Nautical miles and the circumference of the earth

[Timcago]

If a central angle with its vertex at the center of the earth has a measure of 1 degree, the arc on the surface of the earth that subtends the angle has a measure of 60 nautical miles. If the radius of the earth is 3960 regular (statute) miles, how many statue miles are in 1 nautical mile? What is the circumference of the earth in nautical miles?

The circumferene of the earth in nautical miles seems easy. If 1 degree is 60 miles, then 360 degrees would be 360*60 = 21600 miles right? Or do i have to first find how many statute miles are in 1 nautical mile and then convert the 3960 statute miles to nautical miles, and then use the circumference of a circle formula (2*pi*r)?

Anyways, how do i find out how many statute miles are in 1 nautical mile?

 

[Mrspi]

Re: Nautical mile

If a central angle with its vertex at the center of the earth has a measure of 1 degree, the arc on the surface of the earth that subtends the angle has a measure of 60 nautical miles. If the radius of the earth is 3960 regular (statute) miles, how many statue miles are in 1 nautical mile? What is the circumference of the earth in nautical miles?

The circumferene of the earth in nautical miles seems easy. If 1 degree is 60 miles, then 360 degrees would be 360*60 = 21600 miles right? Or do i have to first find how many statute miles are in 1 nautical mile and then convert the 3960 statute miles to nautical miles, and then use the circumference of a circle formula (2*pi*r)?

Anyways, how do i find out how many statute miles are in 1 nautical mile?

You know that 1 degree of a central angle subtends an arc of 60 nautical miles.

Let n = length of 1 nautical mile

A central angle of 1 degree subtends 1/360 of the circumference of the circle. So, 60 n = (1/360)(circumference of earth)

60 n = (1/360)(2 pi 3960)
Multiply both sides of the equation by 1/60 to get "n" by itself:

n = (1/60)(1/360)(2 pi 3960)

I'll let you do the arithmetic....

 

[Timcago]

I got 11pi/30 which is approximately equal to 1.15.

So to answer the question, there are 1.15 statute miles in 1 nautical mile?

and the circumference of the earth is (1.15)(2*pi*3960)= 28661.3 naughtical miles?

 

[skeeter]

I got 11pi/30 which is approximately equal to 1.15.

So to answer the question, there are 1.15 statute miles in 1 nautical mile?
yes

and the circumference of the earth is (1.15)(2*pi*3960)= 28661.3 naughtical miles?
no ... (360 degrees)(60 NM per degree) = 21600 NM, the Earth's circumference in nautical miles.
(1.15 statute miles per nautical mile)(21600 nautical miles) = approx 25000, the Earth's circumference in statute miles