# Arcs and the Earth

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1. Aug 21, 2015

### marciokoko

Is there a way to determine the arc around 1/4 of the earth without measuring it? I mean like thru trig?

2. Aug 21, 2015

### SteamKing

Staff Emeritus
It depends on what you mean by "determine". FYI, trig also involves measurements.

3. Aug 21, 2015

### marciokoko

Ok today I was swimming and I have an app that records my swim sessions, SwimFit. I can tally up the number of meters I have covered since I started swimming and I was wondering how far across the world that would be.

So while in the pool I had no access to data. And I was wondering what I could do to "guess-timate" the distance of 1/4 the circumference of the earth in order to compare it to the meters I have swum since I started swimming.

4. Aug 21, 2015

### SteamKing

Staff Emeritus
The circumference of the earth is a fairly well established quantity, which as far as I know, doesn't change daily. You can look this figure up, take a quarter of it, and compare to the distance your device has recorded.

5. Aug 21, 2015

### Staff: Mentor

Just memorize one key approximate fact. The circumference of the earth is about 25000 statue miles.

6. Aug 21, 2015

### marciokoko

Thanks anorlunda, thats what I meant, something to approximate any of the quantities needed to be able to determine the circumference of the earth of perhaps the radius.
So
Thanks for the humor SteamKing. I know its a well established fact and that it doesnt change. As I mentioned to anorlunda, I was interested in any data that could help point me in the direction without actually having to know 1/4 or 4/4 the circum. :-)

7. Aug 21, 2015

### SteamKing

Staff Emeritus
Or "statute" miles. Let's leave statues out of this.

1 statute mile = 5280 feet = 1609.35 meters approx.

8. Aug 21, 2015

### marciokoko

LOL!

Thanks guys

9. Aug 21, 2015

### nasu

Forget the miles. The meter was once defined so that one quarter of the circumference will be exactly 10,000 m.
The definition have changed several times since then but the meter itself did not change much.

10. Aug 21, 2015

### marciokoko

Cool factoid! Thanks

11. Aug 21, 2015

### SteamKing

Staff Emeritus
Your definition of the meter (and the circumference of the earth, incidentally) is a tad off. 10,000 m is only about 6 statute miles.

The original proposal put forth by French Academy of Sciences was that the meter be equal to one ten-millionth (1/10,000,000) of the distance from the equator to the North Pole.

The academicians operated under the assumption that the earth was a perfect sphere, and the fact that no one had ever visited the North Pole at the time was apparently not considered an impediment to establishing this distance. As subsequent events would prove, this definition of the meter was almost impossible to establish in a practical manner, given the tools and knowledge of the earth at the time, and it was later determined to establish the meter by surveying a set arc of latitude along a suitable meridian. Even this scaled-down project proved difficult to accomplish, with France embroiled in the Napoleonic wars at the time and the inevitable errors which crept into the surveyor's measurements.

https://en.wikipedia.org/wiki/Metre

After many years of surveying and wrangling back and forth over the results, it was decided to establish the meter as the distance between two marks on a special metal bar kept in Paris.

Now, the meter is defined in terms of the speed of light in a vacuum and is no longer based on the measurement of any terrestrial feature.

12. Aug 21, 2015

### nasu

Yes, you are right, sure. 10,000 km. :)

But still, the miles are not relevant. Statute or other kinds.:)
(just kidding).