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    Re: running fix + lunar
    From: Andrés Ruiz
    Date: 2010 Nov 17, 09:49 +0100

    Dear Paul,

    A good didactical explanation of the method.

    This remember me my end of career project where to solve the kinematics and dynamics of a complex mechanism, each component contribute with his own equation F, and the solution, like in the FEM method, is obtained from a set of n equations like:

    F = ∂F/∂t t + ∂F/∂B B + ∂F/∂L L

    In your example F is the altitude or the lunar distance.

    A generalization could be used if n observations are obtained, using the method of least squares.


    At the university I used this method in heat transfer, in deformation and stress calculations for a structure, in thermodynamics, … And I have use it only once in my job when I worked in robotics, for calculate a space manipulator. For hobby and passion: navigation, I have used this method (1)(2) in my program CelestialFix.exe solving for latitude B, longitude L, course R and speed V.


    Severance (3) was the first who published a solution using this method in “Overdetermined celestial fix by iteration“, and Kaplan (4) generalize it for use in the STELLA program.




    (1)     http://fer3.com/arc/m2.aspx?i=112117&y=201003

    (2)     Position and motion from celestial observations

    (3)     http://www.ion.org/search/view_abstract.cfm?jp=j&idno=298

    (4)     http://www.usno.navy.mil/USNO/astronomical-applications/publications/sel-tech-rep


    Andrés Ruiz

    Navigational Algorithms


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