Question

The picture above represents a planet (blue) oribiting a star. This particular planet has a highly elliptical orbit, as shown.
At what point in the orbit is the planet moving fastest?

• A. $1$
• B. $2$
• C. $3$
• D. $4$
• E. We cannot determine where the planet is moving fastest, since Kepler's Laws apply only to planet in our solar system

Answer 1

Answer: (D)

$4$

As the planet is like an isolated system therefore its angular momentum remains conserved , angular momentum of a planet is given by ,

$L=mr\times v$ ,

where $m=$ mass of the planet ,

$r=$ distance of planet from sun ,

$v=$ velocity of planet ,

since $L$ is constant , therefore product of $r$ and $v$ also be constant (mass $m$ of planet doesn't change) , it means when $r$ increases $v$ will decrease and vice-versa ,

now we can see that at point 4 $r$ is smallest therefore $v$ will be highest i.e. planet will move fastest .