What is the Conversion Factor for Nautical Miles to Statute Miles?

In summary, the conversation discusses the calculation of the number of statute miles in a nautical mile using the arc length theorem and the Earth's diameter. The final answer is determined to be 10pi/27 miles, with the instructor's preference for exact answers including pi.
  • #1
TrueStar
95
0

Homework Statement



Given: The diameter of the Earth is 8000 miles

If angle ACB has measure 1', then the distance between A and B is a nautical mile. Approximate the number of and (statute) miles in a nautical mile.


Homework Equations



Arc Length Therom: s=r(theta)


The Attempt at a Solution



I think I have this figured out and I was just over-thinking it, but I'd like to check with others.

1'=1/60 degrees, but this needs to be changed to radians so it can be used in the arc length formula. --- 1/60*pi/180 = pi/10800 radians.

Apply this along with the Earth's radius (8000/2 = 4000 miles) to the arc length formula --- (pi/10800)*4000 = 4000pi/10800 miles. This simplifies out to10pi/27 or about 1.16 miles per nautical mile. However, I will put down 10pi/27 because my instructor wants exact answers.

Did I do this correcty? Thanks in advance!
 
Physics news on Phys.org
  • #2
In a circle there are 360 x 60 minutes of arc.
1' at the equator is a nautical mile.
The equator is pi*8000 statute miles

Since you are only given the Earth's diamter to 1 sig figure then 1.6mi would be an exact answer
 
  • #3
mgb_phys said:
In a circle there are 360 x 60 minutes of arc.
1' at the equator is a nautical mile.
The equator is pi*8000 statute miles

Since you are only given the Earth's diamter to 1 sig figure then 1.6mi would be an exact answer
Wouldn't that be 1.2 miles?
 
  • #4
Maybe I'm using the wrong wording. He wants everything to have pi remain in the answer if pi is part of it. He doesn't want us to plug it into a calculator and submit answers in decimal form.

This is why I say I think the answer is 10pi/27.
 
  • #6
Thank you both for looking at it!
 

FAQ: What is the Conversion Factor for Nautical Miles to Statute Miles?

What is arc length?

Arc length is the distance along a curve or arc. It is measured in units such as meters, feet, or miles.

How is arc length calculated?

Arc length can be calculated by multiplying the radius of the circle or arc by the central angle in radians. The formula for calculating arc length is s = rθ, where s is the arc length, r is the radius, and θ is the central angle in radians.

What is a nautical mile?

A nautical mile is a unit of measurement used in navigation, particularly for measuring distances at sea. It is equal to one minute of latitude, which is approximately 1.15 miles or 1.852 kilometers.

How is a nautical mile different from a regular mile?

A nautical mile is longer than a regular mile, as it is based on the Earth's circumference rather than its diameter. Additionally, nautical miles are used for marine and air navigation, while regular miles are used for land navigation.

Why are nautical miles used in navigation?

Nautical miles are used in navigation because they provide a more accurate measurement of distance on the Earth's curved surface. This is especially important for long-distance travel, such as across oceans, where small errors in distance can lead to significant deviations in course.

Back
Top