Space Propulsion - IAP/TU Wien

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Space Propulsion Spiraling up dε = dt T v m = T v m at every moment, trajectories closely resemble circles (acc. to assumption T 0) v ≅ μ r ε ≅ − μ 2r ε = − μ 2a dε dt dε dr = + dr dt = 2 μ dr 2r dt = T v m ≈ μ T r m ΔV = t ∫ t0 T m dt = r ∫ μ dr 2 r = − μ. 3/ 2 r0 r r 0 0 1 r = μ − r μ r Δ V = v c , 0 − v c , r thrusting ΔV is equal to difference of velocities in initial and final orbit
Space Propulsion Spiraling up time required to spiral up from r 0 to r assumption: T = const. • m = T / I dm/dt = const. • ( ) sp m = m0 − m t − t 0 ΔV = t ∫ t0 T m dt = T m 0 t ∫ t0 m 1− m dt • ( t − t0 ) 0 ⎡ T ⎢ m = − ln 1− • m ⎢ m0 ⎣ ⎤ • ( t − t0 ) ⎥ ⎥ ⎦ Δ V = μ − r 0 μ = r μ ⎛ ⎜1 − r 0 ⎝ r 0 r ⎞ ⎟ ⎠ τ = t − t 0 = m • ⎤⎫ μ ⎞ ⎟ m ⎥⎪ ⎠ ⎦⎪ ⎭ 0 sp 1 exp m • ⎨ − − ⎬ = 0 − ⎢ ⎜ − r0 r ⎟ T ⎥ T m ⎧ ⎪ ⎪ ⎩ ⎡ ⎢ ⎣ ⎛ ⎜ ⎝ μ I −( vc,0 −vc,1 )/ Isp [ 1 e ]
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Space Propulsion Pioneer 10 Pioneer
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Space Propulsion
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Space Propulsion Every particle of
Page 7 and 8: Space Propulsion Circular orbit mV
Page 9 and 10: Space Propulsion 5 3.98x10 V orb
Page 11 and 12: Space Propulsion Gravitational traj
Page 13 and 14: Space Propulsion Gravitational traj
Page 15 and 16: Space Propulsion dA 2 2 P = abπ =
Page 17 and 18: Space Propulsion The orbit of a bod
Page 19 and 20: Space Propulsion Elliptical orbits
Page 21 and 22: Space Propulsion Tsiolkovsky equati
Page 23 and 24: Space Propulsion Total impulse Tota
Page 25 and 26: Space Propulsion jet power definiti
Page 27 and 28: Space Propulsion these purely mecha
Page 29 and 30: Space Propulsion The staging princi
Page 31 and 32: Space Propulsion m i = ρmL + ψ .
Page 33 and 34: Space Propulsion Check for tankage
Page 35 and 36: Space Propulsion coplanar orbit cha
Page 37 and 38: Space Propulsion Example 1: Simple
Page 39 and 40: Space Propulsion Hohmann transfer:
Page 41 and 42: Space Propulsion Velocity increase
Page 43 and 44: Space Propulsion Combined maneuver:
Page 45 and 46: Repositioning, cont‘d Space Propu
Page 47 and 48: Space Propulsion Basically a 3 - bo
Page 49 and 50: Space Propulsion vectorial velocity
Page 51 and 52: Space Propulsion
Page 53 and 54: Space Propulsion CASSINI probe to S
Page 55 and 56: Space Propulsion Liftoff from groun
Page 57: Space Propulsion Spiraling up dv dt
Page 61 and 62: Space Propulsion Comparison of Hohm
Page 63 and 64: Space Propulsion Attitude maneuvres
Page 65 and 66: Space Propulsion Thruster combinati
Page 67 and 68: Space Propulsion Attitude control t
Page 69 and 70: Space Propulsion Kinetics for rotat
Page 71 and 72: Space Propulsion one - axis maneuvr
Page 73 and 74: Space Propulsion Example 6: One-Axi
Page 75 and 76: Space Propulsion Example 7: Precess
Page 77 and 78: limit cycle cont‘d Space Propulsi
Page 79 and 80: Space Propulsion Example 8: Limit-C
Page 81 and 82: Space Propulsion dir. of ext. torqu
Page 83 and 84: Space Propulsion forced limit cycle
Page 85 and 86: eaction wheel, cont’d Space Propu
Page 87: eaction wheel, cont’d Space Propu
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Space Propulsion - IAP/TU Wien

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