### DISCOVER IT 5

At the end of ‘Discover it 3’, I had written that :

“All the stars and planets move in the sky except Dhruva tara. Why ?

The next thing you need to do is to measure the angle made by Dhruva tara above the horizon. Since Dhruva tara does not move, that angle is fixed. It does not change. This angle is just the latitude of the place where you are. If you are in Simla, or Mandi, you can measure your latitude by measuring the angle of Dhruva tara above the northern horizon. How do you measure this angle ? This we will discuss in the next article, where we will also learn to make a geosynchron.”

In my last article, Discover it 4, we learned how to make a geosynchron. In this article we will learn to make an ‘Angle-Dangle meter’ and also learn how to use it to measure distances. It is really quite easy to make an angle dangle meter. You will need a stiff and flat piece of cardboard, or thin plywood, a piece of thin string and two small stones which act as weights at the two ends of the string.

1. Take a piece of string about a metre long. Tie the two small stones, one at each end.

2. Take the rectangular piece of stiff cardboard. Make a small notch at the middle of its upper edge. Hang the string from the notch so that the stones dangle, one on each side of the card.

3. If the notch is at N, draw the line NM which is perpendicular to the upper edge. (Figure 1) When the upper edge AB is parallel to the ground (i.e., when it is in horizontal position), the string and stones will dangle exactly along NM, if you have drawn the perpendicular correctly. Your angle dangle meter is ready for use.

4. To measure the angle of Dhruv tara, (your latitude ), hold the card close to your eye, so that the upper edge AB is along your line of sight and take aim at Dhruv tara, so that A, B, and Dhruva tara are all in the same straight line. (Fig 2). At this position measure angle XNM. This is your latitude. (Why ?)

You can further improve your angle dangle meter to make it more convenient to use. For example, you could fix it vertically on your ball mount, such that both your hands are free when you take aim at a star. How to do this? If you have actually made a ball mount ( as was discussed in Discover it 2) you will have no problem in figuring out how to do it, with a little ingenuity, which I am sure you have in large measure.

You could fix a protractor from your geometry box on your angle dangle meter such that the angle XNM can be read directly, or you could draw a semi circle with N as centre and mark out the angles such that the angle XNM can be read directly while the instrument is in use.

Of course, when you have made your angle dangle meter and fixed it on a ball mount, you have made a fine scientific instrument, with which you can measure the height of a building, the radius of the earth, and the distance of the earth from the sun. How ?

Let us begin by measuring the height of a tall building, without walking up to its terrace. Keep your angle dangle meter with its ball mount on a stool , and move the stool to such a distance away from the building . such that the angle XNM, (when you take aim at the top of the building), is 45 degrees. At this point, the distance of the stool from the building is just equal to the height of the building minus the height of the stool.

Why? Draw a diagram, and convince yourself. You could also keep the stool anywhere, and measure angle XNM from that position, which may be different from 45 degrees. Then use similar triangles.

Using similar triangles, we can measure the height of the building without climbing it. Can we can use similar triangles to measure the distances of the sun and the stars without having to travel there ?

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