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Exercises 4 through 7, we are considering a rocket that ed to 300 km above the surface of the earth, 6.7 x 106 m from the center of the earth. At this point, the engines are cut off and the rocket enters orbit. The angle between and For u is denoted by ф. 4. What velocity must it have attained if it is to remain in a circular orbit at this height? What is the period of this orbit? 5. If its speed is 9000 m/s and φ = π/2, what are the values of the apogee and perigee of the resulting orbit? What is the period of this orbit? 6. If its speed is 9000 m/s and φ = π/3, what are the values of the apogee and perigee of the resulting orbit? What is the period of this orbit? 7. If its speed is 9000 m/s, find the angle ф that will result in an orbit whose perigee is 6.5 x 106 m. What are the values of the eccentricity apogee, and period of this orbit?

4. 7727 m/s, period 5448 s 90 min, 48s. 5. 35675, K 6.03 x 1010, perigee 6.7 x 106 m, apogee 1.4 x 107 m, period 10560 s 176 min. 6, ε = .5878, K = 5.2 × 1010, perigee = 4.3 × 106 m (note that this woul not be a practical orbit), apogee 1.65 x 107 m, period 10560 s 176 min. 7. Clue: use Equations (3.45) and (3.50).

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