1) Liquid Rocket Design: An orbital insertion maneuver requires a AV of 4000 m/s. Assume the spacecraft dry mass without a propellant tank is 350 kg, and the liquid propellant has a density of 60 kg/m. Perform a mission analysis by answering the following questions. Provide your answers in an Excel spreadsheet. Highlight the answers and turn in a printout of your spreadsheet. Make sure to write the equations for your calculations in a separate column next to your solutions. See example on CCLE. a. Find an expression for the thickness of a spherical tank in terms of the tank radius needed for hoop loads. In your Excel spreadsheet, use a factor of safety of 1.25 for this thickness. Use this result to determine the mass of the fuel tank and propellant required for the maneuver using a liquid chemical system with Isp of 320 s and thrust of 26.7 kN. Assume the fuel tank is made with aluminum (PAI = 2700 kg/m & oy = 275 MPa), and the tank pressure is 530 kPa. Note: include the thrust in your force balance equation b. You are approached by a manufacturer that says they can outfit your liquid prop system with a new nozzle that will increase the Thrust Coefficient by 3%. Assume Pc, At are the same. Calculate the % benefit in propellant mass this nozzle provides. Do you recommend using this system? Clearly explain, why or why not.