An eclipse where the Moon's shadow does not reach the Earth

Kamal Lodaya, The Institute of Mathematical Sciences, Chennai

On January 15th 2010, from about 11:30 AM to about 3:30 PM we will have a solar eclipse visible in India.  You know why we have a solar eclipse: the Moon comes between the Earth and the Sun.  (There is an old English word describing this, we say the three are in {syzygy}!) If we are in the Moon's shadow, we cannot see at least part of the Sun.
Between approximately 1:10 PM and 1:20 PM on January 15th, people in southern Tamil Nadu, Kerala and northern Sri Lanka will be directly under the entire Moon's shadow, they will see a {central} solar eclipse.  They will not see a {total} solar eclipse but an {annular} one. This is the longest eclipse (total or annular) until the year 3000!  If you want to know the exact times, look at the eclipse map in this issue of JM and calculate what they are for your place.
In a total solar eclipse (like the one that was seen in a belt stretching from Surat to Arunachal Pradesh on 22nd July 2009) the Moon completely hides the Sun behind it so that no sunlight reaches us. It becomes as dark as night.  We can see the {corona}, the very hot "atmosphere" around the Sun, which is usually hidden in the glare of sunlight.
The amazing coincidence that causes this is that the Moon and Sun are roughly the same size when seen in the sky: if you imagine the sky from the eastern horizon to the western horizon in the shape of a semicircle (or a protractor) taking up 180 {degrees}, the Sun and the Moon both take up around half a degree. One degree is divided into sixty {minutes of arc}.
In an annular solar eclipse, the Moon's shadow blocks out all but a small ring of sunlight.  It is not dark as night.
We can understand why some people can only see a partial eclipse, not a total one: they are not directly under the Moon's shadow, but some distance away from it. People all over India (except those in the deep south) will see a partial eclipse for this reason.
Why is it that people in south India who will be directly under the Moon's shadow will not see a total eclipse? There are two possible reasons.  
The Moon revolves around the Earth, once every month, in an orbit which is not a circle but a slightly flattened circle: an {ellipse}. If you have read about ellipses, then the Earth is at one of the two focus points.  What this means is that sometimes the Moon is around 3.5 lakh kilometres away (we say the Moon is at {perigee}), and sometimes it may be as much as 4 lakh kilometres away (this is called {apogee}). 
If you hold a coin at arm's length, it blocks out the Sun. But if you take it farther away from you, it does not. So the first reason could be that when the Moon is at apogee, it does not completely cover the Sun. The Moon takes up 30 minutes of arc in the sky at apogee rather than 34 minutes of arc at perigee.
The also Earth revolves around the Sun in an orbit which is not a circle but an ellipse. At {perihelion}, we are 14.7 crore kilometres from the Sun and at {aphelion}, we are 15.2 crore kilometres away. At perihelion the Sun is a little bigger in the sky---it takes up 33 minutes of arc in the sky rather than 31 minutes of arc at aphelion. If there is an eclipse the Moon's shadow may not not cover the Sun and leave a ring of sunlight.
In both cases, the tip of the Moon's shadow does not quite reach the Earth!
The Earth is at perihelion on January 3 and the Moon is at apogee on January 10. So which of these reasons is responsible for the annular eclipse of January 15?
In 2009 the Earth was at aphelion on July 3 and the Moon was at perigee on July 21. Does that explain why we had a total solar eclipse and not an annular one on July 22?
How do I know all these numbers? From astronomers who have calculated all this and published it for the rest of the world. Fred Espenak of NASA is one such American astronomer.  He is sometimes called Mr Eclipse.
You might also have heard from astrologers that this eclipse will happen. (Astrologers can also read Fred Espenak's publications.) Unlike astronomers who are interested in telling you what will see at the time of the eclipse, astrologers are interested in telling you what effect the eclipse will have on human beings.
Why aren't astronomers interested in this? Because they know that the Earth weighs 6 million billion billion kilograms (that is 6 followed by 24 zeroes) and the combined gravity of the Sun and the Moon on the whole Earth at the time of the eclipse does not disturb it. The only noticeable effect every new Moon day (whether there is an eclipse or not) is that the ocean's tides are somewhat higher.
What will you see if you go to the south of Tamil Nadu on January 15? First of all, get yourself some eclipse glasses so that you can watch the Sun with your eyes protected. There is no mystery to this: the Sun is very bright. Even when the Moon's shadow has blocked out all but a small ring, the remaining sunlight is enough to dazzle your eyes and hurt them if you keep staring.  With the glasses you will be able to see the pretty picture of the ring of sunlight around the Moon.  If you can project the Sun's shadow onto a wall you can show the play of light and shade to your neighbours.
At the time of centrality, it will not be dark but the light will be gentle, like you see soon after sunrise or a little before sunset. Unlike a total solar eclipse which is over in a few minutes, on the centre line the ring of sunlight is visible for about 10 minutes.  If you know photography, try taking pictures of the Moon covering the Sun and then, after centrality, uncovering it again.
There are many pretty stories about eclipses.  I was in Tawang, Arunachal Pradesh, on July 22nd, when the total solar eclipse took place. Sadly I could not see the Sun's corona because a dark raincloud blocked out the Sun at the time of totality.  But we saw the sky become dark. Suddenly we heard from the famous Buddhist monastery of Tawang, the blowing of many bugles and trumpets. It was a huge racket and people all over Tawang town joined in, whistling and hooting and making catcalls!
I met Lobsang, a Buddhist lama, a few days after that.  I asked him what all that noise was for. He said, "The Sun is our friend. It helps us so much every day.  One day when it is in trouble, can't we do our bit to help it?"
If you sit at home on January 15, the TV channels will show you pictures of the eclipse. You might wonder why take the trouble of going out to see it?  That is not an easy question to answer. Why do some people go to a cricket match to see Sachin Tendulkar bat when they can see it all on TV?
There is nothing like seeing science happen before your eyes. If you go to south India on January 15, take some Buddhists or just any friends at all with you and do your bit for those 10 minutes: make a lot of noise to help out the Sun!