An arc of 1 degree on earth's surface is equal to how many kilometers?

1 Answer
Sep 25, 2016

Answer:

At the equator, #1^o#arc length = 111.32 km, nearly. At Baltimore ( #latitude = 39.48^o N#), this length is 111.16 km, nearly. At the poles, it is 110.95 km, nearly.

Explanation:

The equatorial radius of the Earth is 6378.1 km.

The difference is 21.3 km. The polar radius is 6366.8 km.

At latitude #theta^o# N/S, the radius is #6378.1-(theta/90)(21.3)# km,

nearly.

An arc of 1 radian = the radial distance of the the latitude circle, from

the center.of the Earth.

#1^o= pi/180# radian.

So, the arc length #= (pi/180)(6378.1-(theta/90)(21.3))# km,

At the equator, #theta = 0# and this arc length = 111.32 km, nearly.

At Baltimore, #theta = 39.48^o# and the length is 111.16 km, nearly.

At the poles, #theta = 90^o# and the length = 110.95 km, nearly.

Note that this arc is along a great circle. If the arc arc is drawn by

traversing along a small circle, the length is less. If this small circle is

the latitude circle, apply a factor cos (latitude).