Question

The earth moves around the sun in an elliptical orbit (as shown in figure). The ratio $\frac{ OA }{ OB }= x$. The ratio of the speed of the earth at $B$ to that at $A$ is found to be $x ^{ N }$. The value of $N$ is_______.

Answer 1

Applying conservation of angular momentum at position $A$ and $B$,
$mv _{ A } \times OA = mv _{ B } \times OB$
$\Rightarrow \frac{ v _{ B }}{ v _{ A }}=\frac{ OA }{ OB }= x$
$\Rightarrow x ^{ N }= x$
$\Rightarrow N =1.00$