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AE313_HW5_S10_interplanet - (in other words how often does...

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Due: Friday, March 12, 2010 Name: Embry-Riddle Aeronautical University AE 313 – Space Mechanics Homework 5 Transfers II – interplanetary general transfer and flyby 1. In the Heliocentric Ecliptic Inertial coordinate system, Earth and Jupiter have the following coordinates at a certain date (day 0): AU R AU R Jupiter Earth = = 0 0 5.2 0 0 1 Assuming Earth and Jupiter are in the ecliptic plane on circular orbits and the parking orbit altitude for the Earth is 300 km. Also using an interplanetary GENERAL transfer with PeriHELION at 1 AU and Apohelion at 6 AU. Given: μ sun = 1.3271E+11 km^3/s^2, μ Jupiter = 1.267E+08 km^3/s^2. a) Draw a diagram of the initial geometry. b) Calculate the semi major axis of the transfer orbit. (ANS: 3.5 AU) c) Calculate the time of flight for the transfer orbit between Earth and Jupiter in TUsun and days (Kepler’s equation). d) What is the synodic period for the Earth-Jupiter system?
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Unformatted text preview: (in other words, how often does this launch opportunity occur) e) How many TUs and Days until the next launch possibility? (Hint: 1 TU = 365 days/2 π ) f) Calculate the probe’s velocity with respect to the planets at Earth and Jupiter, respectively. In AU/TU and km/s g) What is the Δ Vburn starting from the 300 km altitude circular orbit about the Earth to get into this trajectory to Jupiter? (in km/s) h) If the radius of periapse at Jupiter is 200,000 km, what is the eccentricity and turn angle of the hyperbolic orbit at Jupiter? i) Assuming that the flight path angle is INCREASED at Jupiter as a result of the flyby – what is the new Heliocentric velocity and flight path angle of the probe after the Jupiter flyby? j) What are the new values for specific mechanical energy (in AU^2/TU^2) and specific angular momentum (AU^2/TU) values after the Jupiter flyby?...
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