Question

A planet is revolving round the sun. Its distance from the sun at Apogee is $r_A$ and that at Perigee is $r_p$. The mass of planet and sun is $m$ and $M$ respectively, $v_A$ and $v_p$ is the velocity of planet at Apogee and Perigee respectively and $T$ is the time period of revolution of planet round the sun.
(a) $T^2=\frac{{\pi }^2}{2Gm}{\left(r_A+r_p\right)}^2$
(b) $T^2=\frac{{\pi }^2}{2GM}{\left(r_A+r_p\right)}^3$
(c) $v_A{r}_A=v_p{r}_p$
(d) $v_A<v_p,r_A>r_p$

• A. a, b, c
• B. a, b, d
• C. b, c, d
• D. all

Answer 1

Answer: (C)

$T^2=\frac{4{\pi }^2}{GM}{a}^3$
$T^2=\frac{4{\pi }^2}{GM}{\left(\frac{r_p+r_A}{2}\right)}^3$
$=\frac{{\pi }^2}{2GM}{\left(r_p+r_A\right)}^3$
$mvr=$ constant
$\Rightarrow vr=$ constant
$\therefore v_A{r}_A=v_p{r}_p$
$\therefore r_A>r_p$
$\therefore v_A<v_p$