# Easier Method to Calculate Earth's Circumference

• marcusau
In summary, the conversation discusses two methods for calculating the circumference of the Earth - Eratosthenes' method and the professor's method. While the speaker understands Eratosthenes' method, they have some confusion about the professor's method and its accuracy. They also mention the potential challenge of using a protractor to measure angles in the professor's method and the uncertainty about the direction of the shadows in the diagram. The speaker suggests comparing the results of both methods to see how they compare.
marcusau
My professor was showing us how to calculate the Circumference of the Earth using Eratosthenes method, as shown here. I completely understand this method. http://www.bsin.k12.nm.us/Curriculum/CAP/completed%20files/astronomy/completed%20files/eratosthenescircumf.html

However he told us he had an easier method and to use it. I'm not sure if it works, however. I have attached the slide from his lecture that explains what he was saying to do. I understand Eratosthene's method because the sun's rays are directly over the southern most stick and the shadow cast by the northern stick then can be used to find the angle that subtends the arc, which is the distance between the two sticks.

I suppose using his method you have to measure the angle cast by both sticks using a protractor, rather than having the option to use geometry like in the original.

Also, I am not sure about the direction of the shadow cast by the sun based on the way he has the sticks are oriented, given the cardinal directions given in the diagram.

Thanks for any help or input.

#### Attachments

• eratosthene.jpg
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The diagram looks like the same method, just that the Sun need not be directly overhead as in your description and the one in your link. It is the difference between the two shadows that counts - if you wait for one of the shadows to have no length, then the math is probably easier.

Hi there,

I can definitely see why you are confused about your professor's method. It seems like there are a few things that are not quite clear.

First of all, I think you are right that your professor's method requires measuring the angles with a protractor instead of using geometry like in Eratosthenes' method. This might make it a bit more challenging to get an accurate measurement.

As for the direction of the shadows, I'm not sure either. It's hard to tell from the diagram which way the sticks are facing and where the sun is. Maybe it would be helpful to ask your professor for clarification on this point.

In any case, I think it's great that you have a good understanding of Eratosthenes' method. That one has been tried and tested for centuries and is considered pretty accurate. I'm not sure about your professor's method, but it might be worth exploring and comparing the results to see how they compare.

## 1. How is the Earth's circumference calculated using an easier method?

The Earth's circumference can be calculated using the easier method of using the formula C = 2πr, where C is the circumference and r is the radius. This formula is based on the fact that a circle's circumference is 2π times its radius.

## 2. Why is this method considered easier?

This method is considered easier because it only requires knowing the value of the radius, which can be easily measured or obtained from existing data, such as the Earth's average radius of 6,371 km. Other methods, such as using triangulation or satellite measurements, may be more complex and require specialized equipment.

## 3. How accurate is this method?

This method can provide a reasonably accurate estimate of the Earth's circumference. However, it should be noted that the Earth is not a perfect sphere and has variations in its shape, so the calculated value may have a small margin of error.

## 4. Can this method be used for other celestial bodies?

Yes, this method can be used to calculate the circumference of other celestial bodies, such as planets, moons, and stars, as long as their radius is known. However, for non-spherical bodies, the calculated value may not accurately represent the actual circumference.

## 5. How has this method been used in history?

The method of using the Earth's radius to calculate its circumference has been used since ancient times, with early estimates made by ancient Greek mathematicians and astronomers. It was also used by the famous explorer Ferdinand Magellan in the 16th century to estimate the Earth's circumference during his voyage around the world.

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