Question

A satellite is in an elliptical orbit around the earth with aphelion of $6\, R$ and perihelion of $2\, R$ where $R$ is the radius of the earth. The eccentricity of the orbit is________

Answer 1

$r _{ p }=2 R ; r _{ A }=6 R$
As we know that
$r_{p}=a(1-e)=a-a e ; r_{A}=a(1+e)=a+ a e$
$\Rightarrow \frac{r_{p}}{r_{A}}=\frac{a(1-e)}{a(1+e)}$
$\Rightarrow r_{p}(1+e)=r_{A}(1-e)$
$\Rightarrow e=\frac{r_{A}-r_{p}}{r_{A}+r_{p}}$
$=\frac{6 R-2 R}{6 R+2 R}=\frac{1}{2}=0.5$