Calculating 1/4 Earth Arc with Trig

In summary, the circumference of the Earth can be estimated by measuring the distance covered by a swimmer in a pool.
  • #1
marciokoko
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Is there a way to determine the arc around 1/4 of the Earth without measuring it? I mean like thru trig?
 
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  • #2
marciokoko said:
Is there a way to determine the arc around 1/4 of the Earth without measuring it? I mean like thru trig?
It depends on what you mean by "determine". FYI, trig also involves measurements.
 
  • #3
SteamKing said:
It depends on what you mean by "determine". FYI, trig also involves measurements.
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
marciokoko said:
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.

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
Just memorize one key approximate fact. The circumference of the Earth is about 25000 statue miles.
 
  • #6
anorlunda said:
Just memorize one key approximate fact. The circumference of the Earth is about 25000 statue miles.

Thanks anorlunda, that's 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 doesn't 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
anorlunda said:
Just memorize one key approximate fact. The circumference of the Earth is about 25000 statue miles.
Or "statute" miles. Let's leave statues out of this.

1 statute mile = 5280 feet = 1609.35 meters approx.
 
  • #8
LOL!

Thanks guys
 
  • #9
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
Cool factoid! Thanks
 
  • #11
nasu said:
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.
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. :frown:

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

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

What is 1/4 Earth Arc?

1/4 Earth Arc is the distance along 1/4th of the circumference of the Earth's surface.

Why is Trigonometry used to calculate 1/4 Earth Arc?

Trigonometry is used because it is the branch of mathematics that deals with the relationships between the sides and angles of triangles. Since the Earth's arc is a curved line, it can be broken down into smaller triangles, and trigonometry can be used to calculate the length of these segments.

What are the steps for calculating 1/4 Earth Arc with Trigonometry?

The steps for calculating 1/4 Earth Arc with Trigonometry are as follows:

1. Determine the radius of the Earth (R).

2. Convert the given angle (θ) to radians.

3. Use the formula 1/4 Earth Arc = (θ/2π) * 2πR to calculate the length of 1/4 Earth Arc.

What are the units for 1/4 Earth Arc?

The units for 1/4 Earth Arc depend on the units used for the radius of the Earth (R) and the angle (θ). If the radius is given in kilometers and the angle is in radians, then the units for 1/4 Earth Arc will be kilometers. If the radius is given in miles and the angle is in degrees, then the units for 1/4 Earth Arc will be miles.

How accurate is the calculation of 1/4 Earth Arc with Trigonometry?

The accuracy of the calculation of 1/4 Earth Arc with Trigonometry depends on the accuracy of the given radius of the Earth (R) and angle (θ). If these values are accurate, then the calculation will be accurate. However, it is important to note that the Earth is not a perfect sphere, so there may be slight variations in the calculated value compared to the actual value.

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