Halliday, Resnick & Walker — Gravitation: Problem Problem_68

Two small spaceships, each with mass \( m = 2000 \text{ kg} \), are in the circular Earth orbit of Fig. 13.31, at an altitude \( h \) of \( 400 \text{ km} \). Igor, the commander of one of the ships, arrives at any fixed point in the orbit \( 90 \text{ s} \) ahead of Picard, the commander of the other ship. What are the (a) period \( T_0 \) and (b) speed \( v_0 \) of the ships? At point P in Fig. 13.31, Picard fires an instantaneous burst in the forward direction, reducing his ship’s speed by \( 1.00\% \). After this burst, he follows the elliptical orbit shown dashed in the figure. What are the (c) kinetic energy and (d) potential energy of his ship immediately after the burst? In Picard’s new elliptical orbit, what are (e) the total energy \( E \), (f) the semimajor axis \( a \), and (g) the orbital period \( T \)? (h) How much earlier than Igor will Picard return to P?