The planet Mars has a mass of 6.4 × 10²³ kg and a diameter of 6790 km.

a i. Calculate the acceleration due to gravity at the planet’s surface.

ii. Calculate the gravitational potential at the surface of the planet.

b. A rocket is to return some samples of Martian material to Earth. Write down how much energy each kilogram of matter must be given to escape completely from Mars’ gravitational field.

c. Use your answer to part b to show that the minimum speed that the rocket must reach to escape from the gravitational field is 5000 m s⁻¹.

d. Suggest why it has been proposed that, for a successful mission to Mars, the craft that takes the astronauts to Mars will be assembled at a space station in Earth orbit and launched from there, rather than from the Earth’s surface.