An interplanetary spacecraft is sent on a Mars flyby mission using a heliocentric Hohmann Transfer from...

 

 

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An interplanetary spacecraft is sent on a Mars flyby mission using a heliocentric Hohmann Transfer from Earth. During Mars approach, the spacecraft passes on the sunlit side of the planet (i.e., between Mars and the Sun). The radius of closest approach at Mars is 4000 km. You may assume that Earth and Mars are in coplanar, circular orbits around Sun with radii of 149.5106 km and 227.8106 km, respectively. The value of the gravitational parameter for Mars is m-43050 km/s. 1. Find the semi-major axis and eccentricity of the resulting heliocentric orbit after flyby. 2. Find the true anomaly of the heliocentric orbit just after flyby. How much and in what direction has the heliocentric line of apsides (line joining periapsis and apoapsis) been rotated as a result of the flyby? 3. How long will it take for the spacecraft to cross Mars' orbital radius again? An interplanetary spacecraft is sent on a Mars flyby mission using a heliocentric Hohmann Transfer from Earth. During Mars approach, the spacecraft passes on the sunlit side of the planet (i.e., between Mars and the Sun). The radius of closest approach at Mars is 4000 km. You may assume that Earth and Mars are in coplanar, circular orbits around Sun with radii of 149.5106 km and 227.8106 km, respectively. The value of the gravitational parameter for Mars is m-43050 km/s. 1. Find the semi-major axis and eccentricity of the resulting heliocentric orbit after flyby. 2. Find the true anomaly of the heliocentric orbit just after flyby. How much and in what direction has the heliocentric line of apsides (line joining periapsis and apoapsis) been rotated as a result of the flyby? 3. How long will it take for the spacecraft to cross Mars' orbital radius again?