Question

A spacecraft has position coordinates x Earth-Moon frame, and speed v- 7.2 km/s. 3. 6500 km, y 4700 km relative to the rotating a. Find the value of the Jacobi constant for the spacecraft. b. Does the spacecraft have enou gh energy to escape the Earth-Moon system?

Answer 1

(a) by taking reference from zero - velocity curve v^2 = 2 phi - c > 0 where c - Jacobi constant v - speed = 7.2 k m/s phi = squareroot (6500)^2 + (4700)^2 (7.2)^2 = 2 squareroot (6500)^2 + (4700)^2 - c c = 2(squareroot (6500)^2 + (4700)^2 - (7.2)^2 = 2(8021.22) - 51.84 = 15,990.60 Jacobi Constant, C = 15,990.60

(a) Jacobi Constant, C = 15,990.60