A planet revolves around the Sun in an elliptical orbit whose Sun–planet distance varies during the revolution.
(i) Define the eccentricity e of an ellipse in terms of its semi-major axis a and linear eccentricity c.
(ii) Prove that when e=0 the orbit becomes a circle and show that, in this special case, the perihelion and aphelion distances are equal.
a. Define the eccentricity e of an ellipse in terms of its semi-major axis a and linear eccentricity c.
b. Prove that when e=0 the orbit becomes a circle and show that, in this special case, the perihelion and aphelion distances are equal.