Answer all questions in the field provided. Scientific notation, if required, can be indicated either by using E-notation or the power symbol (i.e. 5.2 x 1012 = 5.2E12 = 5.2 x 10^12). You will need to (a) give a numerical answer and (b) explain briefly in words or mathematical workings how you obtained your answer for EACH question.
Stay on Target!
Question 1 During one of its orbits around Saturn, star-tracker images detect that the Cassini spacecraft is drifting slowly off-course. In order to keep the spacecraft on-course to intercept Titan, engineers at the Jet Propulsion Laboratory on Earth determine that a short burn from Cassini’s 445 N thruster is required. How long will the thruster need to be fired if Cassini masses 2523 kg and 0.500 ms-1 ()fatly is required for the course correction? Note that the burn is expected to be short enough that the spacecraft’s mass will not change appreciably. (HINT: recall our equation linking Force, burn time and momentum changes)
A New Propulsion Method
Now that Cassini is running low on fuel, the spacecraft is being targeted for disposal in the upper atmosphere of Saturn. The design of the spacecraft left enough fuel in the tank at Saturn for 500 ms-1 of adv to maintain its orbit. Let’s explore how electric propulsion could have changed this mission.
Question 2 First, let us consider the case if Cassini were carrying conventional chemical rockets. These rockets, at best, have an exhaust velocity (speed at which the propellant moves) of 3500 ms-1. Using our equation for conservation of momentum and assuming that the velocity change is all achieved in a single instantaneous burn (i.e. don’t use the Tsiolkovsky Rocket Equation) how much fuel would be needed to provide the 500 ms-1 ()fatly given that Cassini masses 2523 kg?
Question 3 Repeat your calculation from Question 2 calculating how much fuel would be needed to provide the 500 ms-1 ()fatly given that Cassini masses 2523 kg, but this time assume that Cassini is equipped with an ion engine which boasts an exhaust velocity of 30,000 ms-1. In your description, state whether an ion-equipped spacecraft would be capable of doing more science than a similarly equipped chemical-rocket spacecraft.
BONUS – for an additional 0.5 marks, determine the fuel masses in Questions 2 and 3 using the Tsiolkovsky Rocket Equation which recognizes that the propellant is exhausted as a continuous stream, and therefore the propellant exhausted early in the process needs to accelerate both the remaining propellant and the spacecraft.
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