Space Propulsion - IAP/TU Wien

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Simplified equations for external torques Space Propulsion Disturbance Type Influenced primarily by Formula Gravity gradient Constant or cyclic, depending on vehicle orientation Spacecraft geometry, Orbit altitude 3μ Tg = I z − I y Θ ~ 4x10 -5 [Nm] 3 r where T g is the max gravity torque; µ is the Earth's gravity constant (398,600 km 3 Is 2 ), r the orbit radius, Θ the max deviation of the z axis from vertical in radians;I z and I y are moments of inertia about z and y (or x, if smaller) axes. Solar radiation Constant force but cyclic on Earth-oriented vehicles Spacecraft geometry, Spacecraft surface area The worst-case solar radiation torque T sp = P A L ( 1 + q ) cos i s s s ~ 7x10 -7 [Nm] is due to a specularly reflective surface, where P S is the solar constant, 4.617 x 10 -6 N/m 2 ; A s is the area of the surface, L s the center of pressure to center of mass offset, i the angle of incidence of the sun, and q the reflectance factor that ranges from 0 to 1; q = 0.6 is a good estimate Magnetic field Cyclic Orbit altitude, Residual spacecraft magnetic dipole, Orbit inclination T m = DB where T m is the magnetic torque on the spacecraft, D the residual dipole moment of the vehicle in A.m 2 , and B the Earth's magnetic field in Tesla. B can he approximated as2M/r 3 for a polar orbit to half that at the equator. M is the magnetic moment, 8 x 10 25 emu at Earth, and r is radius from dipole (Earth) center to spacecraft in centimeters Aerodynamic Constant for Earth-oriented vehicle in circular orbit Orbit altitude, Spacecraft configuration T ∑ a = F i L i T a is the summation of the forces F i on each of the exposed surface areas times the moment arm L i to the center of each surface to the center of mass, where F = ρC d AV 2 /2 with F the force, C d the drag coefficient (usually between 2.0 and 2.5), p the atmospheric density, A the surface area, and V the spacecraft velocity.
Space Propulsion dir. of ext. torque one-sided limit cycle with an external torque on the spacecraft, rotation occurs until a limit line is reached and a thruster pair is fired for correction total angular momentum H supplied by the propulsion system exactly equals the momentum induced by the external torque T x during mission time t m ; F is time – averaged thrust H = T t = x m Ft m propellant mass required to compensate for the external torque nF I nFL m p = tm = tm = sp LI sp T LI x sp t m cont‘d
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Space Propulsion Pioneer 10 Pioneer
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Space Propulsion
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Space Propulsion Every particle of
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Space Propulsion Circular orbit mV
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Space Propulsion 5 3.98x10 V orb
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Space Propulsion Gravitational traj
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Space Propulsion Gravitational traj
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Space Propulsion dA 2 2 P = abπ =
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Space Propulsion The orbit of a bod
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Space Propulsion Elliptical orbits
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Space Propulsion Tsiolkovsky equati
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Space Propulsion Total impulse Tota
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Space Propulsion jet power definiti
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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 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:
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Page 49 and 50: Space Propulsion vectorial velocity
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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
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Page 67 and 68: Space Propulsion Attitude control t
Page 69 and 70: Space Propulsion Kinetics for rotat
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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
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Page 83 and 84: Space Propulsion forced limit cycle
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Space Propulsion - IAP/TU Wien

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