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Space Propulsion Fuel consumption for orbital maneuvre with total velocity change ΔV Tsiolkovsky: m / m i f = e ΔV Isp required fuel mass: m p = m i − m f = m i ⎡ ⎛ ⎢1 − exp⎜− ⎢ ⎣ ⎝ ΔV I sp ⎞⎤ ⎟ ⎥ ⎠⎥⎦ m p ⎡ ⎛ ⎞ ⎤ ⎢ ⎜ ΔV = m ⎟ f exp −1⎥ ⎢ ⎣ ⎝ I sp ⎠ ⎥⎦
Space Propulsion Example 1: Simple Coplanar Orbit Change Consider an initially circular low Earth orbit at 300-km altitude. What velocity increase would be required to produce an elliptical orbit 300 x 3000 km in altitude? What would be the fuel consumption for a 750 kg (empty) S/C if I sp = 3100 m/s ? The gravity parameter of Earth is μ=398,600.4 km 3 /s 2 Radius of Earth is ≈ R = 6387 km velocity on initial circular orbit: semimajor axis of final elliptical orbit: V 398,600.4 = μ = = 7.726 km s r (300 + 6378.14) / ra + rp a = 2 (300+ 6378) + (3000+ 6378) = = 8028 2 [ km] velocity at periapsis of final orbit: velocity change = V 2μ μ 2(398,600) 398,600 = − = − = 8.350 km s p r a 6678 8028 / ΔV = Vp −V = 8 .350 − 7.726 = 0.624 km / s fuel consumption ⎡ ⎛ V ⎞ ⎤ ⎧ ⎡ (624) ⎤ ⎫ mp m f ⎢exp ⎜ Δ = ⎟ −1⎥ = 750⎨exp −1⎬ = 167. 2 I ⎢ sp ⎩ (3100) ⎥ ⎢ ⎣ ⎝ ⎠ ⎥⎦ ⎣ ⎦ ⎭ kg Velocity changes, made at periapsis, change apoapsis radius but not periapsis radius, and vice versa; the radius at which the velocity is changed remains unchanged. As you would expect, the plane of the orbit in inertial space does not change as velocity along the orbit is changed. Orbital changes are a reversible process.
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Page 9 and 10: Space Propulsion 5 3.98x10 V orb
Page 11 and 12: Space Propulsion Gravitational traj
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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 .
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Page 35: Space Propulsion coplanar orbit cha
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
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Page 53 and 54: Space Propulsion CASSINI probe to S
Page 55 and 56: Space Propulsion Liftoff from groun
Page 57 and 58: Space Propulsion Spiraling up dv dt
Page 59 and 60: Space Propulsion Spiraling up time
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
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eaction wheel, cont’d Space Propu
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Space Propulsion - IAP/TU Wien

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