*Source :* IE Irodov: 1.207.

I used, force by gravitational pull of Sun should provide necessary centripetal force at one extreme $r_1$ where velocity is $v_1$ ( I took that moment as circle as $r_1\perp v_1$) ,$$\implies\dfrac{GM_sm}{r_1^2}=\dfrac{mv_1^2}{r_1}\implies v_1=\sqrt{\dfrac{GM_s}{r_1}}$$

But when I use energy conservation then, $$v_1=\sqrt{\dfrac{2GM_sr_2}{r_1(r_1+r_2)}}$$

Second expression gives me the correct answer, also if I put $r_1=r_2$ second expression reduces to first one, which says to me that we apply centripetal force method only when we have complete circle, not that instantaneous circles, why?