An Approach to Mathematic Functions Basics

by Frank C. Fung ( 1st published in December, 2014. )

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Section XXXIII - Summarizing on the Orbit of a Satellite

Summary for the Section :

• In this Section , we shall summarize our findings on
  • the orbit of a Satellite moving under the influence of a Central Force ,

    with :

    • the Central Force here being a gravitaion-type force varying as the [ Inverse of R-Square ] ,

      i.e. :

      • 

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Recounting the Steps towards finding the Solution :

• Let us now do a re-count of steps taken to find the solution .

  FIRST :

  • In Section XXVII , that :
    • the Acceleration on the Satellite arising from the Central Force is given by :
      • 

  SECOND :

  • In the same Section , we established that :
    • the { Differential Equation with respect to time } is given by :
      • 

      or alternately in this format as presented in Section XXVIII :

      • 

  THIRD :

  • In Section XXIX , that :
    • the { Differential Equation involving [ R ] and [ Theta ] } is given by :
      • 

        ( this being the { Differential Equation involving [ R ] and [ Theta ] in its First Format } ) .

      or alternately , on multiplying throughout by [ K-square over R-square ] :

      • 

        ( this being the { Differential Equation involving [ R ] and [ Theta ] in its Second Format } ) .

  FOURTH :

  • In the last Section , Section XXXII , we established that :
    • the solution for expressing [ R ] in terms of [ Theta ] is of the format :
      • 

• And we do recognize that this last equation above is in the format of either :
  • a Circle or an Ellipse , or
  • a Parabola , or
  • a Hyperbola ;

  and we bring back this equation from Section XXIII :

  • 

    for quick comparison .

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go to the next section : Section XXXIV - Other Central Forces of a Similar Nature

go to the last section : Section XXXII - Solving for [ R ] in terms of [ Theta ]

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Original dated 2014-12-07