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 08 In a two-body boundary-value problem, the initial and terminal position vectors are: r1 =3 i x and r2 = −4 i x +3 i y The gravitational constant is µ =60. Two orbits connecting r1 and r2 are possible for which the magnitude of the velocity vector is v1 = |v1| =5. For each of these orbits calculate the following quantities: 1. The semimajor axis a 2. The parameter p 3. The transfer time t2 − t1 from r1 to r2 . For the orbit having the shorter transfer time, calculate 4. The velocity vectors v1 and v2 at the terminals. 5. The angular momentum vector h and the eccentricity vector e. 6. The true anomaly f1 of the initial position vector and the eccentric anomaly difference E2 − E1
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