Question

A satellite of mass $m$ is revolving around the earth in a circular orbit of certain radius . At certain point of its orbit , the direction of motion of satellite is suddenly changed by angle $\alpha (Givencos\alpha =\frac{3}{5})$ by turing its velocity vector , such that speed remains constant . The satellite, consequently goes to elliptical orbit around earth . Find ratio of speed at apogee to speed at perigee.

• A. $\frac{1}{3}$
• B. 9
• C. $\frac{1}{9}$
• D. 3

Answer 1

The correct option is C $\frac{1}{9}$

$m{v}_p{r}_p=m{v}_A{V}_A=m{v}_0{r}_{0}cos\alpha$

$\Rightarrow v_A{r}_A=v_P{r}_P=\left(\frac{3v_o{r}_o}{5}\right)$

along $\frac{1}{2}m{v}_P^2-\frac{G{M}_{e}m}{r_A}=\frac{G{M}_{e}m}{r_o}+\frac{1}{2}M{v}_o^2$

quardratic equations is $\times (x=\frac{r_o}{r_A})$

$9x^2-50x+25=0$