The sun and the shadows

Venkateswaran Thathamangalam Viswanathan

Teachers have a penchant for asking questions – right? So let us start with one. A simple one to which most of us will have an answer.

Where does the sun rise?

Ah, you think. This is a trick question. With glee on your face, perhaps you are saying, the sun does not rise, it is just that the earth revolves around its axis and so the sun appears to rise and set.

Well, well. Let me change my question. Where does the sun appear to rise?

You are probably trying to figure out the catch in this question, but surely in some corner of your mind you (at least most of you) thought of ‘east’.

We teachers like difficult and tricky questions.

The sun does not appear to rise in the east, except for two days in a year. The point of sunrise is either northeast or southeast for all the other days!

A simple activity will help clarify this point.

Sunrise point changes every day
Images courtesy: T V Venkateswaran

Choose a spot on your terrace with an unhindered view towards the east and mark it. You will have to stand on that spot many times during this exploration, therefore make the mark durable. Watch the sun as it rises above the parapet wall. Ask your collaborator to place a stone on the parapet wall such that the pebble and the rising sun are in a straight line. Come back to the same spot, say after 15 days. Watch the sunrise.

Surprise! The sun is not rising at the point marked by the stone on the parapet wall. Once again, ask your collaborator to place another stone at the point where you, the stone, and the rising sun are in a straight line. Do not remove the first stone, let it be there at the same spot; write down the date on which these observations were made below the stone on the parapet wall. Repeat this activity every 15 days. You may not be able to observe the sun rise every 15 days. Some days, the sun may be covered by clouds, some days it may be raining heavily, but it is ok. Observe and mark the spot with a stone as many times as you can.

If we make an effort, we can find that successive sunrise points are moving towards the southeast for six months and towards the northeast in the next six months. The southeast position is closer to December 21 (winter solstice), and the northernmost place is closer to June 21 (summer solstice).

Further, we can find that the sunrise point is very close to the actual east on two days in a year – the equinoxes.

Shadow time
If I ask you what the time is now, you will either look at the clock in your mobile phone or the clock on the wall. Imagine a time when there were no mechanical (obviously no electrical or electronic) clocks. How did people tell time? By studying the length of their own shadows!

I come from Tamil Nadu and there is an old verse in Tamil that tells one how to compute time from the length of one’s shadow. Choose a rock, telegraph pole or the edge of a pavement as the mark. Adjust yourself such that the shadow of your head kisses the edge of the stone/telegraph pole/pavement. Measure the length of your shadow with your feet by walking towards the stone/pavement.

In the olden days, in the southern part of India they used a time division called ‘nazhikgai’, which is equivalent to 24 minutes. From sunrise to sunset, there were 30 nazhikgais. If your shadow length is 98 feet measure (by your feet! This is important, remember), then from sunrise, it is not more than one ‘nazhikgai’ (or 24 minutes). If it is afternoon and the shadow is pointing towards the east, then a 98 feet long shadow indicates that sunset will occur in less than 24 minutes. If the shadow length is 45 feet, it is two nazhikgai (48 minutes). The table below gives the shadow length measured with our feet and the corresponding time since sunrise (or time remaining for sunset) according to the old Tamil verse.

Length of the shadow (in your feet measure)Corresponding time measure
981
452
283
194
145
10.56
87
68
4.59
3.510
2.511
1.7512
113
0.514
015

This works roughly for Tamil Nadu; I am not sure this will work just the same in your place of residence. Why not try measuring shadow lengths? Prepare a table for your area using the shadow measurement given above.

The setting sun
Now let’s look at how long it will take for the sun to set. Go out or stand in a place where you can see the sun without any hinderance. Now stretch out your hand. Turn your palm in such a way that it is facing you. Align your index finger to the bottom of the sun by keeping the fingers parallel to the horizon (as shown in the image). If there is still space between the palm and the horizon, use the fingers of the other hand as well (see image). Measure the distance between the setting sun and the western horizon with your fingers. If the sun appears to be six fingers above the horizon, it will take one hour and 30 minutes for the sun to set; for every finger, approximately 15 minutes.

Is it really afternoon?
When is it ‘noon’? When the clock shows 12:00, we say. However, this is not the ‘astronomical noon’, the time at which the sun crosses the meridian line at one’s place of residence. So how can one find the astronomical noon at their place? And why does the astronomical noon differ from the clock noon?

If you have access to an open space, place a vertical pole and draw a circle on the ground with the length of the pole as the radius. Observe the shadow cast by the pole, say from 11:30 am to 12:30 pm, marking on the ground the length of the shadow every 10 minutes. Create a graph with the size of the shadow on the Y-axis and the time on the x-axis. The time at which the shadow is the shortest is the local noon or astronomical noon.

Another way to perform the same experiment is by constructing a gnomon. Draw concentric circles on a paper (as shown in the image below) and place a vertical pole (pencil) at the centre. Note the shadow point of the tip of the pencil every five minutes. When two points fall on the same circle, add the clock time of these two points and divide by two; we get the astronomical noon. In the above image, the shadow of the pencil tip falls on the second circle twice at 12:05 pm and 12:20 pm. Add them 12:05+12:20 and divide by two. We get ~12:12; this is the astronomical noon at the location where this observation was made.

Pencil tip shadow markings with timings

The Indian Standard Time (IST) is relative to 82° East longitude in India. Therefore, east of this longitude, the sun will cross the meridian much earlier than 12:00. West of this longitude, the sun will cross the meridian after 12:00.

Line joining two points on a circle where the shadow of the pole falls is the west-east line. Line perpendicular to it gives the north-south line. In the above image, at 12:05 and 12:20 the shadow toched the second concentric circle. The line joining the same is west-east line.

The gnomon can also be used to find the cardinal directions. Suppose you draw a circle with the pole as the centre. Before the astronomical noon, the shadow will touch the circle at a point and after the astronomical noon at another point along that specific circle. Join these points, that line is west-east (see image). You get the north-south line with the pole as the centre to bisect the west-east line. For example, in the image, points related to the shadow at 12:05 and 12:20 are on the second circle; joining them gives us the west-east line and bisecting them provides the north-south line.

Keep observing the gnomon shadows at the instance of astronomical noon every day. You will find an interesting phenomenon.

In Chennai, from August 18 to April 24, the pole’s shadow will be towards the southern direction. On April 25, the direction of the shadow will be west-east. At astronomical noon, there will be no shadow – zero shadow day! However, on April 26, the shadow will be pointing north! It will point towards the north until August 16. On August 17, the shadow will be west-east and at noon, no shadow. Once again, zero shadow day. From the next day, August 18, the shadow of the vertical pole flips to the southern direction.

If you live above the Tropic of Cancer, you cannot observe this flip. The local noon shadows will always point towards the north at your location. But for the rest, located south of the Tropic of Cancer, we can see the shadows flip during the year.

The author is a scientist with the Department of Science and Technology, Vigyan Prasar, New Delhi. He can be reached at [email protected].

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