NIF:Kepler part III

["Rauber, Joel Phys" <RAUBERJ@mg.sdstate.edu>]

First Let me start with a

DISCLAIMER
If I should be able to solve this problem in a satisfactory manner, it does 
not prove or disprove anybodies position in this discussion, as it would 
only represent one example of doing what I've suggested.

Instructions for part III
a) Reread parts I and II and in particular get out the sheet of paper where 
you drew the diagram described in part I

Notation Review:  underscores "_" denote subscripts, "^" denotes 
exponentiation,
ABS( ) is the absolute value function used here to compute the norm of a 
Euclidean vector.

r_1 and r_2 are desplacement vectors!! and indicate the postions of the 
masses m_1 and m_2

Write the 2nd law for the two masses:

(1) . . . m_1 a_1 = G*m_1*m_2*(r_2 - r_1)/(ABS(r_2 - r_1))^3

                                       +    m_1*C*r_1

(2) . . . m_2 a_2 = G*m_1*m_2*(r_1 - r_2)/(ABS(r_2 - r_1))^3

                                          +    m_2*C*r_2

Note a_1 and a_2 are the accelerations of the two masses and are known to be 
zero according to the constraints of the problem (we are working in a frame 
where the two masses are stationary).

Divide equations (1) and (2) by m_1 and m_2 respectively to get

(3) . . . 0 = a_1 = G*m_2*(r_2 - r_1)/(ABS(r_2 - r_1))^3

                                       +   C*r_1

(4) . . . 0 = a_2 = G*m_1*(r_1 - r_2)/(ABS(r_2 - r_1))^3

                                          +    C*r_2


I have to go to class now so this is as far as I've got so far, I'll see if 
there are objections so far. Part IV coming later.

Joel Rauber
rauberj@mg.sdstate.edu