Question

PROBLEM 12.89 A space shuttle S and a se A are in the circular orbits shown. In order for the shuttle to recover the satellite, the shuttle is first placed in an elliptic path BC by increasing its speed by Av 84 m/s as it passes through B. As the shuttle approaches C, its speed is increased by Δ1C = 78 m/s to insert it into a second elliptic transfer orbit CD. Knowing that the distance from O to C is 6860 km, determine the mount by which the speed of the shuttle should be increased as it approaches D to insert it into the circular orbit of the satellite. 610 km

Answer 1

Radius of Earth is, RE 6371 km We have ,-RE +610 km-6371 km +610 km-6981 km 's-RE +290 km-6371 km + 290 km-6661 km The gravitational force is balanced with the centripetal force Grai GMm m 7 7 GM 7 7 ow. gR (%)m" (9.81ms*)(6371x103 m)2 (V4ct-7552.37 m/s 6981 km Actcie And gR 2 (9.81 m/s)6371x103 m 6981 km Vact-7731.65 m/s Therefore, the required speed of shuttle is, 7731.65 m/s +84 km