Homework

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ORBITAL MECHANICS (M.D. 1st year) Homework-2013/2014 1. A mission to Venus is considered. The Venus orbit around the Sun is supposed to be circular, and to belong to the ecliptic plane. The Earth orbit is assumed to be elliptic, being its eccentricity equal to 0,0167. The apocenter velocity of the heliocentric orbit between Earth and Venus is 26,5573 km/s, while the radial component of the velocity vector at the semi -latus rectum passage is 5,8497 km/s; the transfer occurs on the ecliptic plane; the departure occurs when the eccentric anomaly of the Earth is 182,7146 deg. The spacecraft is injected and left by the launcher on a circular parking orbit, the height of which i s 200km. This parking circular orbit belongs to the ecliptic plane too. The impact parameter for the incoming hyperbola to Venus is requested to be 19255,6466 km. The requested final orbit around Venus is circular, 30 deg inclined with respect to the approaching hyperbola plane. The final orbit is tangent, to the approaching hyperbola pericenter. Answer the followings: /square4 Compute the overall cost for the spacecraft propuls ion unit to bring the spacecraft from the Earth parking orbit to the Venusian final orbit. /square4 Compute the transfer time from the Earth to Venus (heliocentric leg only) /square4 Characterize and depict the Earth outgoing hyperbola and the Venus incoming hyperbola. /square4 If no braking occurs at Venus, identify the kepler ian parameters of the heliocentric orbit gained after the Venus GA. k ⊕ = 3,98 ⋅10 14 m3s-2 R⊕ = 6,378 ⋅10 6 m ksun = 1,327 ⋅10 20 m3s-2 RVenus =0,949 R terra MVenus =0,8149m terra RSun-Venus =0.7233 AU RSun-Earth =1 AU=1.4962*10 11 m 2. From a same location, a difference in the visibilit y period for the two stars, Sirius (Canis Major constellation),…