A nautical mile is1.855km and is difined to be the distance on the surface of the earth that substends angl

Question

a nautical mile is1.855km and is difined to be the distance on the surface of the earth that substends angle of 1 arc minutes at the centre of the earth.what is the radius of the earth

Answer 1

1 arc minute = 1 nautical mile = 6080 feet (naut.mile defn.).

Radius of Earth:

Polar (p)= 6356.8 km

Equatorial (q)= 6378.2 km

In between these figures, at radius (r = f[latitude]) 6362.39 km it reconciles to the value of 1'arc = 6080 feet.

[considering the above 'p'&'q' as semi minor & major axes of ellipse and solving for 'r', r corresponds to latitude=59d 12']

Answer 2

Length of arc = radius x angle (in radians).

an angle of 180 degrees is equal to pi radians

a degree is therefore pi/180 radians

a minute of arc is 1/60 of a degree = pi/(180 x 60) radians

therefore

radius of Earth = 1.855 km / (pi/(180 x 60))