Why Seasons Happen: Earth's Tilt, Sun Angle and Daylight

A hot July afternoon in the Northern Hemisphere arrives when Earth is near the farthest point of its orbit from the Sun¹. That one fact breaks the most popular explanation of the seasons and is the fastest way into the real one. Below: the orbit numbers, the tilt, the sun-height math you can run for your own latitude, and what changes when the tilt itself drifts over thousands of years.

Earth’s lopsided orbit does not make the seasons

The popular explanation is distance: Earth sits closer to the Sun in summer, the story goes, and that is why it is hotter¹. The story fails on the calendar. In the Northern Hemisphere it is winter when Earth is closest to the Sun and summer when it is farthest away¹. If distance were the cause, it would be hotter in the northern hemisphere in January than in July³.

The orbit is slightly stretched, and the numbers are small. Perihelion, the closest point, is 147.095 million km from the Sun and aphelion, the farthest, is 152.100 million km⁵. In miles that is 91,400,000 at perihelion and 94,500,000 at aphelion¹. The gap is over 3 million miles, which is not much relative to the whole distance¹. The orbit’s eccentricity, a measure of how far it is from a circle, is 0.0167⁵. Perihelion falls on or about January 3 and aphelion on or about July 4⁴.

Worked example (our arithmetic): how big is the distance effect?

NASA’s own rounded figure for the same difference is about 6 percent more incoming sunlight from July to January⁴. Either way the Southern Hemisphere, which is tilted toward the Sun in January, gets a small distance bonus on top of its summer, and the Northern Hemisphere gets a small penalty on top of its winter. The seasonal swings we feel are far larger than that, so something else is in charge.

Why does axial tilt cause seasons?

Earth’s axis is tilted 23.44 degrees from the perpendicular to its orbital plane⁵. NOAA gives the same tilt as 23.45 degrees². The likely origin is an early collision: it is thought that something big hit the young Earth and knocked it off-kilter, a NASA Space Place account¹.

The tilt matters because of one more fact: as Earth orbits the Sun, its axis always points in the same direction¹. Astronomers call that axial parallelism¹⁰. So half an orbit apart, the same pole faces opposite ways relative to the Sun¹⁰. When the North Pole tilts toward the Sun it is summer in the Northern Hemisphere, and when the South Pole tilts toward the Sun it is winter there¹.

Two effects stack up in the tilted hemisphere. First, it gets more hours of sunlight each day⁹. Second, midday sunlight strikes the ground at an angle nearer the vertical, so it delivers more energy per unit of surface area⁹. The NWS adds a third effect: with the Sun high, less sunlight gets scattered before reaching the ground, because it travels a shorter path through the atmosphere³.

Rotation and revolution are different jobs. Earth spins around its axis once a day, which gives day and night¹. It circles the Sun once every 365.25 days⁹. The tilt is a fixed lean, and the circling is what carries the lean from one side of the Sun to the other.

The four key dates

Near June 21, the summer solstice, the Sun is directly over the Tropic of Cancer at 23.5 degrees north latitude³. About 90 days later, around September 21, the autumnal equinox puts the Sun directly over the equator³. Near December 21, the winter solstice, the Sun is directly over the Tropic of Capricorn at 23.5 degrees south latitude³. The spring equinox near March 21 again has the Sun over the equator³. One orbit takes 365.256 days against the stars⁵, so the four marks are about a quarter of that apart.

The Sun’s latitude at those moments equals the tilt, which is why the tropics sit at 23.5 degrees³. The two hemispheres swap roles: winter in North America is summer in Australia⁹. A Southern Hemisphere resident sees the Sun more northerly in the sky during June, July and August². In North America the winter Sun rises in the southeast and sets in the southwest, and the summer Sun rises in the east, stands overhead at noon and sets in the west².

How high the noon Sun gets: the math

The tilt turns into a formula you can use. The solar angle at noon, measured up from the horizon, is 90 minus the latitude of the location, plus the solar declination, as a UC Irvine course slide sets it out⁷. The declination is the latitude where the Sun is overhead, so it is +23.5 at the June solstice, 0 at the equinoxes and −23.5 at the December solstice³⁷. A course example for Toronto at latitude 44 N works out to 46 at an equinox, 69.5 at the June solstice and 22.5 at the December solstice⁷.

Worked example (our arithmetic): latitude 40 N, using the 23.44 degree tilt as the declination at the solstices⁵⁷

The same energy spreads over more ground when the Sun is low⁹. As a geometric estimate, the share that lands on one square meter of flat ground scales with the sine of the Sun’s height. That is 0.959 at 73.44 degrees and 0.447 at 26.56 degrees, so the June noon delivers about 2.1 times the energy per square meter that the December noon does (our arithmetic)⁹. This is the main reason for the temperature difference, and it is why a tilt change of just a degree or two matters over thousands of years.

At the equator the formula needs one adjustment. At 0 degrees latitude the June solstice gives (90 − 0) + 23.44 = 113.44, which is past straight overhead, so the real height is 180 − 113.44 = 66.56 degrees (our arithmetic)⁷. The December solstice gives the same 66.56, and the equinoxes give 90⁷. Near the equator the Sun is always high, which is why the seasons there are weak.

Try your own latitude

Try latitude 40 on June 21 and December 21, and the result should land close to the 73 and 27 degrees worked above⁷. Then try latitude 0, and then 70.

Daylight by latitude

The tilt also sets how long the day lasts. At the equator, daylight stays within a few minutes of 12 hours all year³. At mid-latitudes it ranges from about 15 hours around the summer solstice to near nine hours close to the winter solstice³. The effect grows toward the poles.

Notice the Arctic Circle latitude: 66.5 degrees is 90 − 23.5³. That is the same tilt number again, showing up as the latitude where the Sun can stay above the horizon for a whole day.

Would seasons exist without a tilt?

Not the familiar four. With zero tilt, the Sun’s declination would stay at 0 all year, so the noon height at latitude 40 N would stay at 90 − 40 = 50 degrees on every date⁷. Our arithmetic above shows what the tilt adds to that: plus or minus 23.44⁵. Daylight at mid-latitudes would stay near 12 hours instead of swinging between roughly nine and 15 hours³. Only the small distance effect would remain, with about 6 percent more sunlight in January than in July⁴.

Other planets show the idea in the data. Venus is tilted 177.4 degrees and Uranus 97.8 degrees, nearly on its side⁶. Mars, Saturn and Neptune lean at 25.2, 26.7 and 28.3 degrees, close to Earth’s 23.4⁶. Mercury, at 0.034 degrees, and Jupiter, at 3.1, lean almost not at all⁶.

Does the tilt change?

Yes, slowly, and by amounts that are tiny on a human timescale. Earth’s tilt averages 23.5 degrees and varies from near 22 to 24.5 degrees³. A NASA description puts the full cycle at about 40,000 years, with the tilt moving between 22.1 and 24.5 degrees⁴. The tilt at the start of 2000 was about 23.4 degrees, and it is now decreasing by about 47 arcseconds per century⁸.

More tilt means more severe seasons, with warmer summers and colder winters, and less tilt means cooler summers and milder winters⁴. As the tilt increases, the seasonal contrast rises in both hemispheres⁴. The Moon has a stabilizing effect on Earth’s tilt¹⁰.

Worked example (our arithmetic): the extremes of the tilt cycle at latitude 40 N⁴⁷

Two other slow cycles change how the seasons play out. The shape of the orbit shifts between elliptical and nearly circular over 90,000 to 100,000 years, and its eccentricity ranges from nearly zero to 0.07⁴. Axial precession, the slow turn of the axis direction, changes the dates of perihelion and aphelion⁴. Today northern summer occurs near aphelion⁴. Combined, the three cycles shape the long climate record⁴.

Common mix-ups

• “Summer means closer.” The Sun is closest around January 3 and farthest around July 4⁴.
• “The tilt flips back and forth.” The axis keeps pointing the same direction as Earth orbits¹.
• “The tilt is 23.5 degrees exactly.” The average is 23.5, the tilt varies between 22.1 and 24.5 degrees, and the current fact-sheet value is 23.44³⁴⁵.
• “Seasons are the same everywhere.” Near the equator daylight stays near 12 hours; at the Arctic Circle the Sun never sets for weeks³.

For another place where a smooth curve and a fixed constant decide a daily experience, see how fast coffee cools. The same idea of a rate depending on a gap sits behind what a derivative is, and hidden math in a normal day walks through more everyday numbers. For the circle constant that every orbit diagram quietly uses, read what pi is, and for the opposite problem of moving energy over wires, see why power lines use high voltage. Every page about the physical world around us is in the world section.