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Sale forbidden Orbital Mechanics Course – Exercises Rights reserved M.Lavagna, 2015 1 1. A spacecraft is travelling around the Sun on a clos ed orbit. This heliocentric orbit has its pericente r at the Earth-Sun distance. The transversal velocity at the peri-center is 30,643 km/s. This heliocentric orbit belongs to the ecliptic plane. The presented heliocentric orbit is entered by the spacecraft at its pericenter, thanks to a gravity a ssist manoeuvre around the Moon, which allows to gain suf ficient energy to reach the Earth sphere of influen ce with a velocity larger than zero with respect to ou r planet. For any gravity assist to be considered t he linkedconic approach is applied. The following is requested:
identify the outgoing branch of the hyperbola around the Earth that inserts the spacecraft in the presented heliocentric orbit, in terms of semi-major axis, ec centricity, true anomaly of the asymptote an relati ve velocity at infinitum; the Moon is encountered at this hyperbola pericenter;
compute the keplerian parameters of the gravity ass ist manoeuvre around the Moon that allows the spacecraft to enter the outgoing branch of the hype rbola around the Earth. The minimum height above the Moon surface – experienced by the spacecraft - is 100 km;
Characterize the Earth centred orbit the spacecraft has to be left on by the launcher to correctly cat ch the Moon for the gravity assist manoeuvre, assuming as the reference plane the Earth Equator;
compare, in terms of ∆v, the cost of inserting the spacecraft in the obta ined Moon transfer orbit from a circular parking orbit of 300km height–by Homann transfer – with respect to the direct injection into the heliocentric trajectory from the same circular parking orbit. The gravity assist at the Moon occurs at…