September is a warm month (in terms of weather). But Summer is over. Why is it so hot? Global Warming? Not really. We have entered the second 'Tropical Summer'. The first was during March-April. Temperatures reached high as 33°C and the heat was almost unbearable. The second is happening now (August - September). Colombo is reporting temperatures above 32°C, Kandy as high as 34°C.
The Earth's (average) orbital plane about the Sun is called the Ecliptic plane. The Earth orbits around the Sun in an elliptical path. The Earth also has an axial tilt ranging from +23.44° to -23.44° relative to the Ecliptic. This tilt gives Earth it's seasons, which starts from Vernal Equinox, Summer Solstice, Autumnal Equinox and Winter Solstice.
An ellipse is an eccentric circle that has two foci, similar to how a circle has a center. An ellipse can be drawn by tying the ends of a string to two pints (the two foci) and tracing a complete round with the string taught. There will an instance when the pencil is closest to one of the pins and another point when the pencil is furthest from that pin.
Planets orbit around the Sun in an elliptical path with the Sun in one of it's foci, in accordance to Kepler's Laws of Planetary Motion. The Sun is not at the center of the ellipse but it is on one of the foci. Therefore, planets orbiting around it would pass a position in it's path where it's closest to the Sun, known as Perihelion (147,098,074 km) and another where it's furthest from the Sun, known as Aphelion (152,097,701 km).
The exact dates and times of these seasons have been accurately calculated by The Astronomical Applications Department of the U.S. Naval Observatory.
- 2008
- Perihelion: January 03 at 00:00 UT (05:30 local time)
- Vernal Equinox: March 20 at 05:48 UT (11:18 local time)
- Summer Solstice: June 20 at 23:59 UT (June 21 05:29 local time)
- Aphelion: July 04 at 08:00 UT (13:30 local time)
- Autumnal Equinox: September 22 at 15:44 UT (21:14 local time)
- Winter Solstice: December 21 at 12:04 UT (17:04 local time)
In order to understand how the tropics have two seasons of summer almost 6 months apart, one must understand the geometry of Earth's tilt and it's orbit around the Sun.
The Celestial Sphere is an imaginary rotating sphere with Earth's center as it's center and Earth's rotation axis as it's rotation axis. Objects in the sky such as the Sun, Moon, stars, planets, etc., can be projected on to the Celestial Sphere. This is done so that there is some reference to these objects, similar to plotting countries in a World Map, using a set of coordinates.
There are several coordinate systems to describe locations of objects in the Celestial Sphere. The Equatorial Coordinate System is one such system. It locates objects relative to the center of the Celestial Sphere using two angles: the Declination Angle, δ and Hour Angle, H. The Declination Angle, δ is analogous to Latitude Angle and the Hour Angle, H is analogous to Longitude Angle.
An observer would not make any sense of Declination Angle and Hour Angle, until he/she transforms them to a local Horizontal Coordinate System. In the Horizontal Coordinate System, the observer's reference plane is his/her horizon, with objects measured in terms of Altitude Angle (Alt) and Azimuth Angle (Az). The Azimuth Angle is measured from due North towards East and Altitude Angle is measured from upwards from the observers horizon. It is clear that the Horizontal Coordinate System makes more physical sense to an observer.
However, it is impractical to refer to objects in Horizontal Coordinate System because the coordinates measured from Colombo would be different to those measured from the North Pole. Astronomers use Declination Angle and Hour Angle (or Right Ascension) to locate objects in the Celestial Sphere in an absolute sense.
The Declination Angle of the Sun, δSun can be approximately given by:δSun = 23.44 × sin((360×(284 + N)/365))
Where N is the day number. (eg. N=31+10=41 for Feb 10).
The above equation is an approximated Sine function and it's accuracy is sufficient for our deductions. And we can deduce the following:
- two instances when δSun = 0, know as Vernal Equinox
- and Autumnal Equinox
- an instance when δSun = +23.44°, known as Summer Solstice
- and an instance when δSun = -23.44°, known as Winter Solstice
For an observer on Earth, would see the Sun rise from the East and peak at a particular point. The point at which the Sun is at it's highest angular elevation (not necessarily be directly above the observer) is called the Solar Noon. Solar Noon is dependent on the Longitude and independent of Latitude. For example, when it's Solar Noon in Colombo, which has a Longitude of 79.86° East, it would be Solar Noon for any place on Earth having a Longitude of 79.86° E. Nagpur, India has a Longitude of 79.20° E, so in Nagpur would almost be at Solar Noon when Colombo is at Solar Noon.
Without getting in too mathematical, lets use an empirical formula called the Equation of Time to determine the local time of the Solar Noon for a given location. The Equation of time takes in to account the elliptical orbital geometry and Earth's tilt.
E = 9.87 sin(2B) - 7.53cos(B) - 1.5sin(B)
where E is the time offset and B is given by:B = 360 × (N-81)/364
Solar Time, TSolar is given by:TSolar= TLM + E - 4(LStd - L)
where: TLM is the Local Mean Time, LStd is the Longitude of the Time Zone and L is the Longitude of the Location.
The Earth rotates 360° of Longitude every 24 hours. Time per degree of Longitude is 4 minutes. The Time Zone will be exact only at it's corresponding Longitude, LStd. For locations away from LStd, a correction must be made to calculate the exact Local Time. Thus, the term 4 (LStd - L) gives the deviation from Standard Time Zone time.
Let's evaluate the Local Mean Times of Solar Noons in Colombo and lets pick dates when the Sun is directly above Colombo at Solar Noon. On these days, δSun is equal to the Latitude of Colombo.
δSun = 6.92° N = +6.92°
δSun = 23.44 × sin((360×(284 + N)/365))
N = 98 = 07 April 2008
N = 246 = 02 September 2008
L = 79.86° E = -79.86°
LStd = 82.5° E = -82.5° for +05:30 UT
LStd - L = -2.64°
4 (LStd - L) = 4 min/degree × 10.56° = 42.24 minutes
TSolar= 12 at Solar Noon
B = 360 × (N-81)/364
when N=98, B98 = 16.813
when N=246, B246 = 163.187
E = 9.87 sin(2B) - 7.53cos(B) - 1.5sin(B)
when N=98, E98=-2.17 minutes
when N=246, E246=1.31 minutes
TSolar=TLM + E - 4 (LStd - L)
TLM = TSolar - E + 4 (LStd - L)
when N=98, TLM,98 = 12h - 2.17min + 42.24min = 12:40
when N=246, TLM,246 = 12h + 1.31min + 42.24min = 12:44
Therefore, Colombo had two Summers with peaks on 07 April 2008 at 12:40 and 02 September 2008 at 12:44. The hotter Summer being in April since Earth is closer to the Sun.