SPORE Mission Design - Georgia Tech SSDL - Georgia Institute of ...

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⃗⃗⃗ [ ̇ ̇ ̇ ] (29) ⃗ ⃗ (30) Inertial Fixed As seen in Equation 31 and 32, rotate the inertial coordinate system by angle α to transform velocity and position into a fixed coordinate system. The following method was used for PESST to find the atmospheric relative position and velocity. ⃗⃗⃗⃗ [ ] ( ⃗⃗⃗ ̂ ⃗⃗⃗⃗ ) (31) ⃗⃗⃗⃗ [ ] ⃗⃗⃗⃗ (32) The angle α is given by the following equation. Here α 0 is the initial angle between the inertial and fixed x-axes (at time t 0 ), Ω E is the rotation of the earth in degrees per second (~0.0042), and t is the amount of time elapsed in seconds since t 0 . For a start time of 9 Feb 2011 17:00:00.000 UTCG as specified in the STK model, α 0 is equal to 34.294°. The above transformation does not take into account the effects of precession and nutation. Therefore it is not equivalent to the STK transformation. Fixed Inertial Use the transpose of the rotation matrix given in Equation 32 to transfer between fixed and inertial axes. These relations are given in Equation 33 and 34. (16) ⃗⃗⃗⃗ [ ] ⃗⃗⃗⃗ (33) ⃗⃗⃗ [ ] ( ⃗⃗⃗⃗ ̂ ⃗⃗⃗⃗ ) (34) The transformation in Equation 33 and 34 does not take into account the effects of precession and nutation. Therefore it is not equivalent to the STK transformation. 4.2 Baseline Orbital Trajectories The LEO and GTO trajectories can be found in Table 6, Table 7, and
Table 8.The altitude of the LEO trajectory is 600 km to reduce the amount of orbital decay over the mission lifetime and the inclination is 90° to attract potential biological payloads. The GTO trajectory was established from the reference trajectory of the Atlas Launch vehicle. For a GTO trajectory, most launch vehicles do not perform an additional burn to zero the inclination at apoapsis. Therefore the SPORE GTO reference trajectory has an inclination equal to that of Cape Canaveral. Periapsis altitude was established from the Atlas launch vehicle trajectory. Specifications for other launch vehicles were comparable. Table 6: Classical Orbital Elements for LEO and GTO reference orbits. Classical Orbital Elements Units LEO GTO Apogee Altitude (ra) km 600.00 35941.00 Perigee Altitude(rp) km 600.00 167.00 Eccentricity (e) -- 0 0.73 Semi-major Axis (a) km 6978.00 24432.10 Argument of Perigee (ω) deg -- 180.00 RAAN (Ω) deg 0.00 0 Inclination (i) deg 90.00 28.50 True Anomaly (ν) deg -- 0 Argument of Longitude (u) deg 0 -- Table 7: LEO and GTO reference orbits defined in the EME2000 coordinate system. EME2000 Coordinate System Units LEO GTO X (Position) km 6978.00 -6545.10 Y (Position) km 0.00 0.00 Z (Position) km 0.00 0.00 (Velocity) (Velocity) (Velocity) km/s 0.00 0.00 km/s 0.00 -9.03 km/s 7.56 -4.90
Page 1 and 2: SPORE Mission Design Nicole Bauer G
Page 3 and 4: Table of Contents Nomenclature ....
Page 5 and 6: Figure 39: Depicts Meyer’s Theory
Page 7 and 8: Figure 1. Diagram of SPORE design s
Page 9 and 10: Table 2.Mass budget for 1U entry ve
Page 11 and 12: Figure 5. Coordinate system used to
Page 13 and 14: Prime Meridian refers to the line o
Page 15: ̇ ̇ ⃗ (If eZ the ω ) (12) ⃗
Page 19 and 20: Figure 6. Deorbit simulation block
Page 21 and 22: Figure 8.SPORE EDL Sequence of even
Page 23 and 24: Figure 11.GTO 1U trajectory with st
Page 25 and 26: Altitude, km Acceleration, Earth g'
Page 27 and 28: 6 x 106 Stagnation Point Heat Rate
Page 29 and 30: 4.7.2 One variable at a time sensit
Page 31 and 32: Change in Peak Acceleration (Earth
Page 33 and 34: latitude (deg) latitude (deg) Both
Page 35 and 36: (a) (b) Figure 29. (a) 2x2U total a
Page 37 and 38: Number of Cases Number of Cases Geo
Page 39 and 40: 4.8 Parachute Selection To keep the
Page 41 and 42: Table 18. Summary of parameters use
Page 43 and 44: Number of Cases Number of Cases 200
Page 45 and 46: worst case heating trajectory from
Page 47 and 48: References 1. D. A. Spencer and R.

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