The area of the sector formed by joining the tips of r2 and r3 around the orbit is B1. The area of the sector formed by joining the tips of r1 and \(\tex...The area of the sector formed by joining the tips of r2 and r3 around the orbit is B1. The area of the sector formed by joining the tips of r1 and r2 around the orbit is B3. Our aim is to use this approximate Equation to find approximate values for the heliocentric distances at the instants of the three observations, and then to refine them in order to satisfy the exact Equation 13.2.5.
I now make use of the sum of the sum-and-difference formulas from page 38 of chapter 3, namely cosAcosB=12(cosS+cosD) and sinAsinB=12(cosD−cosS),...I now make use of the sum of the sum-and-difference formulas from page 38 of chapter 3, namely cosAcosB=12(cosS+cosD) and sinAsinB=12(cosD−cosS), to obtain In these Equations we already know an approximate value for f3 (we’ll see how when we resume our numerical example); the unknowns in these Equations are R3, a and g3, and it is R3 that we are trying to find.