[290]

## 1. Seasons

Seasons are period that return every year and that can be recognized by how the weather and plants and animals behave, or (more generally) how the amount of sunlight per square meter of ground changes. In some areas (especially outside of the tropics) there are warm seasons and cold seasons, and in other areas there are dry seasons and wet seasons.

[525]

There are two different possible causes for changes in the amount of sunlight per square meter ground (without taking clouds into account): the skewness $$ε$$ of the rotation axis of the planet, and the eccentricity $$e$$ of the orbit of the planet around the Sun, which indicates the relative variation in the distance to the Sun. The first one yields changes in the distribution of time over days and nights, and the effects are in the opposite direction in both hemispheres, so when the north has long days, then the south has long nights, and the other way around. The second one yields changes in the temperature but no changes in days and nights, and works in the same direction in both hemispheres (so hotter everywhere or colder everywhere).

These effects can occur also on the other planets, so those can have seasons, too. Only a planet that has its rotation axis perpendicular to its orbit around the Sun and that is always at the same distance from the Sun would have no seasons at all: On such a planet the Sun would be above the horizon equally long every day of the year, and the Sun would trace the exact same path through the sky every day.

We can compare the relative influence of these two effects (due to $$ε$$ and to $$e$$) by the ratio of the annual least and greatest amount of sunlight per square meter of planetary surface per day, averaged over the surface of the whole planet.

The influence of $$ε$$ is approximated by

$$r_ε = −0.3854 \ln(ε + 7.495) + 1.774$$

if $$ε$$ is measured in degrees. The error of this approximation is at most 0.008. $$r_ε$$ is the planetary averaged ratio of the amount of sunlight per square meter per day in winter and the same amount in summer.

The influence of $$e$$ is equal to

$$r_e = \left( \frac{1 + e}{1 - e} \right)^2$$

De values of $$ε$$ (in degrees), $$e$$, $$r_ε$$, $$r_e$$, and the product of the latter two are listed in the following table for all planets and for the Moon.

Table 1: Seasons on the Planets

$$ε$$/° $$e$$ $$r_ε$$ $$r_e$$ $$r_{ε} r_e$$
Mercury 0 0.20 1.00 0.43 0.43
Venus 3 0.0068 0.88 0.97 0.86
Earth 23 0.017 0.45 0.94 0.42
Moon 0 0.017 1.00 0.94 0.94
Mars 25 0.093 0.43 0.69 0.30
Jupiter 3 0.048 0.86 0.82 0.71
Saturn 27 0.056 0.41 0.80 0.33
Uranus 82 0.046 0.041 0.83 0.034
Neptune 28 0.0090 0.40 0.96 0.39
Pluto 57 0.25 0.17 0.36 0.060

For example: the rotation axis of the Earth is tilted over 23°. It follows that $$r_{ε}$$ is 0.45, which means that on a midwinter's day slightly less than half as much sunlight falls on a square meter of earth's surface than on a midsummer's day (ignoring the effects of the atmosphere). The orbit of the Earth has an eccentricity of 0.017. It follows that $$r_e$$ is 0.94, which means that at aphelion about 94% as much sunlight hits the ground as at perihelion.

The last column shows approximately how noticeable the seasons are: the lower the number, the more pronounced are the seasons. Based on these calculations, the seasons are by far the most pronounced on Uranus and Pluto, and the seasons on Mars, Saturn, and Neptune are also more pronounced than those on Earth. The least pronounced seasons can be found on the Moon, Venus, and Jupiter.

The seasons on Mercury are strongly determined by the $$e$$-effect, and the seasons on all other planets except Venus, Jupiter, and the Moon are strongly determined by the $$ε$$-effect. On Mercury, both hemispheres therefore have the same season, on Venus, Jupiter, and the Moon not much at all can be noticed of seasons, and on the other planets both hemispheres have opposite seasons.

If you want to calculate the lengths of days and nights yourself, then you can use the formulas of the Solar Position Page, and especially equation 37 on that page. The length of the day is equal to $$2×H/360°$$ planet days (sols), and the length of the night is equal to the rest of the planet day. If you want to calculate the dates and times of solstices and equinoxes on the other planets, then look at the Seasons Calculation Page.

[225]

## 2. The Beginning of the Seasons

On Earth, the year is divided into four seasons that are tied to the motion of the Sun between the stars. According to the astronomical definitions:

summer begins when

The beginning of the (astronomical) summer is an solstice. In summer, daytime lasts longer than nighttime but gets shorter every day.

autumn begins when

• the night is equally long as the day for the first time since the beginning of spring.
• the Sun is due east at sunrise and due west at sunset for the first time since the beginning of spring.

The beginning of the (astronomical) autumn is an equinox. In autumn, daytime is shorter than nighttime and gets even shorter every day.

winter begins when

• it is the shortest day of the year (with the Sun shortest above the horizon).
• the Sun is lowest in the sky for the year at noon.
• at sunrise, the Sun is furthest from the east point on the horizon, and at sunset it is furthest from the west point, in the direction of the furthest geographical pole.

The beginning of the (astronomical) winter is a solstice. In winter, the daytime is shorter than the nighttime but is getting longer every day.

spring begins when

• the night is equally long as the day for the first time since the beginning of autumn.
• the Sun is due east at sunrise and due west at sunset for the first time since the beginning of autumn.

The beginning of (astronomical) spring is an equinox. In spring, daytime is longer than nighttime and getting even longer every day.

The seasons in the one hemisphere of Earth are shifted by half a year or two seasons compared to the other hemisphere. When it is summer in the northern hemisphere (e.g., in Europe), then it is winter in the southern hemisphere (e.g., in New Zealand), and when it is spring in the south (e.g., in Argentina), then it is autumn in the north (e.g., in Siberia). So, the beginning of a certain season in a certain year does not always fall at about the same time everywhere on Earth.

[296]

The position of the Sun between the stars is practically the same, as seen from any place on Earth. The geocentric ecliptic longitude λ, geocentric right ascension α, geocentric declination δ of the Sun (all measured relative to the equinox of the date) and the average date (in the Gregorian calendar) at the beginning of each season in each hemisphere are

Table 2: Seasons

α δ λ north south date
0 hours spring autumn 20 March
6 hours most N 90° summer winter 21 June
12 hours 180° autumn spring 23 September
18 hours most S 270° winter summer 21 December

The listed dates in the Gregorian calendar are averages around the year 2000, measured in Universal Time (UTC): The actual dates can be a day earlier or later. The exact time of the beginning of the seasons in the Gregorian calendar varies from year to year because

1. a year of the seasons (a tropical year) is about a quarter of a day longer than 365 days, so the time of the beginning of a season gets about a quarter of a day later each year, until a leap day (almost every four years) moves it one day earlier again. Because of this, the time of the beginning can be up to about 5/4 of a day early or late compared to the average.
2. the gravity of the other planets and the Moon can slightly slow down or speed up the Earth in its orbit, so that the seasons begin slightly earlier or slightly later. This usually changes the times by at most about 9 minutes.
3. the beginning times of some seasons are slowly shifting. For example, the dates in June and September are getting earlier by about one day per 1000 years, and the date in December is getting later by about one day per 4000 years.

Between the years 1900 and 2100, the earliest and latest begin times of the seasons are as follows (in TDT, which is roughly equal to UTC):

Table 3: Season Start

Month Earliest Latest Average
March 19 14:06 21 19:14 20 16:34
June 20 06:34 22 15:04 21 10:45
September 21 22:58 24 05:42 23 02:19
December 20 20:50 23 00:19 21 22:33

The first number is the date, and after that the time in hours and minutes is given. For example, the season that starts in December does so on 20 December at 20:50 hours at the earliest, on 23 December at 00:19 hours at the latest, and on 21 December at 22:33 hours on average.

[466]

A simple method (and therefore of limited accuracy) to predict the beginning of the seasons is to add the following time periods for each calendar year:

Table 4: Average Season Lengths

north south
spring autumn 365.24238 days
=
365 days 5 hours 49 minutes 2 seconds
summer winter 365.24164 days
=
365 days 5 hours 47 minutes 57 seconds
autumn spring 365.24203 days
=
365 days 5 hours 48 minutes 31 seconds
winter summer 365.24275 days
=
365 days 5 hours 49 minutes 33 seconds

For the year 2005 the average beginnings are at

Table 5: Average Season Beginnings in 2005

north south
spring autumn 20 March 11:33:19 UTC
summer winter 21 June 06:39:11 UTC
autumn spring 22 September 22:16:34 UTC
winter summer 21 December 18:34:51 UTC

With these timestamps for 2005 and these season lengths you get the on average most accurate timestamps for other years, for the period between the years 1900 and 2100.

So, the northern spring of 2006 begins (approximately) 365 days, 5 hours, 49 minutes, and 2 seconds later than 20 March 2005 12:33:19 UTC, and the northern spring of 2007 again 365 days, 5 hours, 49 minutes, and 2 seconds later.

The listed quantities are the best ones between the years 1900 and 2100, but the true timestamps (between 1900 and 2100) deviate by up to 19 minutes (standard deviation 6 minutes) from the results of the described calculations. It is therefore not useful to present the results of the calculations a precision greater than 1 minute (but you should keep the seconds in intermediate results, to prevent round-off errors). To get more accurate results, the calculations get far more difficult. For this, I can recommend [Meeus].

The longest day is the day that the summer begins. Around that time the length of the daytime period (when the Sun is above the horizon) varies only very slowly. The difference between the longest day and the next longest day is at most 6 seconds in the Netherlands and Belgium. For over a week around the beginning of summer, the length of the day is within one minute of the length of the longest day (assuming equal conditions of the atmosphere). There is a similarly small difference between the length of the shortest day and the length of the next shortest day.

One can also define the seasons in different ways than having them start at an equinox or solstice. Some alternatives are:

• A season begins on the first day of the calendar month in which the solstice or equinox falls. This definition is often used by meteorologists (such as those of the Royal Dutch Meteorological Institute) and seasons according to this definition are therefore sometimes called meteorological seasons. According to this definition, winter begins (in the northern hemisphere) on 1 December, spring on 1 March, summer on 1 June, and autumn on 1 September. Then the middle month of the meteorological winter is on average the coldest month, and the middle month of the meteorological summer is on average the warmest month.
• The equinox or solstice falls in the middle of the season, instead of at the beginning. Each season begins exactly midway between a solstice and an equinox (or vice versa). Midsummer's day (the longest day) then falls in the middle of the summer, rather than at its beginning, and likewise for midwinter's day. Then the seasons begin around 4 February, 5 May, 7 August, and 7 November (in the Gregorian calendar). Some traditional feast days are (or may be) associated with this, such as Saint Valentine's Day (14 February) and Saint Martin's Day (November 11). The seasons mentioned by Marcus Terentius Varro in Rerum Rusticarum Libri Tres (Agricultural Topics in Three Books) from around the year −40 are of this type.
• The same as the previous definition, but shifted to the first day of the calendar month. With that, winter in the northern hemisphere begins on November 1st, spring on February 1st, summer on May 1st, and autumn on August 1st. This is/was the tradition in the Celtic world (such as in Ireland). Some traditional feast days are (or may be) associated with this, such as May Day/Beltane/Walpurgis Night (May 1st) and All Hallow's/All Saints' Day (November 1st). With this, the middle month of winter is the darkest month, and the middle month of summar is the brightest one.

[597]

At the beginning of spring in the northern hemisphere (autumn in the southern hemisphere), the "ideal" Sun is exactly in the vernal equinox, at 0 degrees right ascension and 0 degrees declination and 0 degrees ecliptic longitude and 0 degrees ecliptic latitude. One could define the beginning of northern spring and southern autumn by demanding that the right ascension be equal to 0, or instead that the declination be equal to 0 (on its way to positive values), or instead that the ecliptic longitude be equal to 0.

Because the ecliptic latitude of the Sun is usually not exactly equal to 0 (see question 595), the center of the Sun passes near but not exactly through the vernal equinox, so when the right ascension is exactly 0 then the declination and ecliptic longitude aren't, and the other way around. So, the exact time that you find for the beginning of spring/autumn varies a bit, depending on the definition that you've chosen (right ascension equal to zero, or declination equal to zero, or ecliptic longitude equal to zero).

Which time you find also depends on which simplifications were used in calculating the position of the Sun, and on the date of the ecliptic or equatorial coordinate system that you use to see if the chosen condition for the beginning of spring/autumn is met. Because of the precession of the equinoxes, the vernal equinox slowly moves, and with it the equatorial and ecliptic coordinate systems. If great precision is required, then one should specify the date of the coordinate system, and whether small effects like nutation have been taken into account.

Around the equinoxes (beginning of spring and autumn), the Sun's declination changes at a rate of about 0.4 degrees per day. The greatest ecliptic latitude of the Sun is about 0.0003 degrees, so the declination of the Sun can be that much greater or smaller than if the Sun always had ecliptic latitude exactly equal to zero. The Sun then takes about a minute to move by 0.0003 degrees of declination. If a difference of that magnitude is important to you, then you need to take into account the chosen definition. If the newspaper says that "spring begins at 14:43 hours today", then you don't know exactly which definition was used, but if small effects like nutation and the ecliptic latitude of the Sun were not taken into account then the time won't change by more than about a minute, which is the precision of the statement.

I think that the best definition of the beginning of spring in the northern hemisphere is that it is the instant at which the declination of the Sun as seen from the center of the Earth and measured relative to the true equinox and ecliptic of the date is equal to 0 degrees (on its way to positive values).

## 3. The Length of the Seasons

The next table shows how long the (astronomical) seasons are on average around the year 2000, and how much those lengths change on average each year. The $$λ$$ is the geocentric ecliptic longitude of the Sun at the beginning of the season.

Table 6: Season Lengths

λname length change
north south days seconds/year
spring autumn 92.7578 −67
90° summer winter 93.6490 +28
180° autumn spring 89.8424 +66
270° winter summer 88.9930 −26

## 4. The Names of Solstices and Equinoxes

A solstice or equinox marks the beginning of a season. There are two equinoxes per solar year, so we need to have a way of indicating which one we mean, and the same for the two solstices each year. We can mention the season of which the solstice or equinox marks the beginning (for example, the summer solstice or the autumn equinox), but those are different on each hemisphere of Earth. We can also mention the month in which the solstice or equinox falls (for example, the March equinox or the December solstice), but those are not the same in all calendars (not all calendars in the world have months of March and December), and they need not be the same every year for a given calendar (if that calendar does not follow the seasons closely enough). The name "vernal equinox" is used for the equinox that marks the beginning of spring in the northern hemisphere, and the name "autumnal equinox" is sometimes used for the equinox that is not the vernal equinox, but in the southern hemisphere that autumnal equinox actually marks the beginning of spring! That's why it is useful if there are also names for equinoxes and solstices that do not depend on the season or on the calendar. The independent names that I propose are listed in the following table, together with the other names.

Table 7: Names for Solstices and Equinoxes

λ north south gregorian independent
spring equinox autumn equinox March equinox ascending equinox
90° summer solstice winter solstice June solstice northern solstice
180° autumn equinox spring equinox September equinox descending equinox
270° winter solstice summer solstice December solstice southern solstice

For example: the equinox that happens when the Sun has a geocentric ecliptic longitude of 0° can be called the spring equinox in the northern hemisphere and the autumn equinox in the southern hemisphere, the March equinox in the Gregorian calendar, and the ascending equinox independently from hemisphere or calendar. The "ascending" part of the ascending equinox is the same as the "ascending" part of the ascending node: The ascending node of an orbit is the place in the orbit where the planet passes from south to north of the ecliptic, and in the same way the ascending equinox is the equinox through which the Sun passes from south to north of the celestial equator.

[581]

## 5. Detecting the Moment of an Equinox

It is quite difficult to detect the moment of an equinox. About 2000 years ago people used instruments such as an equatorial ring (http://en.wikipedia.org/wiki/Equatorial_ring) for that. A disadvantage of such an instrument is that it must be aligned very accurately, otherwise it yields false results. And to do the alignment properly you need to know accurately what your latitude is and where the north point is. Without something like an equatorial ring, you can determine the time of the equinox no better than to about the nearest day.

[584]

## 6. Opposite Seasons at Different Places on Earth

The seasons on one side of the equator (for example in Egypt) are the opposite from what they are on the other side of the equator (for example in Australia). When it is summer in Egypt then it is winter in Australia.

You can see for yourself how this works if you have a world globe and a flashlight. A typical world globe (for an example, see http://upload.wikimedia.org/wikipedia/commons/thumb/9/9f/GEO_Globe.jpg/220px-GEO_Globe.jpg) does not have the north and south poles at exactly the top and bottom, but a bit off to the side. This represents that the rotation axis of the Earth does not make a right angle with the orbit of the Earth around the Sun.

Put the globe on a small but stable table in the middle of the room. The rotation axis of the Earth always points in the same direction relative to the stars (actually, it moves but so slowly that we can ignore it here), so you must not change the orientation of the globe once you have put it on the table. For example, you can have the north pole of the globe point toward the door of the room. You can turn the globe around its axis (representing the rotation of the Earth around its axis) but you must not rotate the foot of the globe (you must keep the north pole pointing toward the door).

Now stand a few meters away from the globe in the direction where the north pole of the globe points and then shine a flashlight towards the globe. Ideally, the flashlight should be at the same height from the floor as the globe. This represents the Sun illuminating the Earth. If someone else turns the globe around its axis (careful not to move or rotate the foot of the globe) then that represents the Earth rotating around its axis. The parts of the globe that receive light from the flashlight experience daytime, and the rest experiences nighttime.

Because the flashlight is in the direction where the north pole of the globe points, the north pole of the globe is always in the light of the flashlight, even when the globe rotates all the way around its axis. This represents midsummer's day in the northern part of the world. A small area near the north pole also remains in the light 24 hours a day, because the north pole is tilted toward the flashlight (Sun). The boundary of that area is the arctic circle at 67 degrees latitude.

On the other side, the south pole and an area around it (above 67 degrees south latitude) remain in darkness 24 hours a day, because the south pole is tilted away from the Sun then. It is midwinter's day over there.

If it is daytime on the north pole, then it is nighttime on the south pole, because they are on opposite sides of the planet. Northern areas then get more sunlight than usual, and southern areas then get less sunlight than usual. This explains why the seasons are opposite on opposite sides of the equator.

If you take the flashlight and walk around the table that has the globe on it, keeping the light pointing toward the globe, then that represents the Sun moving around the Earth relative to the stars (actually, the Earth moves around the Sun, but for this experiment it is easier to move the Sun around the Earth, and the results are the same).

If you have walked a quarter of the way around the table, then that represents an equinox (the beginning of spring or autumn). From the location of the flashlight, you can now see both poles of the Earth. All places on Earth then have 12 hours of daylight and 12 hours of nighttime. If you walk another quarter of the way around the table, then that represents a solstice (the beginning of winter or summer). Now the south pole of the Earth is in the light 24 hours a day, and the north pole is always in darkness. If you complete your walk around the table then that represents a full year.

languages: [en] [nl]

http://aa.quae.nl/en/antwoorden/seizoenen.html;
Last updated: 2016−05−10