An Approach to Mathematic Functions Basics

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

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Section XXV - A Statement of Purpose for Part VI

A Statement of Purpose for Part VI :

• In this Part VI of the paper , we shall establish :
  • the differential equations and the solutions thereof for the orbit of the Satellite .

The General Flow for Part VI :

• In Section XXVI coming up next :
  • We shall set up the [ Polar Co-ordinates Reference Frame ] and briefly go over :
    • the Position Vector , the Velocity Vector and the Acceleration Vector for the Satellite .

• In Section XXVII :
  • We shall fix a [ point-mass ] at the Point-Of-Origin so that it exerts a gravitational pull on the Satellite , and
    • we shall also set up the core { Differential Equation governing the behavior of the Satellite } .

• In Section XXVIII :
  • We shall set up the Differential Equation involving [ R ] and [ Theta ] .

• In Section XXIX :
  • We shall set up our { Standardized Set of Initial Conditions } ,
    • specifically catering to the { Circluar Orbit } being a possible solution , always .

• In Section XXX :
  • We shall take a quick look at the characteristics of the Circular Orbit .

• In Section XXXI :
  • We shall establish the [ straight-line ] as the orbit of the Satellite ,
    • when the [ point-mass ] at the Point-Of-Origin disappears .

• In Section XXXII :
  • We shall solve the Differential Equation involing [ R ] and [ Theta ] .

• In Section XXXIII :
  • We shall summarize our findings on the possible orbits of the Satellite .

• In Section XXXIV :
  • We shall take a quick look other Gravitation-Type Central Force , i.e. :
    • 

      where [ N ] varies .

• In Section XXXV :
  • We shall re-do the Differention Equation for [ N = 2 ] ,
    • using [ z ] being the reciprocal of [ R ] as the key variable .

• In Section XXXVI :
  • We shall do the Differential Equation for [ N = 3 ] ,
    • again using [ z ] as the key variable .

• In Section XXXVII :
  • We do a graphic presentation of the orbits for [ N = 3 ] .

• In Section XXXVIII :
  • We shall make several observations on the Orbits of the Satellite ,
    • based on Kinetic Energy and Potential Energy considerations .

• In Section XXXIX :
  • We shall outline a proposal for further studies on the Orbital Shapes of the Satellite .

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go to the next section : Section XXVI - Setting up the Polar Co-ordinates Reference Frame

go to the last section : Section XXIV - The Reasons for bringing in the Orbit of a Satellite

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Original dated 2014-12-07