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 $1.2r_A$ find the orbital velocity at $(1.2r_A)$:

• 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

Answer: (A)

For two points on same orbit $L=m{v}_A{r}_A=mv{r}_B$

$v_A=\frac{V{r}_B}{r_A}...(i)$

For two points on different orbits.

$v=\sqrt{\frac{GM}{r}}\frac{v_0}{v_A}={\left(\frac{r_A}{1.2r_A}\right)}^{1/2}$

$v_0=v_A{\left(\frac{r_A}{1.2r_A}\right)}^{1/2}$

$=\frac{v{r}_B}{r_A}{\left(\frac{r_A}{1.2r_A}\right)}^{1/2}$

$=\frac{v{r}_B}{r_A\sqrt{1.2}}$