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

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Azimuth (Σ A ) is the angle in the satellite local horizontal plane between the projection of the velocity vector onto this plane and the local north direction measured as positive in the clockwise direction. The local horizontal defined in the BODY FIXED (rotating) coordinate system. Ranges from 0 to 360 degrees. Velocity (V A ) is the magnitude of the BODY FIXED (rotating) velocity vector. This takes into account rotation of the earth relative to the satellite. 4.1.6 Coordinate Frame Transformations Orbital Elements EME2000 The perifocal r and v vectors are calculated from the orbital elements as follows. This transformation is covered in detail in Reference12. ⃗⃗⃗⃗⃗ ( ) [( ) ̂ ( ) ̂] (1) ⃗⃗⃗⃗ √ ( ) [( ) ̂ ( ) ̂] (2) These vectors are transformed to a inertial (EME2000) coordinate system via the following 3-1-3 rotation. This transformation is covered in detail in Reference 12. Where ⃗ [ ( ) ( ) ( )] ⃗⃗⃗⃗⃗ (3) ⃗ [ ( ) ( ) ( )] ⃗⃗⃗⃗ (4) ( ) [ ] (5) ( ) [ ] (6) Inertial (EME2000) Orbital Elements Use the following relationships to transfer an inertial (EME2000) r and v vector into orbital elements. This transformation is covered in detail in Reference 12. ⃗ ⃗ (7) ̂ ⃗ (8) ‖ [( ) ⃗ ( ⃗ ⃗ ) ⃗ ]‖ (9) ( ) (10) ( ) (11)
̇ ̇ ⃗ (If eZ the ω ) (12) ⃗ (If ⃗ ⃗ the υ ) (13) ⃗ ⃗ (If RZ > 0 then u < 180) (14) Cartesian Spherical Coordinates The spherical coordinates (R, θ, φ, V i , Γ i , Σ i ) or (R, λ, δ, V A , Γ A , Σ A ) are related to the Cartesian coordinates (X, Y, Z, ̇ ̇ ̇) in the following manner. To find atmospheric relative spherical coordinates use Fixed Cartesian coordinates. To find inertial relative spherical coordinates use EME2000 Cartesian coordinates. √ (15) (16) t (17) [ ] (18) ⃗ [ ̇ ̇ ̇ ] (19) ⃗ ⃗ [ ̇ ̇ ̇ ] (20) (21) t ̇ (22) Spherical Cartesian Use the following equations to calculate Cartesian coordinates from spherical. To get EME2000 Cartesian coordinates use inertial relative spherical coordinates. To get Fixed Cartesian coordinates use atmospheric relative spherical coordinates. (23) (24) (25) ( ) (26) ( ) (27) ( ) (28)
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: Prime Meridian refers to the line o
Page 17 and 18: Table 8.The altitude of the LEO tra
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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