The shortest path between two points on a Sphere, also known as an Orthodrome. To find the great
circle (Geodesic) distance between two points located at Latitude and Longitude
of
and
on a Sphere of Radius , convert Spherical
Coordinates to Cartesian Coordinates using

(1) |

(2) |

The great circle distance is then

(3) |

The equation of the great circle can be explicitly computed using the Geodesic formalism. Writing

(4) | |||

(5) |

gives the , , and parameters of the Geodesic (which are just combinations of the Partial Derivatives) as

(6) | |||

(7) | |||

(8) |

The Geodesic differential equation then becomes

(9) |

(10) |

(Gradshteyn and Ryzhik 1979, p. 174, eqn. 2.599.6), which can be rewritten as

(11) |

(12) |

(13) |

**References**

Gradshteyn, I. S. and Ryzhik, I. M. *Tables of Integrals, Series, and Products, 5th ed.* San Diego, CA:
Academic Press, 1979.

Weinstock, R. *Calculus of Variations, with Applications to Physics and Engineering.* New York: Dover,
pp. 26-28 and 62-63, 1974.

© 1996-9

1999-05-25