Space Propulsion - IAP/TU Wien

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Space Propulsion Example 5: Repositioning Consider a geosynchronous 1t spacecraft that is required to reposition by 2-deg, counter to the velocity vector (westward), in a maneuvering time of one sidereal day (one orbit). What is the fuel consumption for that maneuver, assuming an Isp of 3100 m/s? Δφ S/C moves in reposition ellipse „placeholder“ S/C orbits in GEO example 5, cont‘d
Repositioning, cont‘d Space Propulsion The elements of a geosynchronous orbit are r = 42,164.17 km (circular) P = 86,164.09 s V = 3.07466 km/s ΔP is equal to the time required for 2 deg of motion on a geosynchronous orbit 0 Δϕ 2 *86,164.09 ΔP = P = = 360 360 478.689 [ s] The period for the spacecraft on the elliptical reposition orbit is semimajor axis of the reposition orbit P = 86,164.09 + 478.689 = 86,642.78 [s] 2 2 P μ (86,642.78) (398,600) a = 3 = 3 = 42,320 2 2 4π 4π [ km] velocity at periapsis of an elliptical orbit with semimajor axis a V 2μ μ 2(398,600) 398,600 = − = − 3.08032 r a 42164 42320 = [ km / s] velocity change to place the spacecraft on the reposition ellipse 3.08032km/s - 3.07466km/s = 5.66 m/s The same velocity change (in the opposite direction is necessary for recirculation of repositioning orbit Propellant consumption under assumption of negligible mass change ⎡ ⎛ V ⎞ ⎤ ⎧ ⎡11.32⎤ ⎫ m p m f ⎢exp⎜ Δ = ⎟ −1⎥ = 1000⎨exp −1⎬ = 3.66 I ⎢ sp ⎩ ⎣ 3100 ⎥ ⎢ ⎣ ⎝ ⎠ ⎥⎦ ⎦ ⎭ [ kg]
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Space Propulsion - IAP/TU Wien

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