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13.12: Sector-Triangle Ratio
https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Celestial_Mechanics_(Tatum)/13%3A_Calculation_of_Orbital_Elements/13.12%3A_Sector-Triangle_Ratio
I now make use of the sum of the sum-and-difference formulas from page 38 of chapter 3, namely $\cos A \cos B = \frac{1}{2} (\cos S + \cos D)$ and $\sin A \sin B = \frac{1}{2} (\cos D - \cos S ),$ ...I now make use of the sum of the sum-and-difference formulas from page 38 of chapter 3, namely $\cos A \cos B = \frac{1}{2} (\cos S + \cos D)$ and $\sin A \sin B = \frac{1}{2} (\cos D - \cos S ),$ to obtain In these Equations we already know an approximate value for $f_3$ (we’ll see how when we resume our numerical example); the unknowns in these Equations are $R_3$ , $a$ and $g_3$ , and it is $R_3$ that we are trying to find.

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