Combine solar height and day duration in a seasonal energy argument
Axial tilt changes how solar rays meet a surface and how long the Sun remains above its horizon. Opposite hemispheres therefore have opposite seasonal geometry at the same moment. Orbital distance alone cannot explain that simultaneous reversal; this controlled model holds the normal-ray input fixed to isolate orientation.
Learning outcome: Compare opposite latitudes at fixed declination, then compare solstice/equinox at one latitude. Retain the integrated factor and duration rather than treating a noon snapshot as an entire-day average.
Starting recap
Keep celestial and local frames, solar and sidereal time, phase and eclipse geometry, and source rendering versus direct observation distinct.
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At latitude+30° and declination+23.44°, noon altitude 83.44°, ideal daylight 13.93286 h and mean input factor 0.360329. At latitude−30° with the same declination, noon altitude 36.56°, daylight 10.06714 h and mean factor 0.161435. One common orbital distance coexists with opposite seasonal geometry.
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Why is noon Sun height alone insufficient to compare a full day’s received energy?
Experiment
Compare opposite latitudes at fixed declination, then compare solstice/equinox at one latitude. Retain the integrated factor and duration rather than treating a noon snapshot as an entire-day average.
Combine noon height and day duration before seasonal energy
Worked teaching model · synthetic values · Original circular-orbit geometry, axial obliquity 23.44°. Point Sun, no atmosphere/refraction, solar input normalized to a surface normal to rays. Sunrise hour angle acos(−tanφ tanδ); daily mean horizontal irradiance factor=[H 0 sinφ sinδ+cosφ cosδ sinH 0]/π with H 0 in radians. No weather or actual daily temperature prediction.
Reset keeps your prediction, captures and practice history.
Axial tilt changes both solar elevation and daylight duration; the hemispheres respond oppositely.
The daily integral weights the entire Sun path, not noon height alone. Circular orbit fixes incident normal-ray input to isolate tilt; atmosphere, clouds, thermal storage and actual weather remain outside this geometry.
| Quantity | Value | Unit |
|---|---|---|
| Noon geometric altitude | 83.44000 | degrees |
| Daylight duration | 13.93286 | mean solar hours, ideal |
| Sunrise hour-angle magnitude | 104.4965 | degrees |
| Daily mean horizontal input factor | 0.3603290 | fraction of normal-ray flux |
| Noon horizontal input factor | 0.9934528 | ratio |
Use the supplied screen-based records and diagrams. No direct Sun viewing, instrument aiming or outdoor observation is required or requested.
Axial tilt changes both solar elevation and daylight duration; the hemispheres respond oppositely.
The daily integral weights the entire Sun path, not noon height alone. Circular orbit fixes incident normal-ray input to isolate tilt; atmosphere, clouds, thermal storage and actual weather remain outside this geometry.
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At the equator and equinox, find noon altitude, duration and normalized mean input.
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