12 December 2011
Every time there's an eclipse, as my neighbour very religiously bathes four times, chants his mantras and performs the various rituals associated with this, most inauspicious of occult events, I, equally religiously, am usually to be found on my terrace, with camera mounted on tripod, trying to catch the event on SD card. This time, rather than just put up a series of images, I thought I'd write a few words on the perception of eclipses and the hows and whys of them.
This is how our ancestors thought of eclipses:
This myth involved is as follows: After the immortality-inducing nectar comes out of the churning of the ocean, the devas decide not to share it with the asuras. They appeal to Vishnu, who comes down in his (cross-dressed) Mohini form, as a mesmerizing woman, who distracts the Asuras. (S)he then steals the Amrit and distributes it to the Devas. One Asura, Rahu, who's in the form of a snake, tries to switch sides, is found out by the sun and moon, who inform Mohini, who beheads him with the discus, creating two entities, Rahu and Ketu. These two, the head and body of the snake, forever hunt after Surya and Chandra - the sun and the moon. Occasionally they catch them, munch them up, and because the sun and moon themselves are immortal, they come back to life soon after. And so the endless cycle of chase, devouring and resurrection continue on and on.
Cute myth from the dawn of our civilizations!
The sun and moon are the only celestial bodies who's shape we can make out with the naked eye, so their sudden disappearance would almost certainly have caused extreme panic to our earliest ancestors, so they invented myths about why these things occur. Around the world, there are similar myths of various animals swallowing up the sun and moon - to the Vikings, it was two wolves, for the Chinese it was dragons, and so on. The circular bit being “cut out” of the moon or the sun makes this a very obvious explanation - it looks like a bite mark, so something must be eating it up!
Naturally, I'm not going to accept this explanation, and neither did the ancients, once they started studying the matter at hand.
As usual, Aryabhata has a more realistic proposition to the myth, in the very last bit of his book:
The moon consists of water, the Sun of fire, the Earth of earth, and the earth's shadow of darkness. The moon obscures the Sun and the great shadow of the Earth obscures the moon When at the end of the true lunar month, the Moon, being near the node, enters the sun, or when at the end of the half-month, the Moon enters the shadow of the Earth that is the middle of the eclipse which occurs sometimes before and sometimes after the exact end of the lunar month or half-month. (Aryabhatiya, Golapada verses 37 and 38)
That's better! The eclipse is caused by the shadow of the Earth in a Lunar and the shadow of the moon in a solar eclipse…
Afterwards, he goes on to describe a method to calculate the duration of the eclipse. This method was apparently accurate enough that when Guilaume le Gentil, a French astronomer visited Pondicherry during a lunar eclipse on the 30th of August 1765, he found that the charts he had with him for calculating the duration were worse than Aryabhata's method, which was used by Tamil astronomers of the time. His charts were 68 seconds too long, and Aryabhata's method was 41 seconds too short. However, the same table was better to calculate the duration of totality than Aryabhata's method.
First, we all know that the orbit of a planet, or a satellite is an ellipse. For the Earth and Moon, this ellipse is very very close to being a circle. 1with an eccentricity of between 0.0034 and 0.058, with 0 being a circle and 1 being very elliptical, like comets. Halley's comet has an eccentricity of 0.967, for example Also, the orbit of the moon is tilted with respect to the orbit of the earth, and the rotation of the earth is tilted in and of itself.
The period of the earth's orbit is a year, and the period of the moon's orbit is a lunar month 2I will refer to lunar months as a “month” from now - the current Gregorian concept of month is a compromise solution. Every half-month, the moon is either on the same side of the earth as the sun, or on the opposite side.
If the moon were orbiting on the same plane as the earth's orbit, we'd have an eclipse every single month; in fact, we'd probably never have a full moon. The shadow of the earth would fall on the moon for about a quarter of a month. But since it's inclined to the earth, on full-moon day, the sun's light falls on the moon, lighting up its surface fully.
There are two points where the moon actually crosses the earth's orbit. When it goes from North to South, it's called the descending node, and when it goes from South to North, it's called the ascending node. When these nodes intersect the plane of the earth's orbit, we have an eclipse.
This conjunction of nodes, moon and sun occur in cycles, but these cycles aren't so easy to predict. They have a variable period - that is, the time between eclipses varies. Today, we use several cycles to predict this conjunction.
These two nodes - they travel along the sky, just like planets and are called “shadow” planets - are given the mythological names Rahu and Ketu, in Indian astronomy. The ascending node is called Rahu and the descending one is called Ketu. So, we can safely abandon the idea of the severed head of a snake eating the moon!
I don't believe that Aryabhata was unaware of the method of calculating the time of the eclipse, he just chose to leave it out of his treatise. Maybe the method exists in one of his lost works…
But happily, Bhaskara II does give the method in Siddantha Siromani. In fact, a fairly detailed chapter is devoted to eclipses of the moon alone!
The initial procedure to be adopted to compute an eclipse. To know the occurence of a solar eclipse, find the exact moment of the New Moon, which is indicated by the conjunction of the longitudes of the Sun and the Moon. To know the occurence of a lunar eclipse, compute the exact moment of the full Moon, which is indicated by the fact that the moon is on the opposite longitude to the sun. Also compute the longitude of the Node (Rahu) for the moment. (if they meet, then an eclipse will occur).
The “longitude” referred to here is the longitude of the sun or the moon on the celestial sphere, which is centered on the earth. When the sun and moon are on the same longitude, and the node is also on that longitude, we have a solar eclipse. When the moon and the node are on the same longitude, and the sun is on the opposite one, we have a lunar eclipse. That is, if the moon crosses the ecliptic plane at the exact time that the sun is crossing the moon's plane, we have an eclipse. If the crossing doesn't happen at the exact same time, we have a normal full or new moon.
He also goes on to describe how exactly to do this, and as with Aryabhata, how to calculate the duration of the eclipse. This method is quite involved, but it uses successive approximations to calculate the date of the next eclipse, from time of the last one by solving for a position where both bodies and any one node meet in the celestial sphere. I'm not going to write those equations out, but instead, I leave you with my photos of the eclipse!