To save shielding weight on a Mars mission, it is desired to take advantage of the shielding effects provided by the liquid hydrogen fuel tanks with regard to protecting the crew from the gamma radiation emanating from the liquid propulsion system's nuclear reactor. The vehicle configuration is illustrated in the figure below. During engine operation, the liquid hydrogen (saturated at 20K ) in the tank is depleted such that the hydrogen level in the tank decreases at a rate of 2.5(cm/sec). The amount of power produced by the NTR associated with the 6MeV gamma rays is 2kW. Assuming that the reactor can be treated as a point radiation source, determine: - The whole body dose (in Sv) due to 6MeV prompt fission gamma rays received by an astronaut located at the center of the habitat after the engine firing is complete. - A plot of the 6MeV prompt fission gamma ray dose (in Sv) received by the astronaut as a function of time. - The dose (in Sv) due to 6MeV prompt fission gamma rays which the astronaut would have received assuming that the hydrogen provided no shielding. Assume that the astronaut has a mass of 75kg and an effective cross-sectional area of 8000cm2. Also assume the hydrogen in the fuel tank is fully depleted at the end ongine thrusting and that there is no radiation shielding other than the hydrogen in the tank. If any other assumptions are required to solve the problem, they should be clearly stated and justified. Comment on the effectiveness of using the hydrogen tank as a means of reducing the radiation dose to the crew