The Spiralling Binary System of Black Holes

Cover The Spiralling Binary System of Black Holes
The Spiralling Binary System of Black Holes
Blackburn, James Kent, 1957-
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(5.20) The total energy of the binary system of point masses, including the rest mass energy of the two masses, is given by u M a E N = M total - M 9 '°' a ' = M total - -£- . (5.21) GO 0.05 i — i — i — i — i — ] — i — i — i — i — i — i — i — i — i — I — i — i — i — i — i — i — i — i — r 0.00 \ CM 2 l I c o 01 z W -0.05 -0.10 -0.15 -- _q pa L - Ll ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 20 40 60 80 100 S N ewton/(M 1 +M 2 ) FIGURE 6: Single Parameter Newtonian Circular Orbits. The binding e...nergy per reduced mass as a function of separation per total mass. A single curve describes all possible Newtonian orbits in terms of one parameter, the scaled total angular momentum j total- 61 An interesting result occurs when the following rescaling is performed: (En - M total ) = 1 P ' Via, (5.22) TT-'ii-. (5-23) When equation (5.22) is plotted as a function of equation (5.23), a single curve results which represents all possible stable circular orbits of a binary system in Newtonian mechanics, as shown in Figure 6.

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