Problem: A satellite is launched into Earth orbit by a Delta II launch vehicle (LV).  The Delta LV's engines do not perform as expected, and at upper-stage burnout the satellite has the following states: altitude is 250 km, inertial velocity is 7.58 km/s, flight-path angle is 0.6 deg.  The satellite mass after burn-out and separation is 2,300 kg.

a) Determine the velocity impulse (DV) required to obtain a circular orbit when the satellite reaches its apogee.

b) If the satellite uses its on-board propulsion system for the circularization burn, determine the propellant mass required for the circularization burn (assume the on-board hydrazine engine has an I_sp = 280 sec).

Problem: A new heat shield is being tested experimentally by launching a payload that consists of a re-entry capsule with mass m = 200 kg, drag coefficient C_D = 1.7, and radius r = 0.65 m.  Design an acceptable engine cut-off state (r, V, and g) that satisfies the following mission constraints:  1) the re-entry capsule's maximum deceleration is 12 g, and 2) the flight time from engine cut-off to entry interface (EI) must be greater than 15 min to allow payload separation procedures.  In addition, determine the inertial velocity and flight-path angle at EI.