how to measure the size of the earth wuth the help of two sticks and a rope?

Answer 1

with 2 sticks and a rope??? tough one.

I know how to measure it with 1 stick and a meter, though... hope it will be enough:

1) put your stick in the ground (perpendicular to the ground, obviously)
2) wait for noon and measure the shadow (or measure it all day long and only keep the longest measurement)
3) walk south during a year. (measuring how much you travel, all the time)
4) put your stick in the ground (perpendicular to the ground)
5) measure the shadow

a little trigonometry does the trick.

for that, you use 2 assumptions:
1) sun is far away, therefore sunrays arrive on earth parallel to each other
2) earth has the shape of a ball


PS: I suppose your 2 sticks and a rope method works the same way, probably with the rope as a measuring tool or something.

Answer 2

You will need to know trigonometry. This assumes you on a perfectly level surface, like a smooth ice rink and gravity does not affect the rope.

Tie the rope to the top of both sticks. Place one stick in the ground and take the other stick out until the rope is tight and place it into the ground so that are at the same height. Measure the distance the rope is to the ground at the stick, it should be the same if you have both in the ground the same distance. Then go to the middle of the rope and measure the distance from the middle of the rope to the ground. This distance should be less then the distance measured at the sticks. You will also need to know the distance between the sticks.

Once you gather all of these measurements you should be able to calculate the diameter/circumference of the earth. Now this is where the hard trig problems come in. Unfortunately it will be very long and tedious to explain but yes you can figure out the diameter/circumference of the earth using this method.

I would suggest that you sit down with a trig. teacher or some knowledgeable person (an engineer maybe) and have them go through the calculations with you. so that you can learn what is involved.

Answer 3

If your rope is around 2000 meters long and has measurements marked on it at least down to the centimeter level, (i.e. if your rope is a tape measure), and your sticks are the same length and long enough (both exactly 2 meters, for example) there's an easy way.

Place one stick perpendicular in the ground. Use your rope to measure 2000 meters due East (due West would work, too) and place the second stick.

Use the rope to measure 22.86 meters due West of the first stick. The idea is that you want to know when the Sun is exactly 5 degrees above the horizon. 2/22.86 (or .0875) equals the tangent of 5 degrees.
The shadow will get shorter as the Sun rises. When it reaches the 22.86 meter mark, tug on the rope so your friend can measure the shadow from his stick. Since he is further East, his shadow should be slightly shorter (Since I already know the circumference of the Earth, I think his shadow will measure 22.78 meters - an 8 centimeter difference in only 2000 meters).

Using the tangent formula, again (2/22.78) calculate the angle of the Sun relative to his stick (about 5.018 degrees, a gain of .018 degrees in only 2000 meters).

Divide 360 degrees by 0.018 degrees. Multiply your result by your 2000 meters and you have the circumference of the Earth (due to rounding, etc, you would be doing good to get within 75 km of the actual circumference, but that's not bad).

In reality, a rope of 2000 meters is unlikely, so you need a way to communicate with the second measurer. Besides, waves travel through a rope too slow. The Earth is rotating at .004 degrees per second, so any delay in measuring throws in an error in your calculations.

You need tall sticks and low angles to make the shadow as long as possible, since you're unlikely to get a measurement accurate to less than a centimeter once you take into account an imperfect ground (you do want as flat and level a surface as possible for both measurements).

The theory's pretty simple, but this would be quite a trick to pull off the actual experiment. Lots of complicating factors to try to eliminate or account for. It makes you appreciate how the first estimates of the Earth's size could be so far off.

Answer 4

assuming that the earth is perfectly spherical one cannot put a stick perpendicular to the ground because the ground will have a curvature (arc in 2 dimensions)
Insert both the sticks in the ground, at some distance from each other, such that they are perfectly vertical. you can use the rope to make sure that the sticks are vertical....tie the rope to the top of the stick and trace the loci at the other end such that it forms a perfect circle and the other end is always touching the ground.....thus the rope will trace a cone in three dimensions.....if you are able to trace such a cone the sticks are vertical.
once you have the sticks inserted vertically in the ground tie the rope at the absolute bottom of one stick(stick A).....tie the other end of the rope to the other stick(Stick B) such that the rope is perpendicular to the first stick(stick A) and the rope is taut.....the rope can be perpendicular to the stick because no curvatures are involved..both rope and stick are straight
once you have this arrangement in place it is a simple matter of applying Pythagoras theorem to calculate the radius(say R) of the earth....we know the length of the rope (say O) and the length of the stick(stick B) from ground to where the rope is tied (say S)
thus:

(R+S)^2=R^2+O^2....R is the only unknown

the basic assumption of course is that the earth is perfectly spherical

Answer 5

Draw a global outline with the help of one stick and a rope. Put another stick in the postition of equator. Take note of the diameter of the earth from any reference. With the help of the diameter and circumference of the drawn circle, calculate the size of the earth. I can't answer any more if this is a tricky question.

Answer 6

Tie one end of the rope to the stick, Walk all the way around the earth back to your origianl stick. Measure the rope. QED

Answer 7

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