Rising Sun and Moon Calculator

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Reviewed by: David Chen, Celestial Dynamics Specialist

Accurately predict the rise and set times for the Sun and Moon based on your specified geographic coordinates and date. This calculator is essential for planning astronomy, photography, navigation, and religious observances.

Rising Sun and Moon Calculator

Sun Rise Time: –:–

Moon Set Time: –:–

Detailed Calculation Steps

Click ‘Calculate’ to view the detailed astronomical process used to determine the times.

Rising Sun and Moon Calculator Formula

The exact formulas for celestial mechanics are highly complex, involving orbital elements, Julian Dates, Mean Anomalies, and the Observer’s position. This client-side module uses a simplified, iterative trigonometric approximation based on the observer’s location and date.

Sun Hour Angle $H$: $\cos(H) = (\sin(h_0) – \sin(\phi)\sin(\delta)) / (\cos(\phi)\cos(\delta))$
Where $\phi$ is Latitude, $\delta$ is Declination, and $h_0$ is the Horizon Angle.

Formula Source (High Authority Reference): NOAA Solar Position Calculations (PDF) | U.S. Naval Observatory Data (External)

Variables

  • Latitude (deg): The angular distance of a location north or south of the Equator. Crucial for determining the length of the day and night.
  • Longitude (deg): The angular distance east or west of the Prime Meridian. Essential for local time correction.
  • Date (YYYY-MM-DD): The specific date for which the rise/set times are required. Celestial positions are highly time-dependent.
  • Timezone Offset (Hours from UTC): Used to convert the calculated Universal Time (UT) back to the user’s Local Time.

Related Calculators

Solar Azimuth and Altitude Calculator Monthly Lunar Phase Calendar Sidereal Time Converter Meteor Shower Peak Predictor

What is Rising Sun and Moon Calculator?

A Rising Sun and Moon Calculator is a tool that uses principles of celestial mechanics and geometry to predict the precise moments when the upper edge of the Sun or Moon first appears above (rise) or disappears below (set) the observer’s local horizon. These calculations are critical because they account for atmospheric refraction, the observer’s elevation, and the body’s parallax, which can alter the observed time by several minutes compared to a simple geometric model.

Unlike basic daily timekeeping, astronomical calculations require constant position updates. The Moon’s orbital path is highly complex and non-uniform, meaning its rise/set times can shift significantly from one day to the next. For instance, the Moon can rise at various times, and occasionally, it may not rise or set at all within a 24-hour period, depending on the latitude. This calculator helps mitigate the need for complex look-up tables.

How to Calculate Rising Sun and Moon (Example)

  1. Determine Julian Day: Convert the input date (e.g., 2025-01-01) into a Julian Day Number (JDN), the continuous count of days since the beginning of the Julian period.
  2. Calculate Solar Declination: Use the JDN to find the Sun’s position, specifically its declination ($\delta$), which is its angular distance north or south of the celestial equator.
  3. Determine Local Siderial Time (LST): Calculate the LST based on the input longitude and Universal Time, which defines the ‘star time’ at the observer’s location.
  4. Solve the Hour Angle Equation: Use the LST, Latitude ($\phi$), and Declination ($\delta$) to solve the trigonometric equation for the Hour Angle ($H$) where the Sun’s altitude is zero (accounting for refraction).
  5. Convert to Local Time: Convert the resulting Hour Angle back to Universal Time (UT), and finally apply the Timezone Offset to get the final, accurate Local Time for rise and set. (A similar but more complex process is used for the Moon.)

Frequently Asked Questions (FAQ)

Is the time outputted by the calculator highly accurate?

While the underlying models are highly accurate, this simplified client-side module provides a very close approximation, suitable for general planning. Professional navigation or space exploration requires highly specialized ephemeris data.

Why is the Moon’s rise time different every day?

The Moon orbits the Earth, but the Earth is also orbiting the Sun. This combined motion means the Moon’s position relative to a fixed point on Earth changes dramatically each day, causing its rise/set times to shift by about 50 minutes on average.

What is the difference between astronomical and civil twilight?

Sunrise and sunset refer to the moment the Sun’s edge crosses the horizon. Civil twilight is the period when the Sun is 6 degrees below the horizon—enough light for activities. Astronomical twilight is when the Sun is 18 degrees below, and the sky is completely dark for optimal star gazing.

What if the calculator returns ‘Does Not Rise’ or ‘Does Not Set’?

This occurs mainly for the Sun in polar regions (above 66.5 degrees latitude) during summer or winter, or for the Moon at various high latitudes, where the celestial body stays above or below the horizon for a full 24-hour period.

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