Question

The orbital velocity of a satellite at point $B$ with radius $r_B$ is $v$. The radius of point $A$ is $r_A$.When satellite is at $A$, the orbit is increased in radial distances uniformly, so that $r_A$ becomes $1.2r_A$ , find the orbital velocity at $\left(1.2r_A\right)$

• A. $\frac{v{r}_B}{r_A\sqrt{1.2}}$
• B. $\frac{v{r}_A}{1.2r_B}$
• C. $\frac{v{r}_B}{1.2r_A}$
• D. $\frac{v{r}_A}{r_B\sqrt{1.2}}$

Answer 1

The correct option is A $\frac{v{r}_B}{r_A\sqrt{1.2}}$

For two points on same orbit
$L=m{v}_A{r}_A=mv{r}_B$
$v_A=\frac{v{r}_B}{r_A}$
For two points on different orbits.
$v=\sqrt{\frac{GM}{r}}$
$\frac{v_n}{v_A}={\left(\frac{r_A}{1.2r_A}\right)}^{\frac{1}{2}}$
$v_n=v_A{\left(\frac{r_A}{1.2r_A}\right)}^{\frac{1}{2}}$
$v_n=\frac{v{r}_B}{r_A}{\left(\frac{r_A}{1.2r_A}\right)}^{\frac{1}{2}}=\frac{v{r}_B}{r_A\sqrt{1.2}}$