From Fig. 3 and Eqn. (17) we see that:

(18) |

(19) |

(20) |

The distance between two points , on a geodesic arc is best obtained, after differencing Eqn. (21), by using the identity , where . This avoids excessive loss of significant digits when the two points are close together.

Vincenty[5] has rearranged a subset of the resulting equations into nested forms more suitable for computation:

In equations (22) the origins of and have been shifted from the equator to the initial point (), where the reduced latitude is and the azimuth of the geodesic is .

2002-03-21