Question

What is the shortest distance between two points `(61^@40.177',33^@23.101')` and `(59^@26.266',13^@03.807')` `("latitude","longitude")` on earth?

Answer 1

Great circle distance is `1411.55` miles.

Explanation:

First of all here angles (latitudes and longitudes) are given here in degrees and minutes and hence need to converted into degrees (with decimals) so that I can use scientific calculator provided with MS Windows. Further, I will be using up to six places (or more) of decimal for accuracy.

Hence `33^@23.101'=(33+23.101/60)^@=33.385016^@`.

Similarly `13^@03.807'=13.06345^@`, `61^@40.177'=61.669616` and `59^@26.266'=59.437767^@`

Further, although we are using degrees as longitudes and latitudes are available in degrees, `d` should be found in radians, to get great circle distance (GCD - it is the shortest distance between two points on the surface of a sphere, here earth) and then this distance would be `d xx R`. Now using the formula,

`d=cos^(-1)(sin33.385016^@sin13.06345^@+cos33.385016^@cos13.06345^@ cos(61.669616 – 59.437767)^@`

= `cos^(-1)(0.5502624xx 0.2260299+0.8349918xx0.97412xxcos(2.231849))`

= `cos^(-1)(0.5502624xx 0.2260299+0.8349918xx0.97412xx0.9992414)`

= `cos^(-1)(0.12437576+0.8127652)`

= `cos^(-1)(0.93714096)`

= `0.35645154` - in radians

`GCD=0.35645154xx3960=1411.55` miles.