Imagine that someone discovers an alien spaceship in a perfectly circular orbit at exactly 4 AU from our Sun. Now imagine that in response, we scramble to assemble a spaceship of our own in low Earth orbit. Our spaceship has an orbital speed around Earth of about 7 km/s, while Earth is moving around the Sun at about 30 km/s. a. How long does it take the alien spaceship to go around the Sun once? b. Which of the following statements are false, true, or partially true? Explain your answers for all of the following statements. If partially true, correct the statement to be entirely true. i. The most fuel-efficient way to get our spacecraft to rendezvous with the alien spacecraft is to wait until the alien spacecraft and Earth are as close as they get and then blast off in the direction of the alien spacecraft. ii. To get our spacecraft to rendezvous with the alien spacecraft we should use a Hohmann transfer orbit. The aphelion of the Hohmann transfer orbit should correspond to the spacecraft's initial position in LEO at the time of launch. iii. It would take us more than two years to get to the alien spaceship if we followed Hohmann transfer orbit from Earth. iv. Once our spacecraft reaches the position of the alien spacecraft, it does not need to do anything else (e. g. fire thrusters) to complete the rendezvous.