The robotic spacecraft is in a parking Earth orbit at the altitude of h=400. The spacecraft is injected with zero initial path angle into a departure trajectory (like the case of the Hohmann transfer orbit). The spacecraft has a rocket engine with the specific impulse of 300 sec to accomplish the mission. A Vs VEarh T Viars T Fig. | Fig. 2 Fig. 3 Mission Analysis The analysis wants to evaluate the mission parameters lead angle between the Earth and Mars, injection delta-V to the transfer orbit, time of flight, and propellant mass consumption percentage w.r.t. to the initial spacecraft mass, for four scenarios (looking at Fig. 1, where 0 is the true anomaly of the transfer orbit): 1. The spacecraft reaches Mars when 0=180 (Hohmann arrival) 2. The spacecraft reaches Mars when 6=160 3. The spacecraft reaches Mars when 6=140 4. The spacecraft reaches Mars when 6=120 Define z=180- 0, plot the results of the above mission parameters as a function of z. Data Rean :149.6 10 km p Earth: 3.986 10 km/s* Mean Earth radius: 6738 km Rumess: 227.9 10km p Sun: 132.712 10 km''/s' a) What is the change in percentage of the injection delta-V and propellant mass consumption w.r.t. the Hohmann transfer in the case of minimum time of flight? b) Fig. 2: Which is the direction (w.r.t. the Earth velocity) of V. of the departure trajectory? Why? ) Fig. 3: Which is the direction (w.r.t. the Mars velocity) of the V= of the arrival trajectory? Why