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Solar & Lunar Ephemerides Engine

Sky Watch & Celestial Mechanics

Zero-bloat, client-side astronomical calculators calibrated against the US Naval Observatory (USNO) Astronomical Almanac 2024 and Jean Meeus' Astronomical Algorithms.

Sunrise & Sunset in Braila, Romania

US Naval Observatory (USNO) Astronomical Almanac 2024 p.C24 & NOAA Solar Model

Formulacos(H) = (cos(90.833°) - sin(δ)·sin(φ)) / (cos(δ)·cos(φ))
Sunrise
06:41
Official Horizon (90°50′)
Sunset
19:27
Official Horizon (90°50′)
Solar Noon
13:04
Highest solar culmination
Day Length
12h 47m
Golden Hour Photographic Windows (Sun < 6° Elevation)
Morning Golden Hour
06:4507:20
Warm dawn sidelight for landscapes
Evening Golden Hour
18:4819:23
Soft sunset illumination for portraits

How the sunrise and sunset calculator works

This calculator converts a date and geographic position into the apparent times at which the Sun crosses the local horizon. It also reports solar noon, daylight duration, and the morning and evening photographic windows for the selected location.

Method & formula

The solar ephemeris supplies declination and the equation of time. The horizon hour angle follows cos(H₀) = [sin(h₀) − sin(φ)sin(δ)] / [cos(φ)cos(δ)], using the conventional apparent sunrise altitude h₀ ≈ −0.833°.

Inputs

Choose a supported city or enter latitude and longitude, then select the calendar date. Coordinates determine local horizon geometry; the browser time zone converts the computed UTC event to the displayed civil time.

How to read the result

Sunrise and sunset refer to the apparent upper edge of the solar disk. Solar noon is the midpoint of the calculated daylight interval, not necessarily 12:00 on the clock. Day length is the elapsed time between the two horizon crossings.

Assumptions & limits

The result assumes a level astronomical horizon and standard near-horizon refraction. Mountains, buildings, observer elevation, unusual pressure or temperature gradients, and political time-zone settings can shift the visible event by several minutes.

Reference: NOAA Solar Calculator methodology, US Naval Observatory conventions, and Jean Meeus, Astronomical Algorithms.

Lunar Phase & Illumination Visualizer

Jean Meeus, Astronomical Algorithms 2nd ed. Chapter 49 (Phases of the Moon)

FormulaIllumination = (1 - cos(2π · Phase)) / 2
99% Cycle
New Moon
0.1% Illuminated
Visible fraction of the lunar disc facing Earth
0% (New)50% (Quarter)100% (Full)
Moon Age29.2 daysin 29.53d synodic cycle
Phase Angle (k)355.7°geometric elongation
Astronomical Algorithm Note: Moon phases are governed by the synodic month (mean length: 29.53058867 days). Phase zero corresponds to the conjunction of the Moon and Sun (New Moon), while phase 0.50 denotes the exact opposition (Full Moon).

Understanding lunar phase and illuminated fraction

The visualizer estimates the Moon’s position within the synodic cycle for any selected date, labels the corresponding phase, and converts that cycle position into the fraction of the lunar disk illuminated from Earth’s perspective.

Method & formula

Illumination is modeled as k = [1 − cos(2πp)] / 2, where p is the normalized synodic phase. Values near p = 0 represent New Moon, p = 0.25 First Quarter, p = 0.5 Full Moon, and p = 0.75 Last Quarter.

Inputs

Only the date is required. Moving one day backward or forward lets you follow the waxing and waning sequence. The displayed phase age measures progress through the approximately 29.53-day mean synodic month.

How to read the result

Illumination percentage describes how much of the visible disk is sunlit; it is not the Moon’s brightness at the ground. Waxing means the illuminated fraction is increasing, while waning means it is decreasing.

Assumptions & limits

This is an educational phase model, not a topocentric observing forecast. Local moonrise, altitude, atmospheric extinction, libration, Earth–Moon distance, clouds, and the exact instant of a principal phase affect what an observer actually sees.

Reference: Jean Meeus, Astronomical Algorithms, with the standard synodic-phase illumination relationship.

Golden Hour & Blue Hour Photography Calculator

Optimal solar lighting angles for landscape, portrait, and architectural photography

FormulaGolden Hour: 0° < Solar Elevation < +6° | Blue Hour: -6° < Solar Elevation < -4°

Morning Photography Windows

Morning Blue Hour~9000K Cool Light
06:1106:22

Deep indigo skies balanced with city streetlights. Ideal for urban architecture.

Morning Golden Hour~3500K Warm Light
06:4507:20

Low horizontal light, long soft shadows, mist illumination, and rich golden highlights.

Evening Photography Windows

Evening Golden Hour~3200K Warm Light
18:4819:23

Flattering warm skin tones for outdoor portraits and dramatic rim lighting on hair and leaves.

Evening Blue Hour~8500K Cool Light
19:4619:57

Vibrant saturated blue skies as street lamps ignite. Perfect for long exposure tripod captures.

Why Golden Hour Transforms Photography (Rayleigh Scattering)

When the sun is low on the horizon (solar elevation under 6°), sunlight passes through roughly 10 times more atmosphere than at solar noon. Rayleigh scattering selectively disperses short blue wavelengths (proportional to 1/λ⁴), allowing only longer golden, amber, and red wavelengths to reach the camera sensor. The resulting diffuse lighting minimizes harsh facial shadows and drastically expands dynamic range.

How golden hour and blue hour are determined

Instead of assuming every photographic window lasts exactly one hour, this calculator finds when the Sun crosses defined elevation bands. Their duration changes with latitude, season, date, and the observer’s longitude.

Method & formula

SkyMotion defines golden hour from 0° to +6° solar elevation in the morning and the reverse band in the evening. Blue hour uses the −6° to −4° band before sunrise and the reverse crossing after sunset.

Inputs

Select a location and date. The same solar-position engine used for sunrise and sunset calculates each altitude crossing and converts it into local clock time.

How to read the result

Golden-hour output marks low-angle direct sunlight that often produces warm tones and longer shadows. Blue hour marks a twilight interval dominated by diffuse sky light. Treat the times as planning windows, not guarantees of a particular color palette.

Assumptions & limits

Golden hour has no single universal photographic definition. Clouds, aerosols, terrain, urban obstructions, elevation, camera white balance, and exposure choices strongly affect the observed light even when the solar elevation is correct.

Reference: NOAA/USNO solar-position geometry; photographic windows are explicit SkyMotion altitude-band definitions.

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