Question

Two commercial statellites, Seeker $I$ and Seeker $II$, have circular orbits of $R$ and $2R$, respectively, about the same planet. What is the orbital velocity of seeker $II$ if the orbital velocity of seeker $I$ is $v$?

• A. $\frac{v}{2}$
• B. $\frac{v}{(2{)}^{1/2}}$
• C. $v(2{)}^{1/2}$
• D. $2v$

Answer 1

The correct option is B $\frac{v}{(2{)}^{1/2}}$

Let the mass of planet be $M,$ then orbital velocity is given by
$V={\left(\frac{GM}{r}\right)}^{0.5}$ , where $r$ is radius of orbit.
If $V_1,V_2$ are orbital velocities of $I$ and $II$ respectively. Then,
$V_1={\left(\frac{GM}{R}\right)}^{0.5}$ and
$V_2={\left(\frac{GM}{2R}\right)}^{0.5}$.
taking the ratio we get
$\frac{V_2}{V_1}={\left(\frac{GM}{2R}\right)}^{0.5}\times {\left(\frac{R}{GM}\right)}^{0.5}=\frac{1}{2^{0.5}}$
so, $V_2=\frac{V_1}{2^{0.5}}=\frac{v}{2^{0.5}}$