3 calculators · 242 city pages
Sky Watch
Three astronomical calculators supported by 242 city-specific solar pages and dated lunar references.
Open Sky Watch9 interactive calculators·scientifically referenced
Calculate the sky, motion, and geometry around you.
Same universe. Same physics. Results you can inspect.
Practical astronomy, mechanics, and geometry tools with visible formulas, assumptions, worked examples, and authoritative references.
No accountInstant resultsMethods disclosed
Start calculating
Complete directory Choose a tool, not a category
Open the core calculator directly. Contextual pages are available when you need a specific city, speed, height, or format.
Sunrise & Sunset
Solar noon, daylight, and horizon crossings for 121 cities.
Local solar time
Moon Phase
Phase age, illuminated fraction, and waxing or waning state.
29.53-day cycle
Golden Hour
Altitude-based golden and blue-hour photography windows.
0° → +6° Sun
Free Fall
Ideal fall time and impact speed across planetary gravity.
10 m → 1.43 s
Braking Distance
Reaction plus physical braking distance across road surfaces.
Speed² relationship
Projectile Motion
Range, apex height, flight time, and a live trajectory plot.
2D vacuum model
Aspect Ratio
Proportional dimensions for video, displays, and photography.
16:9 → 1920×1080
Golden Ratio
Golden sections, harmonics, and modular design scales.
φ = 1.618033…
Pythagoras
Interactive right-triangle sides, angles, and SVG geometry.
3² + 4² = 5²
Explore by discipline
Three focused physics labs
3 calculators · 72 worked pages
Motion Lab
Three mechanics calculators with contextual examples for heights, speeds, surfaces, planets, and projectiles.
Open Motion Lab3 calculators · 24 worked pages
Geometry Lab
Three proportional-geometry tools for layouts, screens, image formats, and right-triangle calculations.
Open Geometry LabLearn the method
All articles The physics behind the result
Long-form explanations connect each calculator to its assumptions, derivation, and real-world limits.
sky7 min
Why is the Sky Blue? The Physics of Rayleigh Scattering and Atmospheric Optics
An in-depth pedagogical analysis of atmospheric Rayleigh scattering, the inverse fourth power wavelength law, and why the human visual cortex perceives a blue rather than violet daylight sky.
Read articlemotion8 min
How the Braking Distance Formula Works: Mechanics, Friction & Stopping Physics
A comprehensive technical derivation of vehicular braking distance, coefficient of friction (mu), perception-reaction delay, and why doubling your vehicle speed quadruples your required stopping distance.
Read articlegeometry8 min
The Golden Ratio in Nature: Sacred Geometry, Phyllotaxis & Spiral Mathematics
An authoritative mathematical and botanical examination of the divine proportion phi (1.618033...), Fibonacci spirals, Romanesco fractals, and optimal spatial packing in natural growth systems.
Read articlesky8 min
How Sunrise and Sunset Times Are Calculated: Solar Geometry, Refraction and Time Zones
A practical derivation of sunrise and sunset calculations, including solar declination, hour angle, atmospheric refraction, observer coordinates, elevation, and civil time conversion.
Read articlemotion8 min
Free Fall with Air Resistance vs Vacuum: Why Real Objects Reach Terminal Velocity
Learn when the vacuum free-fall equation is accurate, how aerodynamic drag changes acceleration, and why mass, shape, area, and air density determine terminal velocity.
Read article Transparent methodology
Built to be checked, not merely trusted.
SkyMotion exposes formulas, model assumptions, limitations, and references beside the tools. Calculations are maintained by Traian Anghel, a physics teacher based in Brăila, Romania.
Reference stack
- USNO & NOAASolar position and horizon conventions
- Jean MeeusLunar phase and astronomical algorithms
- NISTSI constants and standard gravity
- Classical mechanicsKinematics, energy, and geometry
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