Solstices and Seasons

D. Indumathi, The Institute of Mathematical Sciences, Chennai

The Sun appears to rise in the east and set in the west after moving west-wards in the sky. While many people believed this was a true motion, now we know that this is not so. It is the Earth which is moving around the Sun, and the eastward rotation of the Earth makes the Sun appear to rise and set. This is the heliocentric theory (helios=Sun, centric=centred so the name means that the Sun is at the centre and the Earth and other planets go around it). There are complications arising from various sources. One is that the the path of the Earth around the Sun is an ellipse, not a circle. Another is that Earth is tilted on its axis by 23.5 degrees. The angle is taken with the plane of the ellipse.

¡ellipse figure¿ Caption: An ellipse can be constructed by tying a string to two pins and drawing like this with the pencil stretching the string taut. Each pin constitutes one focus of the ellipse. (From Newtonian Physics, by Benjamin Crowell).

The Sun is at one focus. So the Earth is sometimes closer to the Sun and at other times farther away. The Earth’s axis is always pointing in the same direction, so it is pointing at the Sun for half the time, and away from it during the other half. See the figure.

¡North_{s}eason.jpg > Atthefarthestpoint, itissummerintheNorthernhemisphere(thatis, overIndia)andattheclosestpoint, itiswinter.T hismayseemamazingbuttheseasonsarenotdeterminedbythedistancetotheSun.T heyaredeterminedbythetiltoftheEarth, whichdecideshowmuchsunlightisfallingontheEarth′ssurface.T henorthernhemispheretiltstowardstheSunfromaround20Marchto22September.Atthistime, theEarthisfarthestfromtheSun, butitissummertimebecauseofthetilt.T heSun′sraysareableto”washover”alargesurfaceofthenorthernhemisphereatthistime, withthemaximumaround21June.Soitishotatthistime.Ontheotherhand, itiswinterinthesouthernhemisphere(inAustraliaandtheSouthpole).W hentheEarthgoeshalf− wayaroundtheSun(in1/2year), itsaxisistiltedsothatthesouthernhemisphereispointedtotheSun.Soitissummerthere, andwinterforus, withthemaximumefffectaround21December.Seethefigure.

¡Seasons.gif¿ For Australians, therefore, summer occurs when the Earth is closest to the Sun and they would not be surprised!

The Solstices Think of a ball bobbing up and down in water. When it is not moving, suppose that half the ball is in water and half is outside. The water line thus is at the half-way point. This is the equator. When it starts bobbing, the ball sinks further in, and then rises out. The Sun does the same thing: it appears to move over the year up and down with respect to the Equator; it is overhead at the Equator days and nights are of equal length. This is called an equinox. Then the Sun drifts upwards so that it is overhead at more northward points, reaching a maximum latitude of 23.5 degrees north, called the Tropic of Cancer (approximately the latitude of Ahmedabad). Then it turns back, once again crossing the equator (the second equinox). It continues ”bobbing” downwards till it reaches a latitude of 23.5 degrees south (the Tropic of Capricorn). Then it turns back and returns to the equator to end the journey of one year. To ancient astronomers, therefore, the Sun appeared to reach the Tropics and then turn back. These points were called Solstices (Sun-still when the Sun was still and unmoving, without drifting north or southward in the sky). There are two equinoxes and two solstices in one year. The winter solstice is just over, on Dec 21, 2008. In 2009, they are on Jun 21, at 05:45 (summer solstice) and Dec 21, at 17:47. The equinoxes will be on Mar 20, at 11:44 and Sep 22, at 21:18. It is interesting to note that Pongal or Sankaranti actually celebrates the winter solstice. In almost all communities, all over the world, they indicate a change in season.

The apparent motion of the Sun It is easier to understand the seasons from Earth’s point-of-view. After all, all human beings live here, and not (yet!) in outer space. The following facts must be kept in mind (we only consider the northern hemisphere, but you can easily work out the results for the southern hemisphere).

1. The extreme positions of the Sun are at the two Solstices. 2. The Sun can be overhead (at any time of year) only in the tropics. 3. Beyond the tropics, that is beyond 23.5 degrees latitude, sunlight is always coming at an angle, in fact, from a southerly direction. 4. So the apparent movement of the Sun depends on the latitude you are watching from.

¡Solstice-0.jpg¿ In the figure, imagine that you are standing on an island in the middle of the ocean on the Equator so that no buildings or trees block your view of the Sun. You are standing facing north (which is left in the figure) so the Sun rises on your right hand side. The island is deserted and there is nothing else to do, so you record the position of the Sun every hour, from sunrise to sunset. The dots indicate these positions. There are two sets of dots. These are the positions you will observe at the two solstices. In the winter Solstice, the Sun is over the tropic of capricorn, to the south of you (on the equator). So the Sun is rising and setting in the sky towards the south (right-side set of dots in the figure). In the Summer, the Sun is over the tropic of cancer, to the north of you, so you will observe the left-side set of dots. So the Sun at noon is to the south in winter and to the north in summer.

¡Solstice-20.jpg¿ Now, imagine you are in India but not too far north (Kolkata, Mumbai, for example). The next figure has you (again on a desert island, facing north!) at a latitude of 20 degrees, still below the tropic of cancer. During the Summer solstice, the Sun appears to rise in the north-east and set in the south-west. When the Sun is overhead at 23.5 degrees, it is practically overhead at noon for you too. However, sunrise and sunset positions are shifted more to the north. When it is winter time, the Sun is far away, over the tropic of capricorn, so the Sun is in the south at noon. This means that the Sun is rather low in the sky and not overhead at noon. At sunrise and sunset times, the Sun is not as far south as it is at noon. Once you are at a latitude beyond the tropic of cancer (North India, including Allahabad, Delhi, Srinagar), the Sun is always to the South, whether in winter or in summer. The Sun in summer appears to rise more and more in the northeast and et in the northwest, while being in the south at noon (the highest point in the sky). As you go to higher and higher latitudes, this effect is exaggerated strongly, so that, for instance, in London, the Sun in summer will clearly be seen to ”swing” in the sky, from northeast (sunrise) to south (noon) to northwest (sunset). Since it marks a very long path in the sky, you can see (from the figure on the inside back cover for 50 degree latitude) that there are many dots so that the length of the day in summer is also very long in such places. In contrast, the right-side set of dots shows very few dots and thus a very short day in winter. The figure for 20 degrees, while showing a shorter day for winter, does not show a drastic difference. In Chennai (at 13 degree latitude), there is about 45 minutes difference in the length of a summer and winter day. Finally, at even larger latitudes, over the poles, the Sun simply circles the sky in summer, leading to 6 months of endless day, followed by 6 months of endless night in the winter when no light from the far-away Sun reaches the north pole. This happens at all latitudes that are above 66.5 degrees, the so-called Arctic circle. Note that the entire sequence is interchanged for people living in the southern hemisphere (wouldn’t it have been nice if India were partly in each hemisphere?) so the terms summer solstice and winter solstice is actually misleading. Nowadays, they are called the northern and southern solstice when the Sun is over the northern or southern tropics. What interesting complexity arises from the tilt of the Earth’s axis. Without this, there would have been no seasons and life would have been boring!

Graphical content courtesy Wikipedia: http://en.wikipedia.org