One trajectory that can be used to send spacecraft from the Earth to Mars is an elliptical orbit that has the Sun at one focus, its perihelion at the Earth and its aphelion at Mars. The spacecraft is launched from the Earth and coasts along this ellipse until it reaches Mars, when a rocket is fired to either put the spacecraft in orbit around Mars or cause it to land on Mars. (a) Find the Semi-major axis of the ellipse. (Hint: Draw a picture showing the Sun and the orbits of the Earth, Mars and the spacecraft. Treat the orbits of Earth and Mars as circles.) (b) Calculate how long (in days) such a one-way trip to Mars would take.