You are part of the trajectory design team for the European Space Agency's up- coming ExoMars...

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You are part of the trajectory design team for the European Space Agency's up- coming ExoMars rover. The spacecraft containing the rover will be placed into an elliptical heliocentric (Sun-centered) orbit with a semi-major axis of 1.3 AU and ec- centricity of 0.5. Mars is on a circular heliocentric orbit with a radius of 1.5 AU. Assume that the orbits of both the spacecraft and Mars lie in the same plane. Also assume that the eccentricity vectors for both orbits are aligned such that the true anomalies for each orbit are referenced to the same location. The diagram below notionally shows the orbit geometries. Desired intercept fi S Mars Spacecraft x Your goal is to make sure that the spacecraft intercepts Mars; when the spacecraft's radial position is equal to 1.5 AU, the spacecraft and Mars should have the same true anomaly. Assume that the spacecraft starts with a true anomaly of zero while Mars starts at a true anomaly of fo. To ensure that the intercept occurs, calculate 1. The true anomaly at intercept, fi. Note that there are two possible true anoma- lies for intercept, choose the value that would occur earlier in time. 2. The initial true anomaly of Mars, fo, which ensures that the spacecraft and Mars arrive at the intercept true anomaly, fi, at the same time. Assume that the gravitational parameter of the Sun is 1.327 1020 m/s. You are part of the trajectory design team for the European Space Agency's up- coming ExoMars rover. The spacecraft containing the rover will be placed into an elliptical heliocentric (Sun-centered) orbit with a semi-major axis of 1.3 AU and ec- centricity of 0.5. Mars is on a circular heliocentric orbit with a radius of 1.5 AU. Assume that the orbits of both the spacecraft and Mars lie in the same plane. Also assume that the eccentricity vectors for both orbits are aligned such that the true anomalies for each orbit are referenced to the same location. The diagram below notionally shows the orbit geometries. Desired intercept fi S Mars Spacecraft x Your goal is to make sure that the spacecraft intercepts Mars; when the spacecraft's radial position is equal to 1.5 AU, the spacecraft and Mars should have the same true anomaly. Assume that the spacecraft starts with a true anomaly of zero while Mars starts at a true anomaly of fo. To ensure that the intercept occurs, calculate 1. The true anomaly at intercept, fi. Note that there are two possible true anoma- lies for intercept, choose the value that would occur earlier in time. 2. The initial true anomaly of Mars, fo, which ensures that the spacecraft and Mars arrive at the intercept true anomaly, fi, at the same time. Assume that the gravitational parameter of the Sun is 1.327 1020 m/s.