Assume that these orbital elements remain good for Vesta and for Ceres in the year 2080. Vesta. a = 2.3617272 AU e = 0.08889958 i = 7.14° Ω = 103.8467° ω = 151.1467° T = 2456923.543 Ceres. a = 2.7680973 AU e = 0.07575951 i = 10.5917° Ω = 80.3229° ω = 72.7187° T = 2456552.887 Part A. Prove that a boost-and-coast elliptical transfer orbit having its perihelion at Vesta at the moment of departure—0h UT on 1 June 2080—exists. Part B. Determine 1. The position of the Ceres intercept in heliocentric ecliptic coordinates. 2. The time in transit. 3. The arc of true anomaly from departure to arrival. 4. The Keplerian elements of the transfer orbit. 5. The delta-vees needed for transfer orbit insertion at departure and for velocity matching at arrival.