Simple Earth Circumference Question

[DaveMaron]

Hello. This is my first post. I just started physics this year, and I forgot how to do some simple trigonometry, but I'm not quite sure where to look.

1. My question is: If I know the circumference of the Earth at the Equator is about 2.49 x 10 to the Fourth,

How do I find the Circumference of the Earth 45 Degrees North?





2. Homework Equations : None



3. None...

Obviously it would be smaller, but I'm not quite sure how much.

Thanks for the help.

 

[DaveMaron]

Nevermind, I found the answer.

Use the radius of the Earth (6.4 x 10 to the sixth) as the Hypotenuse for the 45 Degree Triangle. Divide the radius by the Square root of two and this will give you the radius from the Tip of the 45 degree angle to the Center of the Earth. Multiply this by 2 x Pie to get the Circumference.

Thanks.

 

[rock.freak667]

Nevermind, I found the answer.

Use the radius of the Earth (6.4 x 10 to the sixth) as the Hypotenuse for the 45 Degree Triangle. Divide the radius by the Square root of two and this will give you the radius from the Tip of the 45 degree angle to the Center of the Earth. Multiply this by 2 x Pie to get the Circumference.

Thanks.

I can't remember the topic name, but I recall if you move along the same latitude, you use the same radius. But if you move along a longitude, the new radius r is give by r=Rcosθ, where θ is the angle of longitude. Sorry I replied too late, but it seems you got it out so all is well.