Question

The speed of the planet at the perihelion P in the figure is $v_P$ and the sun-planet distance SP is $r_P$. Relate ($r_P,v_P$) to the corresponding quantities ($r_A,v_A$) at the aphelion A. Will the planet take equal time to traverse BAC and CPB?

Answer 1

$L=I\omega$

$L=M{r}^2\omega$ $v=r\omega$

From conservative of angular momentum

${\overline{L}}_A={\overline{L}}_p$

$\overline{r_A}\times \overline{P_A}=\overline{r_B}\times \overline{P_B}$

$m{r}_A^2\frac{V_A}{r_A}=m\frac{V_B}{r_B}{r}_B^2$

$V_A{r}_A=V_B{r}_B$

$V_p{r}_p=V_A{r}_A=Arealvelocity$.............(1)

Areal velocity don’t change with the position of the planet.

From the diagram Area $curvatureBPCS<CABS$

$\therefore$ In BPC time will take small in compare to CAB.