I've been looking at some sections in GR textbooks that deal with the orbital decay of the binary pulsar PSR B1913+16 (Straumann's General Relativity: With Applications to Astrophysics and Padmanabhan's Gravitation have some pretty good sections on this) , and I noticed something strange to do with the way they handled energy loss used in calculating the period change dT/dt of the system.(adsbygoogle = window.adsbygoogle || []).push({});

In both books, they first found the energy loss per period of the system <dE/dt>, and then used this to calculate the period change of the system dT/dt where the relation between the rate of change of energy and the rate of change of period was given by 1/T dT/dt = 2/3E dE/dt (I'm not too sure if this formula is 100% correct as I don't have the books in front of me at the moment). Now, I thought that since we are dealing with energy loss per period, the above formula should have been 1/T dT/dt = 2/3E <dE/dt> , but in both books they seemed to just drop the fact that an energy loss per period was used and treated it as if it was an instantaneous energy loss. Thus their calculation of energy loss "per period" came out with an answer with units of erg per second instead of erg per period as I would have expected, where they then used this answer and the above relation between period change and energy change to find dT/dt with units of seconds per second.

Why was it possible for Straumann and Padmanabhan to treat <dE/dt> (energy loss per period) as dE/dt (instantenous energy loss)?

I apologize for the lack of formulas, but I'm on campus right now and both of my books are at home.

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# Orbital decay of PSR B1913+16 and the use of averaged dE/dt vs. instantaneous dE/dt

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