Why does it get dark earlier when the sun is lower in winter?
Standing in the same place, watching the sun in winter and summer take two different paths.
In summer, it's still bright after dinner, but in winter, the sun is almost setting after school. First choose a place and let the sun travel through the day: see how high it goes overhead and how long it stays above the horizon.
Guess first
When it's summer in the Northern Hemisphere, is it also summer in the Southern Hemisphere?
Show answer and explanation
usually winter — The tilt of the Earth's axis causes the two hemispheres to receive opposite sunlight and have opposite seasons.
Then connect experience and science
First look at the sunny day you are familiar with
The sun rises, goes higher, and sets again. The golden solid line in the picture is the section above the horizon, and the gray dotted line indicates the direction blocked by the earth.
Fixed location, comparing the sun's path throughout the day
Same place, another season
Near the summer solstice in the Northern Hemisphere, the sun's path is higher and a longer section is above the horizon. During the winter solstice it is lower and shorter.
Solar declination varies from approximately −23.44° to +23.44°
Why does the path change?
The Earth's axis is tilted relative to the orbital plane. As the Earth orbits, the direct sun's position moves between north and south; the path of the sun you see changes accordingly.
δ = asin(sin ε × sin λ)，ε ≈ 23.44°
Switch to the southern hemisphere and check your thoughts again
At the same time, the northern hemisphere is tilted toward the sun, while the southern hemisphere is farther away, so the seasons on both sides are opposite. It's not like the whole earth gets warmed together when it's close to the sun at the same time.
The same solar declination, different latitudes have different altitudes and day lengths
Expand the calculation
δ = asin(sin ε sin λ)；ε = 23.44° sin h = sin φ sin δ + cos φ cos δ cos H cos H₀ = −tan φ tan δ 昼长 = 2H₀/15 Hour
First use the solar longitude λ to find the declination δ, and then bring it into the local latitude φ. The day length formula is only valid when there are ordinary rises and falls; extreme day and night are judged separately, and refraction is not included in this lesson.
give it a try
First select "Summer Solstice · About June" and "Winter Solstice · About December" to compare; the slider will display the solar term range and approximate months.
No need to memorize symbols
- ε
- The inclination of the Earth's axis relative to the orbital normal, approximately 23.44°
- λ
- Solar longitude: Vernal equinox 0°, summer solstice 90°, autumnal equinox 180°, winter solstice 270°
- δ
- Solar Declination: Position north and south relative to the celestial equator
- h
- Geometric height of the sun's center
Algorithm, accuracy and scope of application
Chapter 27 uses the solar ecliptic longitude of 0°, 90°, 180°, and 270° to define the equinoxes. This lesson combines Chapters 13 and 15 to explain its daily observation significance. The tilt of the earth's axis is the cause, and the change in declination is a mathematical expression; the solar longitude does not change strictly uniformly with the calendar date. The declination angle is fixed at 23.44°, the solar latitude is set to 0, and the declination is fixed within a single day. Local solar time is approximately converted into hour angle by H=15(t−12); day length is estimated based on the ideal 24-hour solar day, not the sidereal hour in the previous sidereal lesson. The polynomial and periodic corrections to the bisection moment in Chapter 27 are not implemented, nor do they simulate real annual temperatures. The length of sunshine in the picture comes from geometry, and the effect is not exaggerated to change the distance between the earth and the sun.
my understanding check
At 40° north latitude, the midday sun is usually on the summer solstice compared to the winter solstice?
higher — The sun's declination is more northerly during the summer solstice and appears higher in mid-northern latitudes.
The days are longer at the same place. What does that correspond to in the picture?
The path is above the horizon longer — The length of the day is related to how long the sun is above the horizon.
Can this model give you a sunrise accurate to the second at your doorstep?
cannot — A simplified geometric model is used here, excluding specific date ephemeris, refraction, solar radius and terrain.
The tilt of the Earth's axis causes the sun to take different paths in the sky throughout the year, giving us different heights of the sun and different lengths of daylight.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 27 chapter