The discussion revolves around the derivation of the formulas for perihelion and aphelion distances in elliptical orbits, specifically focusing on the semi-major axis (SMA) and eccentricity. Participants explore the underlying principles and definitions that lead to these formulas.
Participants do not reach a consensus on a specific derivation method, and multiple approaches to understanding the formulas are discussed without resolution.
Some assumptions about the definitions of eccentricity and the properties of ellipses are not fully explored, and the discussion does not resolve the mathematical steps needed to derive the formulas from first principles.
It follows from the definition of the eccentricity: the focal points of an ellipse are at a distance ## \pm e a ## from the center. And for perihelion and aphelion, as for any points on the ellipse, the sum of the distances to the foci must be ## 2a ##.bruhh said:I know the formulas for perihelion and aphelion distances in an orbit with SMA a and eccentricity e are a(1-e) and a(1+e), respectively. However, why is this? I can't seem to find any derivations for this anywhere and also cannot figure this out myself.