Why is the specific angular momentum equal to this?

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The discussion centers on the derivation of specific angular momentum in relation to elliptical orbits, specifically the equation h = wr^2 = ab * n. The user seeks a method to derive the relationship ab * n without using calculus or eccentricity-related equations. They initially express confusion but later clarify their understanding of the angular momentum concept. The focus then shifts to finding a geometric or algebraic approach to derive the equation b² = ra * rb. The conversation highlights the importance of understanding angular momentum in the context of orbital mechanics.
Bob Jones
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From a wiki's vis-viva equation page, it is given that the specific angular momentum h is also equal to the following:

h = wr^2 = ab * n

How can ab * n be derived to be equal to the angular momentum using elliptical orbit energy/momentum/other equations without having to use calculus or equations involving eccentricity?
 
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Oh... Wait. This is the old version of this. I understand how it works now. Could someone tell me how geometrically or algebraically you can derive b2 = ra * rb?
 

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