getElementById("sunSetTime").innerHTML = '–:–';
document.getElementById("moonRiseTime").innerHTML = '–:–';
document.getElementById("moonSetTime").innerHTML = '–:–';
document.getElementById("moonPhase").innerHTML = '–';
return;
}
// — Core Calculation Logic (Simplified) —
// This is a highly simplified approximation. For precise results,
// astronomical libraries or more complex algorithms are required.
// This example uses a basic formula that gives a rough estimate.
// Convert date to Julian Day (for the date at noon UTC to avoid issues with day boundaries)
var jd = julianDay(year, month, day);
// — Sun Calculations —
var sunLon = sunLongitude(jd); // Sun's longitude in degrees
var sunDecl = sunDeclination(sunLon); // Sun's declination in degrees
var equationOfTime = calcEquationOfTime(jd); // Equation of Time in minutes
var sunHourAngle = sunRiseHourAngle(lat, sunDecl); // Hour angle for sunrise/sunset
// Sunrise/Sunset times in UTC (local mean time adjusted for longitude)
var sunRiseUTCMinutes = 720 – (sunHourAngle * 4) – lon – equationOfTime; // 720 minutes = 12:00
var sunSetUTCMinutes = 720 + (sunHourAngle * 4) – lon – equationOfTime;
// Convert UTC minutes to HH:MM format
var sunRiseLocal = formatTime(convertUtcMinutesToLocal(sunRiseUTCMinutes, tzOffset));
var sunSetLocal = formatTime(convertUtcMinutesToLocal(sunSetUTCMinutes, tzOffset));
// — Moon Calculations (Very Simplified Approximation) —
// Moon's position is much more complex. This is a placeholder.
// A real calculator would use ephemeris data or a dedicated lunar model.
var moonLon = moonLongitude(jd); // Moon's approximate longitude
var moonDecl = moonDeclination(moonLon); // Moon's approximate declination
var moonRiseHourAngle = moonRiseHourAngleApprox(lat, moonDecl); // Approximate hour angle
var moonRiseUTCMinutesApprox = 720 – (moonRiseHourAngle * 4) – lon – calcMoonEquationOfTime(jd); // Rough Eq of Time for Moon
var moonSetUTCMinutesApprox = 720 + (moonRiseHourAngle * 4) – lon – calcMoonEquationOfTime(jd);
var moonRiseLocal = formatTime(convertUtcMinutesToLocal(moonRiseUTCMinutesApprox, tzOffset));
var moonSetLocal = formatTime(convertUtcMinutesToLocal(moonSetUTCMinutesApprox, tzOffset));
// — Moon Phase Calculation —
var phase = calculateMoonPhase(jd);
// Display Results
document.getElementById("sunRiseTime").innerText = sunRiseLocal === "Invalid Time" ? "–:–" : sunRiseLocal;
document.getElementById("sunSetTime").innerText = sunSetLocal === "Invalid Time" ? "–:–" : sunSetLocal;
document.getElementById("moonRiseTime").innerText = moonRiseLocal === "Invalid Time" ? "–:–" : moonRiseLocal;
document.getElementById("moonSetTime").innerText = moonSetLocal === "Invalid Time" ? "–:–" : moonSetLocal;
document.getElementById("moonPhase").innerText = phase;
}
// — Helper Functions (Astronomical Calculations – Simplified) —
// Converts Gregorian date to Julian Day number
function julianDay(year, month, day) {
var m = month;
var y = year;
if (m <= 2) {
m += 12;
y -= 1;
}
var A = Math.floor(y / 100);
var B = 2 – A + Math.floor(A / 4);
var JD = Math.floor(365.25 * (y + 4716)) + Math.floor(30.6001 * (m + 1)) + day + B – 1524.5;
return JD;
}
// Calculates the approximate Sun's longitude for a given Julian Day
// This is a very basic approximation. More accurate formulas exist.
function sunLongitude(jd) {
var n = jd – 2451545.0; // Days since J2000.0
var meanAnomaly = 357.5291 + 0.98560028 * n; // degrees
meanAnomaly = meanAnomaly % 360;
if (meanAnomaly < 0) meanAnomaly += 360;
// Use approximation for eccentricity
var eclipticLongitude = meanAnomaly + 1.915 * Math.sin(toRadians(meanAnomaly)) + 0.020 * Math.sin(toRadians(2 * meanAnomaly));
eclipticLongitude = eclipticLongitude % 360;
if (eclipticLongitude < 0) eclipticLongitude += 360;
// Add the mean longitude of perihelion (approx 102.9372 degrees for J2000)
eclipticLongitude += 102.9372;
eclipticLongitude = eclipticLongitude % 360;
if (eclipticLongitude < 0) eclipticLongitude += 360;
return eclipticLongitude;
}
// Calculates the Sun's declination from its ecliptic longitude
function sunDeclination(eclipticLon) {
var obliquity = 23.439 – 0.00000036 * (julianDay(2000, 1, 1.5) – 2451545); // Earth's axial tilt
var declination = Math.asin(Math.sin(toRadians(obliquity)) * Math.sin(toRadians(eclipticLon)));
return toDegrees(declination);
}
// Calculates the Equation of Time in minutes for a given Julian Day
function calcEquationOfTime(jd) {
var n = jd – 2451545.0; // Days since J2000.0
var meanAnomaly = 357.5291 + 0.98560028 * n;
var meanLongitude = 280.460 + 0.9856474 * n;
meanLongitude = meanLongitude % 360;
if (meanLongitude < 0) meanLongitude += 360;
var eclipticLongitude = meanLongitude + 1.915 * Math.sin(toRadians(meanLongitude)) + 0.020 * Math.sin(toRadians(2 * meanLongitude));
var obliquity = 23.439 – 0.00000036 * (jd – 2451545); // Approximate obliquity
var rightAscension = Math.atan2(Math.cos(toRadians(obliquity)) * Math.sin(toRadians(eclipticLongitude)), Math.cos(toRadians(eclipticLongitude)));
rightAscension = toDegrees(rightAscension);
// Normalize RA to be between 0 and 360
var ra_degrees = toDegrees(Math.atan2(Math.sin(toRadians(eclipticLongitude)) * Math.cos(toRadians(obliquity)), Math.cos(toRadians(eclipticLongitude))));
if (ra_degrees 1) return NaN; // Sun is circumpolar (never sets or never rises)
if (cosH < -1) return NaN;
var H = Math.acos(cosH);
return toDegrees(H); // Returns half the duration in degrees
}
// Approximates Moon's longitude
function moonLongitude(jd) {
// This is a highly simplified approximation. Real calculations are complex.
var n = jd – 2451545.0; // Days since J2000.0
var meanAnomalyMoon = 134.9634 + 13.0649929 * n;
meanAnomalyMoon = meanAnomalyMoon % 360;
if (meanAnomalyMoon < 0) meanAnomalyMoon += 360;
// Adding some main terms for approximation
var moonLonApprox = meanAnomalyMoon + 6.289 * Math.sin(toRadians(meanAnomalyMoon)) + 1.274 * Math.sin(toRadians(2 * meanAnomalyMoon – 21.314)) + 0.257 * Math.sin(toRadians(2 * meanAnomalyMoon));
moonLonApprox = moonLonApprox % 360;
if (moonLonApprox 1) return NaN; // Moon is circumpolar
if (cosH < -1) return NaN;
var H = Math.acos(cosH);
return toDegrees(H);
}
// Very basic approximation for Moon's Equation of Time (in minutes)
function calcMoonEquationOfTime(jd) {
// Moon's EOT is significantly more complex and varies more rapidly.
// This function provides a very rough estimate.
var n = jd – 2451545.0;
var meanAnomalyMoon = 134.9634 + 13.0649929 * n;
var meanLongitudeMoon = 218.3165 + 13.1763966 * n; // Mean longitude of Moon
// Simplified approximation of Moon's RA and EOT
var moonLon = moonLongitude(jd); // Re-calculating for consistency
var moonRA = moonLon – 1.915 * Math.sin(toRadians(meanAnomalyMoon)) – 0.020 * Math.sin(toRadians(2 * meanAnomalyMoon)); // Approximated RA
// EOT = Mean Sidereal Time – RA (simplified)
// Need Mean Sidereal Time for the date
var GMST = 280.46061837 + 360.98564736629 * (jd – 2451545.0) + 0.000387933 * Math.pow((jd – 2451545.0)/1000, 2) – Math.pow((jd – 2451545.0)/10000000, 3);
GMST = GMST % 360; if (GMST < 0) GMST += 360;
var EOT_degrees = GMST – moonRA; // This is a placeholder logic
return EOT_degrees * 4; // minutes
}
// Calculates Moon Phase (0=New Moon, 180=Full Moon)
function calculateMoonPhase(jd) {
// Based on http://www.benjanjones.com/moon-phase-calculator/
var days = jd – 2451550.0; // Days since Jan 4, 2000 (New Moon)
var synodicPeriod = 29.530588853; // Synodic period of the Moon in days
var phase = (days % synodicPeriod) / synodicPeriod;
if (phase < 0) phase += 1; // Ensure phase is between 0 and 1
var phaseDegrees = phase * 360;
var phaseName = "";
if (phase 0.96) phaseName = "New Moon";
else if (phase < 0.25) phaseName = "Waxing Crescent";
else if (phase < 0.5) phaseName = "First Quarter";
else if (phase < 0.75) phaseName = "Waxing Gibbous";
else if (phase = 0.04 && phase = 0.25 && phase = 0.50 && phase = 0.75 && phase = 0.96 && phase < 0.98) phaseName = "Waning Crescent"; // Adjusted range slightly
return phaseName + " (" + Math.round(phase * 100) + "% illuminated)";
}
// — Utility Functions —
// Converts degrees to radians
function toRadians(degrees) {
return degrees * Math.PI / 180;
}
// Converts radians to degrees
function toDegrees(radians) {
return radians * 180 / Math.PI;
}
// Formats minutes into HH:MM string, handling day rollover
function formatTime(totalMinutes) {
if (isNaN(totalMinutes)) return "Invalid Time";
var daysOffset = Math.floor(totalMinutes / 1440); // 1440 minutes in a day
var minutesToday = totalMinutes % 1440;
if (minutesToday = 12 ? "PM" : "AM";
hours = hours % 12;
hours = hours ? hours : 12; // the hour '0' should be '12'
var formattedHours = hours < 10 ? "0" + hours : hours;
var formattedMinutes = minutes < 10 ? "0" + minutes : minutes;
var timeString = formattedHours + ":" + formattedMinutes + " " + period;
// Indicate if time is on a different day
if (daysOffset === 1) timeString += " (Next Day)";
else if (daysOffset === -1) timeString += " (Previous Day)";
return timeString;
}
// Converts UTC minutes to local time, considering timezone offset
function convertUtcMinutesToLocal(utcMinutes, tzOffset) {
if (isNaN(utcMinutes)) return NaN;
// tzOffset is typically hours, convert to minutes
var offsetMinutes = tzOffset * 60;
var localMinutes = utcMinutes + offsetMinutes;
// Normalize to a 24-hour cycle (0 to 1440 minutes)
while (localMinutes = 1440) {
localMinutes -= 1440;
}
return localMinutes;
}
// Initialize default values on load if needed
window.onload = function() {
// Optional: Set current date as default
var today = new Date();
document.getElementById("year").value = today.getFullYear();
document.getElementById("month").value = today.getMonth() + 1; // Month is 0-indexed
document.getElementById("day").value = today.getDate();
// You could also fetch user's timezone, but it's unreliable and often requires server-side.
// For now, we require manual input.
// Example for fetching timezone (might not be accurate):
// try {
// var userTimezoneOffset = new Date().getTimezoneOffset(); // Offset in minutes
// document.getElementById("timezone").value = -(userTimezoneOffset / 60); // Convert to hours, reverse sign
// } catch(e) {
// console.log("Could not automatically detect timezone.");
// }
};