Computer algebra check of the potential and orbital equation
Subject: Computer algebra check of the potential and orbital equation
Date: Thu, 27 Mar 2008 04:36:01 EDT
This computer result is the same as my hand calculation just sent over.
After a number of strange results I recalculated the formula for the potential, Eq. (12). Obviously the parameter L sub r is not the angular momentum but the angular momentum per unit mass, therefore a factor of m is missing in several places. Furthermore, a factor of ½ was missing in the Newtonian part of the potential which has appeared now. I suggest correcting the formulas in paper 108.
I came to this because solution of eq. (45) was very problematic. 1/alpha was the order 10^45 and u of order 10^-11. With the corrected L or lowercase L the missing square of the mass should make this more handable, we will see.
Attached the corrected derivation of eq. (12) and the corresponding Maxima code where I verified this. Carroll made a real mess with the units.
A question: To my opinion the constant Er must be unity due to the choice of lambda being the proper time. But then we cannot modify the total energy any more, it is ½ m c^2. Have you an idea?
Horst
Attachment: Energy.pdf
Attachment: Pot.pdf