Earth is moving around the sun in an elliptic | vedclass

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(C) In central force motion,the angular momentum of the body remains conserved.Angular momentum is given by $L = \vec{r} 	imes \vec{p} = mvr \sin 	h

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$R$

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(C) In central force motion,the angular momentum of the body remains conserved.Angular momentum is given by $L = \vec{r} 	imes \vec{p} = mvr \sin 	heta$.At points $A$ and $B$,the velocity vector is perpendicular to the position vector,so $	heta = 90^\circ$ and $\sin 90^\circ = 1$.Thus,$L = mvr$.Let $v_A$ and $v_B$ be the speeds of the Earth at $A$ and $B$,respectively,and $r_A = OA$ and $r_B = OB$ be the distances from the Sun.By conservation of angular momentum:$m v_A r_A = m v_B r_B$$\Rightarrow \frac{v_A}{v_B} = \frac{r_B}{r_A} = \frac{OB}{OA}$Given that $\frac{OB}{OA} = R$,we have $\frac{v_A}{v_B} = R$.Therefore,the ratio of Earth's velocities at $A$ and $B$ is $R$.

Earth is moving around the sun in an elliptical orbit as shown. The ratio of $OB$ and $OA$ is $R$. Then the ratio of Earth's velocities at $A$ and $B$ is

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