Question

A satellite is revolving in an elliptical orbit and its speed is $v$ at the nearest distance $a$ from the earth. The speed of the satellite at farthest distance $b$ will be

• A. $\frac{va}{b}$
• B. $\frac{vb}{a}$
• C. ${\left(\frac{a}{b}\right)}^{3/2}v$
• D. ${\left(\frac{b}{a}\right)}^{3/2}v$

Answer 1

The correct option is A $\frac{va}{b}$

Given, the velocity of satellite at nearest distance a is $v$.
Let the velocity at farthest distance be $v_f$.
Angular momentum of the satellite is conserved in this motion i.e. $L=mvr$ is same at every point of the orbit.
If $L_n,L_f$ are the angular momentums at nearest and farthest points of orbit, then
$L_n=L_f$
$mva=m{v}_{f}b$
Simplifying this, we get,
$v_f=v\frac{a}{b}$