Question

The orbital velocity of a satellite at point $B$ with radius $r_B$ is $n$. The radius of points is $r_A$. If the orbit is increased in radial distances so that $r_A$ becomes $1.2 r_A$ find the orbital velocity at $(1.2 r_A)$:

• A. $\frac{vr_{B}}{r_{A} \sqrt{1.2}}$
• B. $\frac{vr_A}{1.2r_B}$
• C. $\frac{vr_B}{1.2r_A}$
• D. $\frac{vr_{A}}{r_{B} \sqrt{1.2}}$

Answer 1

Answer: (A)

For two points on same orbit $L = mv_Ar_A = mvr_B$
$v_A = \frac{Vr_B}{r_A}\,...(i)$
For two points on different orbits.
$v = \sqrt{\frac{GM}{r}} \frac{v_{0}}{v_{A}} = \left(\frac{r_{A}}{1.2r_{A}}\right)^{1/2}$
$ v_{0}=v_{A}\left(\frac{r_{A}}{1.2r_{A}}\right)^{1/2} $
$= \frac{vr_{B}}{r_{A}}\left(\frac{r_{A}}{1.2r_{A}}\right)^{1/2} $
$= \frac{vr_{B}}{r_{A}\sqrt{1.2}}$