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Math Help - Could you help to calculate precession of the Mercury in a new way?

  1. #1
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    Could you help to calculate precession of the Mercury in a new way?

    As you know Mercury orbits with precession: http://physics.ucr.edu/~wudka/Physics7/Notes_www/node98.html

    Could you help to calculate precession of the Mercury in this new way?
    See picture:
    http://www.part.lt/img/f628e573d6f02...10de240722.png

    Lets use Newton's law for gravitational attraction.

    But lets assume that inertial mass m is changing due motion and due gravitation by equation

    m = m0 / sqrt( 1-(z/c)^2 )

    where
    m0 rest mass of the Mercury ( which is used to calculate gravitational force and kinetic mass )
    m kinetic mass of Mercury ( which is used to calculate momentum )

    For z lets consider two possible versions:
    version 1
    z = | v + v_escape |
    and version 2
    z = 2*| v + v_escape |*| v - v_escape | / ( | v + v_escape | + | v v_escape | )

    where v and v_escape are vectors
    v - real velocity of the Mercury
    v_escape - escape from the Sun velocity (at the location of the Mercury)
    v_escape vector points straight away from the Sun.

    Now you can use Newton gravitation law with rest mass m0
    and kinetic mass m could be used to calculate momentum of the Mercury.

    Could you help to calculate precession by using mentioned assumptions?
    Thank you.
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  2. #2
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    Re: Could you help to calculate precession of the Mercury in a new way?

    I have made some corrections to acceleration formula
    http://www.part.lt/img/562af2c949145...8bca6b6221.png
    and have made numerical integration.
    Now it looks it fits very well with experimental data
    ( about 0.103 arc seconds per revolution ).
    But I still have no idea how to solve it analytically.
    Maybe some advice? Thank you.
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  3. #3
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    Re: Could you help to calculate precession of the Mercury in a new way?

    Recently I have obtained likely even better solution for the acceleration I already mentioned.
    http://www.part.lt/img/eb4c24f748f6e...fbe6051663.png
    Maybe now the question about the precession also can be solved easier. What do you think?
    Maybe some ideas how?
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