Case of the Central Force disappearing totally

An Approach to Mathematic Functions Basics

Section XXXI - The Case of the Central Force disappearing totally

In this Section , we look at a special case , namely :
- the case of the Central Force disappearing totally .

Let us recall that we have set up , in Section XXIX , the [ Standardized Set of Initial Conditions ] :
- via quantities [ R-sub-zero ] and [ V-sub-zero ] ,
  - as per the diagram on-the-left below .
We shall now let the Central Force disappear totally , so that :
- the Satellite will now shoot off in a straight-line ,
  - as per the diagram on-the-right above .
Then ,
- for any point [ Point P ] on the said Straight-Line Orbit ,
  - [ R ] being the { distance O-P } as shown above is given by :
Very simply and straight-forward indeed .

We simply note here that :
- For any Centarl Force being a gravitation-type force of the format :
  - with [ N ] being greater than or equal to [ 2 ] ;
  the Straight-Line is always the resultant orbit when the Central Force disappears totally .