Every fact in the three day, night and seasons lessons is listed here with where it comes from. The numbers in [brackets] on the lesson pages link to this list.
How we rate sources
High: space agencies (NASA), peer-reviewed open textbooks (OpenStax, Rice University) and professional scientific societies (American Physical Society).
Medium-high: reputable science news reporting directly on a primary document.
Medium: single-author essays and popular history sites. We only use these for history details, and never on their own: each one is paired with a second source.
Wikipedia was not used as a source. Numbers are rounded (for example 9.8 m/s² for Earth's gravity). The text was drafted with help from AI (Claude) and then checked against these sources. Corrections: hello@echoesof.science.
Where the numbers are rounded or simplified: sources give Earth's tilt as 23.4°, 23.44°, 23.45° or 23.5°; the lessons use about 23.4° (and 23° in simple sums). The dates of solstices and equinoxes shift by a day or so from year to year. The noon-Sun formula α = 90° − φ + δ is the northern-hemisphere form of the formula on PVEducation (α = 90° + φ − δ, subtracting from 180° when the result is above 90°); both give the same angles. The idea that sunlight spread over a bigger area heats less is the main reason for the seasons, but the air and the oceans also delay the hottest and coldest weather by a month or more (OpenStax).
All sources
[1] What Causes the Seasons?
NASA Space Place · Reliability: High
Type: Space agency, children's science site
Earth spins around its axis, making one complete turn each day; Earth's tilted axis causes the seasons; the hemisphere tilted towards the Sun has summer and gets more direct rays; the hemisphere tilted away gets rays at more of an angle and has winter; the two hemispheres have opposite seasons; Earth is closest to the Sun (about 91.4 million miles) in January and farthest (about 94.5 million miles) in July, so distance does not cause the seasons.
Earth completes one rotation every 23.9 hours and one trip around the Sun in 365.25 days, which is why a leap day is added every four years; its axis is tilted 23.4 degrees; this tilt causes the yearly cycle of seasons: the hemisphere tilted towards the Sun gets more direct heating and has summer, and six months later the pattern flips.
NOAA NESDIS (U.S. satellite and information service) · Reliability: High
Type: Government science agency, education page
Earth is tilted 23.45 degrees; it is about 91,400,000 miles from the Sun in January and about 94,500,000 miles in July; the North Pole is tilted towards the Sun in June and the South Pole in December.
The tilt (23.5°), not distance, causes the seasons; Earth's distance from the Sun varies by only about 3% and it is closest in January; sunlight hitting the ground at a slant is spread over a larger area (in the textbook's example more than twice as large in winter); the Sun is up about 15 hours in June and 9 hours in December in the USA; around 21 June the Sun is overhead at the Tropic of Cancer (23° N) and places north of the Arctic Circle (67° N) get 24 hours of daylight; around 21 March and 21 September every place has about 12 hours of day and 12 of night; near the equator days are about 12 hours all year; at the poles there are six months of daylight and six of darkness; noon Sun at the equator is 90° on 21 March and about 67° on 21 June; the Tropic of Cancer's latitude equals the tilt and the Arctic Circle's latitude is 90° minus the tilt; the warmest and coldest weather comes a month or more after the solstices because air and water heat and cool slowly.
Royal Museums Greenwich (Royal Observatory) · Reliability: High
Type: National museum and observatory
The solstice is the moment a hemisphere is most tilted towards the Sun; in the Northern Hemisphere the June solstice (21 June) is the longest day and shortest night; the winter solstice comes six months later (21 December in 2026); 'equinox' comes from the Latin aequinoctium, 'equal night'; Earth's axis is tilted at 23.44°.
PVEducation (C. Honsberg and S. Bowden) · Reliability: Medium-high
Type: Online textbook by university solar-energy researchers
Gives the maximum (solar noon) elevation of the Sun as α = 90° + φ − δ, with φ the latitude (positive north, negative south) and δ the declination, which depends on the day of the year; if the result is above 90°, subtract it from 180°.
PVEducation (C. Honsberg and S. Bowden) · Reliability: Medium-high
Type: Online textbook by university solar-energy researchers
Gives the relation S_horizontal = S_incident · sin α, where α is the elevation angle of the Sun: the radiation falling on a horizontal surface is the incident radiation times the sine of the Sun's elevation.