You are planing a mission to Mars. You want to send a 3-ton spacecraft there (3 tons wet mass, it is the initial mass of the spacecraft). As all the engineers working for you are calling in sick, you will have to design the mission yourself. To assess the amount of fuel required to leave the Earth, you first need to compute the different Avs: 1- What is the excess velocity required v (in km/s) when leaving the Earth to reach Mars orbit, assuming a Hohmann transfer trajectory? 2- What Av should be provided to your spacecraft to leave from a 500 km low-Earth orbit (in km/s)? 3- Your spacecraft has an engine that uses a fuel providing a specific impulse of 350s. How much propellant will be required to acheive the Av computed above? (give your answer in kg) Instead of doing the above Av and spending a significant part of your mass on propellant, you decide to use the space elevator that a colleague of yours just designed. It allows to bring payloads up to an altitude of 55'000km. 4- At what altitude should be the center of mass of the elevator system (as always, assume that center of mass = center of gravity)?