MIT OpenCourseWare http://ocw.mit.edu 16.346 Astrodynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.Exercises 07 A spacecraft is in orbit about a planet whose gravitational constant is µ = 12. At some instant of time, when the vehicle is at the point P1 for which r1 =4 i x , a velocity change ∆v1 is made to place the vehicle in a new orbit to intercept a target at the point P2 for 2which r2 =4 i x +4√3 i y . The velocity at P1 , before the impulse, is v0 = 3 √3 i y . 1. Calculate the elements a, p and h of the orbit before the impulse. 2. Calculate the optimum ∆v1 by first using an appropriate iteration algorithm to obtain the orbital parameter. Then determine the corresponding chordal and extended radial components of the optimum velocity The resulting velocity vector should be v1 = i x + √3 i y 3. Find the new orbital elements. 4. Illustrate the calculations with an appropriate vector
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