Here are some more perceptive questions.
a) A satellite was launched from Earth to Mars. What is the optimal point of interception of the satellite with mars' orbit in relation to where it was originally launched from earth to ensure minimal fuel is required for the journey? (2 marks)
b) A satellite is going to use the slingshot effect to gain maximum speed towards a distant star. At what point within the earth's orbit (see diagram) would it be optimal for the spacecraft to use the slingshot effect, and from what direction should it approach and what direction should it leave to maximise speed (assume the spacecraft can approach from anywhere) (3 marks)
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c) Calculate the centripetal force on a satellite travelling at a velocity of 40km/h and a radius of 3x10^6 km around a planet of mass 5x10^20 kg.