Answer to Question #93211 in Classical Mechanics for Sridhar

Question

A planet is revolving around the sun as shown in the figure. The radius vectors joining the sun and the planet at points A and B are 90×10^6 km and 60×10^6 km respectively. The ratio of velocities of the planet at A and B when its velocities make 30° and 60°with major axis of the orbit is
Ans 1/√3

Answer 1

From the conservation of angular momentum:

$$mv_ar_a \sin{30}=mv_br_b \sin{60}$$

$$v_a(90) \sin{30}=v_b(60) \sin{60}$$

$$\frac{v_a}{v_b}=\frac{(60) \sin{60}}{(90) \sin{30}}=\frac{2}{\sqrt{3}}$$