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The mission is to send a probe from the Earth to Jupiter

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The mission is to send a probe from the Earth to Jupiter. The probe will hitch a ride as secondary payload on a large rocket. The primary payload is a large GEO satellite going to a geostationary orbit. Hence there are two payloads, the large GEO satellite and the probe. The large GEO satellite and probe will first be launched into a 375 km LEO equatorial circular parking. The large GEO satellite will then be boosted via a minimum energy Hohmann transfer ellipse to a geostationary orbit. You have been tasked to come up with a mission plan for the Jupiter probe. Your goal is to calculate the initial and final portion of a Venus-Earth-Earth Gravity Assist (VEEGA) trajectory to Jupiter. 1. (about 24 calculations) For the Phase I departure from the Earth, investigate four different departure options. For all four options assume that the probe's velocity "at infinity" with respect to Earth, V,o , equals 3,600 m/s: - a. Velocity change required if the probe fires its own motor to complete an Oberth escape from the 375 km circular parking orbit, A Vh„,,sips,„ = - b. Velocity change required if the probe hitches a ride to geostationary orbit with the GEO satellite and then the probe fires its own motor to complete an Oberth escape from the geostationary orbit, A I/bum/probe = - c. Velocity change required if the probe detaches from the GEO satellite immediately after the first transfer burn to geostationary orbit and then the probe's motor immediately fires thereafter to complete an Oberth escape. Assume no altitude change occurs during this maneuver and the probe detaches at the LEO altitude, A ithoost probe= For this hyperbolic escape trajectory also find the: Planetocentric Velocity at perigee after the probe has completed its bunt, Vp= ? Velocity change contribution provided by the large rocket's upper stage as it goes from the 375 km parking orbit onto the GTO trajectory, A Vbause_rock,,= ? Eccentricity of the Oberth escape, e= ? Location of perigee of the hyperbolic escape trajectory with respect to Earth's heliocentric orbital velocity vector, 1/20 = - d. The probe first hitches a ride to geostationary orbit. It then retrograde fires its motors to enter a 375 km perigee ellipse around the earth and at perigee it then fires its motors again to complete an Oberth escape, A 140.1 probe = 2. (about 16 calculations) For the Phase II cruise from Earth to Venus assume that the probe's heliocentric intersection angle, Q„, with respect to the Sun as it departs Earth on its heliocentric elliptic fast transfer trajectory equals 0 degrees. For the fast transfer ellipse from Earth to Venus (using V„,= 3,600 m/s with respect to Earth) find the heliocentric: Eccentricity, e= Perihelion, rp = Aphelion, r„ = Position angle where the fast transfer trajectory crosses Venus orbit, v = ? Time of flight from Earth to Venus, TOF = 3. (about 15 calculations) Assume the Venus gravity assist flyby occurs at a periapsis height, lif„ of 350 km above Venus's planetary surface. For the gravity assist flyby with Venus, find: ? Probes heliocentric velocity with respect to the Sun as it arrives to Venus, Vi= ? Probes heliocentric intersection angle with respect to the Sun as it arrives to Venus, A= • Probes velocity "at infinity" with respect to Venus as the probe enters Venus SOI, Vim= • Planetocentric hyperbolic flyby trajectory eccentricity, c= - Incoming angle, 4; , between the planetary velocity, V pi, and incoming V*

Turning angle, 1) — Direction of flyby Outgoing angle, 4, , between the planetary velocity, VII , and the outgoing 117 c — Outgoing heliocentric velocity, K, — Probes velocity "at infinity" with respect to Venus as the probe leaves Venus SO1, Kti= Heliocentric elevation angle as the probe leaves the SOI of Venus, fla — Approach distance, d = 
4. (about 2 1 calculations) Now let's skip to the Phase III arrival at Jupiter. Assume that the probe arrives with a V (at Jupiter's SOI) of 7,000 m/s and with a heliocentric intersection angle, , of 0 deg. Also assume an elliptical parking orbit about Jupiter with an orbit period of 48 hours. Select a periapsis altitude such that 20% of Jupiter's surface is visible in the satellite's field of view (E V). For the probe find the planetocentS: 
a-
Velocity at perigee of the incoming hyperbolic trajectory, 11„,— Eccentricity of the incoming hyperbolic trajectory, e Location of perigee of the arrival trajectory with respect to Jupiter's heliocentric orbital velocity vector, v = Velocity change required to enter the elliptical parking orbit around Jupiter, A r„.„,„ = The height of the periapsis of the parking orbit, h,,= The height of the apoapsis of the parking orbit, h„= 
5. (33 specific items to plot) Plot the following trajectories. There should be four separate plots. There are templates on Canvas that may be used, Scale the velocity vectors relative to the planet's velocity vector, see example on Canvas. Use a protractor to draw the angles accurately. Use a ruler to plot vector lengths accurately. Plot and label the following: 
a. For the Phase I departure from the Earth plot the following for option (c): Vpiano ,