Question

A Satellite is in an elliptic orbit around the earth with an aphelion of 6R and perihelion of 2R. Find the eccentricity of the orbit.

• A. $\frac{1}{6}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{1}{2}$

Let $r_a$ and $r_p$ denote distance of aphelion and perihelion of the elliptical orbit of the satellite.

$r_a=a(1+e)$ and $r_p=(1-e)$ ($a$ is semi major axis of ellipse)

As $r_a=bl$ and $r_p=2R$

$\frac{a(1+e)}{a(1-e)}=\frac{6R}{2R}=3$ where $e=\frac{1}{2}$

So eccentricity $=\frac{1}{2}$