Let r1 and r2 be the minimum and maximum distances (perihelion and aphelion, respectively) of the ellipse r ed 1 e cos( 0) from a focus Show that a r1 ed (1 e), r2 ed (1 e), b Major diameter 2ed (1 e2) and minor diameter 2ed 1 e2 ...

a The point closest to the pole is at 0 ...

Let r1 and r2 be the minimum and maximum distances (perihelion and aphelion, respectively) of the ellipse

Question:

Let r1 and r2 be the minimum and maximum distances (perihelion and aphelion, respectively) of the ellipse r = ed/[1 + e cos(θ - θ0)] from a focus. Show that
a. r1 = ed/(1 + e), r2 = ed/(1 - e),
b. Major diameter = 2ed/(1 - e2) and minor diameter = 2ed/√1 - e2.