An Approach to Mathematic Functions Basics

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

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Section XXIV - The Reasons for bringing-in the Orbit of a Satellite

Summary for the Section :

• In last Section , we came upon the [ yellow straight-line ] admist the Circle , Ellipse , the Parabola and the Hyperbola .
  • And the equation for the [ yellow straight-line ] is :
    • 

    while the equation for the circle-ellipse-parabola-hyperbola are of-the-format :

    • 

  The issue in-question here is :

  • whether the [ straight-line ] belong in the same group as the circle-ellipse-parabola-hyperbola .

• In Part Six of this paper coming up next :
  • we shall be looking at the Orbit of a Satellite moving under a Central Force ,
    • in a attempt to resolve the issue .

  We shall explain why it would be appropriate to do so in theis Section .

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What we intend to do to resolve the issue :

• In our analysis to follow in Part VI ,
  • we shall be looking closely at a Satellite moving under the influence of a Central Force ,
    • with the Central Force here being a Gravitation-Type Central Force of the format :
      • 

  What we would like to do here is as follows :

  • First ,
    • We fix a [ Point-Mass ] at the Point-Of-Origin ,
      • and this [ Point-Mass ] shall exert a gravitational pull on the Satellite .

  • Second ,
    • We shall start-off with intial conditions so that the Satellite will move in a Circular Orbit initially .

  • Third ,
    • We will permit the [ Point-Mass ] to disappear all-of-a-sudden , so that :
      • the Satellite will shoot-off in a straight-line .

  • Fourth ,
    • We will permit the mass of the [ Point-Mass ] to vary to obtain the different [ orbital shapes ] .

• And what we shall try to establish here is :
  • the [ Circlar Orbit ] and the [ Straight-Line Orbit ] are anchoring [ orbital shapes ] for all values of [ N ] ;

  • changes in the mass of the [ Point Mass ] will result in different [ orbital shapes ] ; and

  • infinitesimal changes in the { mass of the [ Point Mass ] } and in the { value of [ N ] } will result in changes in the [ orbital shapes ] ,
    • but the mapped changes in the [ orbital shapes ] are necessarily unbroken .

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go to the next section : Section XXV - A Statement of Purpose for Part VI

go to the last section : Section XXIII - Linkage System for the Circle / Ellipse / Parabola / Hyperbola

return to the MATH Functions Basics HomePage

Original dated 2014-12-07