Why is the specific angular momentum equal to this?

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SUMMARY

The discussion centers on the derivation of specific angular momentum in orbital mechanics, specifically the equation h = wr² = ab * n. Participants seek a geometric or algebraic explanation for the relationship b² = ra * rb without resorting to calculus or eccentricity equations. The conversation highlights the importance of understanding the vis-viva equation and its implications in elliptical orbits. Ultimately, the focus is on simplifying complex concepts for better comprehension.

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  • Understanding of specific angular momentum in orbital mechanics
  • Familiarity with the vis-viva equation
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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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