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Chris Bush Week 9: March 22 nd , 2007

Chris Bush Week 9: March 22 nd , 2007. D&C Group High Thrust Trajectories ET, dE, aM, dM, aE. Bush 1. Orbit Diagrams. Earth Taxi (LEO to HEO). HEO to HMO. Bush 2. Final Results. HEO to HMO (Outbound). HMO to HEO (Inbound). Earth Taxi (LEO to HEO). Bush 3. Local Gravity. Bush 4.

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Chris Bush Week 9: March 22 nd , 2007

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  1. Chris BushWeek 9: March 22nd, 2007 D&C GroupHigh Thrust Trajectories ET, dE, aM, dM, aE Bush 1

  2. Orbit Diagrams Earth Taxi (LEO to HEO) HEO to HMO Bush 2

  3. Final Results HEO to HMO (Outbound) HMO to HEO (Inbound) Earth Taxi (LEO to HEO) Bush 3

  4. Local Gravity Bush 4

  5. HEO to HMO (Outbound) • Transfer is constrained by 3 year free return trajectory. • We use 1.5 year free return trajectory that completes 2 orbits. • This orbital period specifies the semi-major axis. • Use Lambert’s equation and iteratively solve for a time of flight that allows the CTV to rendezvous with Mars for a given time of departure from Earth. • Determine the heliocentric velocity of Earth and Mars at the departure and arrival times respectively. • Determine the required deep space maneuver • Determine the required velocity of the transfer orbit at both departure and arrival • Determine v_infinity at both departure and arrival • Determine delta_v for departure and arrival • Iterate this algorithm for various departure dates to find optimal transfer windows Bush 5

  6. HMO to HEO (Inbound) • Same analysis as HEO to HMO except that a free return trajectory is not specified • Semi-major axis is chosen as average of distance of Mars from sun at departure and distance of Earth from sun at arrival. Bush 6

  7. Earth Taxi (LEO to HEO) • We constrain the transfer orbit to a 2 day period and an altitude of periapsis of 250 km. • Period specifies the semi-major axis. • Iteratively solve for an eccentricity that allows the transfer orbit to be tangential to both LEO and HEO. • Subsquently, we calculate the two tangential burns. Bush 7

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