A planet orbits around a star S, as shown in the figure. The semi-major axis of the orbit is a. The perigee, namely the shortest distance between the planet and the star is 0.5 a. When the planet passes point \mathrm{P} (on the line through the star and perpendicular to the major axis), its speed is v_{1}. What is its speed v_{2} when it passes the perigee?
Answer Choices
A. v_{2}=\frac{3}{\sqrt{5}} v_{1} .
B. v_{2}=\frac{3}{\sqrt{7}} v_{1}.
C. v_{2}=\frac{2}{\sqrt{3}} v_{1}.
D. v_{2}=\frac{\sqrt{7}}{\sqrt{3}} v_{1}.
E. v_{2}=4 v_{1}.
