(f) (g) (h) (i) (j) The perigee point of the Molniya 1-44 orbit was at an altitude of 550 km measured from the surface of the Earth. The orbital period of the satellites was set to be half a sidereal day which is 11.963 hours. The radius of the Earth can be taken as 6371 km. You may assume that the Earth can be treated as a uniform spherical mass. (a) (b) (c) (d) (e) Structural mass kg What is the apogee altitude of the Molniya 1-44 (i.e., the height above the Earth's surface)? What is the eccentricity of the orbit? What is the ratio of the speed at perigee to the speed at apogee? Suppose the the Molniya satellite is given a burn at perigee to move it from its high elliptical orbit to a circular orbit that maintains the perigee altitude above the Earth's surface. What reverse burn is required? What is the period of the new orbit? What is meant by a 'tundra orbit'? Stage Boosters 3770 (each) Stage 1 Stage 2 Stage 3 1160 6798 1976 Table 2.1 Total mass Specific kg 43400 100600 24800 6660 apogee Earth The Molniya 8K78M rocket has a specification similar to the rocket described by Table 2.1. There are four strap-on boosters. The payload is 2000 kg. Note that the table provides structural mass and total mass so you will have to work out the propellant mass from these two quantities. 310 Burn Impulse s time s 315 330 340 120 291 241 250 Find the structural ratios of the Stages 1, 2 and 3. Find the payload fraction of Stage 2. What are the relative thrusts provided by the boosters and the stage 1 rocket when the rocket takes off? What is the speed of the rocket when the four boosters are exhausted? How would your answer to (h) change if the main engine in Stage 1 was found to be defective and failed to fire, leaving just the boosters to provide thrust? perigee In another scenario, engineers work on communication with the defective Stage 1 and manage to start the motors 20 seconds after launch. What would your answer to (h) be now? Total 30 marks 2 marks 1 mark 2 marks 5 marks 2 marks 3 marks 3 marks 5 marks 3 marks 4 marks