Physics - Practical physics Question with Solution | TestHub

Velocity at A in a circular orbit $V_A=\sqrt{\frac{GM}{r_1}}=GM=g{R}^2$ $\sqrt{\frac{g{R}^2}{r_1}}=R\sqrt{\frac{g}{r_1}}$ Velocity in elliptical orbit is given by the expression, $v^2=2g{R}^2\left(\frac{1}{r}-\frac{1}{2a}\right)$ Where $a=\frac{r_1+r_2}{2}$ Velocity at Perihelion of the transfer orbit, ${\nu }_{AP}^2=2g{R}^2\left(\frac{1}{r_1}-\frac{1}{2a}\right)$ $\left({\dot{v}}_{AP}\right)=R\sqrt{2g\left(\frac{1}{r_1}-\frac{1}{r_1+r_2}\right)}=R\sqrt{\frac{2g{r}_2}{r_1\left(r_1+r_2\right)}}$ $r_1{V}_{AP}=r_2{V}_{Ba}$ Velocity at aphelion of the transfer orbit $\left(v_{B_a}\right)=R\sqrt{\frac{2g{r}_1}{r_2\left(r_1+r_2\right)}}$

Velocity increment, $\Delta V_a=R\sqrt{\frac{g}{r_2}}\left(1-\sqrt{\frac{2r_1}{r_1+r_2}}\right)$