Question

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

Answer 1

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).