Space Propulsion - IAP/TU Wien

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1 2 3 4 5 6 7 8 9 Evaluate μ = GM Sun Space Propulsion The total energy per mass of the orbit is constant so by evaluating the kinetic and gravitational potentialenergy at one point in the orbit (EQ 10) we obtain The energy per mass of the spacecraft determines the orbits semi-major axis (EQ 11): This then gives the circular velocity of the orbit (EQ 3) The period of the orbit is given by Kepler's third law: The areal velocity is know from the initial conditions (velocity and position) of the spacecraft; α being the angle between radiusvector and S/C direction The other method of determining areal velocity gives us the eccentricity of the orbit, by taking the ellipse area as Aell = πa2(1-e2)1/2 We now know the size and shape of the orbit and can determine the extent of the orbit from (EQ 16) and (EQ 18) The final parameter is the true anomaly as determined by the angle the craft is from perihelion of the new orbit (see ellipse equation in Section 2.3.1) 2 E V GM = − m 2 r GM a = − 2 v c = 3/ 2 ⎛ a ⎞ P = P ⎜ ⎟ earth ⎝ aearth ⎠ 1 A = r . V .sinα 2 A A = P GM a ell sun ( E / m) sun πa = 2 ⎛ AP ⎞ ε = 1 − ⎜ 2 ⎟ ⎝ a π ⎠ r p = a( 1 − ε ) r a = a( 1 + ε ) 2 1− ε P 2 ⎞ ( 1− ε ) − ⎟ ⎠ 1 ⎛ a cos Θ = ⎜ 1 ε ⎝ r 2 sun
Space Propulsion Elliptical orbits passing through same point with identical velocities into different directions
Page 1 and 2: Space Propulsion Pioneer 10 Pioneer
Page 3 and 4: Space Propulsion
Page 5 and 6: 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: Space Propulsion The orbit of a bod
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
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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
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Space Propulsion Kinetics for rotat
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Space Propulsion one - axis maneuvr
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Space Propulsion Example 6: One-Axi
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Space Propulsion Example 7: Precess
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limit cycle cont‘d Space Propulsi
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Space Propulsion Example 8: Limit-C
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Space Propulsion dir. of ext. torqu
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Space Propulsion forced limit cycle
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eaction wheel, cont’d Space Propu
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eaction wheel, cont’d Space Propu
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Space Propulsion - IAP/TU Wien

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