8. SpaceX has proposed a vehicle capable of an 80-day transit from Earth to Mars. The return trip is questionable. Recall that a Hohmann transfer requires 0.709 year, or 259 days. a) What AV is necessary to leave the orbit of the Earth about the Sun for this fast elliptic transfer? How does this fast elliptic AV compare to the first Hohmann AV? b) If the spacecraft is initially in a 200 km circular orbit about the Earth, what departure AV is required for injection directly into the 80-day fast elliptic transfer? What mass ratio is required for this AV burn, assuming a liquid methane/LOX rocket Isp of 380 seconds? c) What is the relative velocity difference between the spacecraft and Mars at arrival? How does this AV compare to the second Hohmann AV?