296 space vehicle dynamics and control problems 4.2 a spacecraft initially in a 200-km circular parking orbit above th e earth 8 km) is injected into a hohmann heliocentric transfer orbit to med that the motion of mars and the space- craft lie in the ecliptic plane. the radius of the earth's orbit about the sun is r = 1.496 × 108 km (= 1 au) and the radius of the orbit of mars about the sun is r3 = 1.523691 au. the gravitational parameters of the sun and (ro = 637 the outer planet mars. it is assu earth are: μ。= 1.32715 × 1011 krm3/s-and μ㊥ = 3.98601 x 105 km3/s2 (a) estimate the trip time t from the earth to mars along the hohmann transfer orbit. (b) com pute the perihelion velocity vp of the hohmann heliocentric transfer orbit, the earth's velocity vb+ the hyperbolic escape velocity voo/e-and av㊥ required at perigee, also sketch the escape hyperbola by showing the aphelion velocity va of the hohmann heliocentric transfer orbit, the velocity of the target planet mars, denoted as ve, and the required for a soft landing on the target planet mars ,058 km3/s2 and the hyperbolic approach velocity voo/s- (d) compute δ"8 the gravitational parameter of mars is 1 equatorial radius of mars is rⓧ = 3,379 km =43 (e) assuming that the spacecraft is required to approach the taroet n the sunlit side, sketch the approach hyperbola for a b soft landing mission d, va, ve, uoo/b+ δ vo , and ro . y showing o0 , v = 29.784 km/s. uoo/田= 2.945 km/s, up- km/s, v0 = 24.13 km/s, va 259 days, i 1.395 km/s, uc = 7.784 km/s, δ v㊥ = 3.612 = 2 1.48 km/s, uo。/ⓧ = 2.648 km/s, and total av requirement for a soft landing mission s, v km/ to mars is about 9.3 km/s.