In central force motion, the angular momentum of body remains conserved.
i.e., Angular momentum,
$L = r \times p =m\, vr$
[at minor and major axis $v$ and $\vec{ r }$ are perpendicular]
So, if $v_{1}$ and $v_{2}$ be the speed of earth at $A$ and $B$, respectively
Then, $m\, v_{1} r_{1}=m \,v_{2} \,r_{2}$
$\Rightarrow \frac{v_{1}}{v_{2}}=\frac{r_{2}}{r_{1}}=\frac{O B}{O A} $
$\Rightarrow \frac{v_{1}}{v_{2}}=R$
