Orbital transfer From an Elliptical Initial Orbit

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Orbital transfer From an Elliptical Initial
Orbit
Vallado, Chapter 6, Sections 6.3.1, 6.3.2
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QuestionWhere is the most fuelefficient place
to transfer from an initial elliptical orbitto a
final circular orbit?
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Maximum Torque DV
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DV Comparison
Case 1
Case 2
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Burn 1 at Perigee
Final Orbit
Initial Orbit
Transfer Orbit
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Compute DV1
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Semi-Major Axisof transfer orbit
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Substitute and Simplify

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Substitute and Simplify (contd)
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Normalized DV1 Working Formula
Energy (Magnitude) of Initial orbit
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Burn 2 at Apogee
Final Orbit
Initial Orbit
Transfer Orbit
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Compute DV2
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Semi-Major Axisof transfer orbit
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Substitute and Simplify
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Continue Simplifying
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Normalized DV2 Working Formula
Energy (Magnitude) of Initial orbit
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Collected EquationsInitiate Transfer at Perigee
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DV Comparison
Case 1
Case 2
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Burn 1 at Apogee
Initial Orbit
Final Orbit
Transfer Orbit
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Compute DV1 Burn 1 at Apogee
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Normalized DV1 Working Formula
Energy (Magnitude) of Initial orbit
Burn 1 at Apogee
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Burn 2 at Apogee (transfer orbit)
Final Orbit
Initial Orbit
Transfer Orbit
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Compute DV2Burn 2 at Transfer Orbit Apogee
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Semi-Major Axis of transfer orbit
All you need to do is ..
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Normalized DV2 Working Formula
Energy (Magnitude) of Initial orbit
Burn 2 at Perigee
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Collected EquationsInitiate Transfer at Apogee
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Delta-V Plots
Initial
Effect of initial orbit Ellipticity
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Delta-V Plots (contd)
Initial
For this example Final orbit is Circular thus
curves are monotonic
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Rapogee a (1e)
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(No Transcript)
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Delta V ratio 2
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Example Calculation
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Comparative plot
Cheaper To transfer From apogee
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Example Calculation (2)
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Comparative Plot
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Can We Exploit an InitialElliptical parking
Orbitto gain an advantage for transferring to a
Higher Final orbit?
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Same Orbital Energies Different Velocities
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???????????DV gains
Not much too to work with here .
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???????????DV gains
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Determines allowable Eccentricity on orbit For
a given average Altitude Zmin gt 80km
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The Bottom Line
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Something to Think About?
Can we exploit this region To design a transfer
maneuver that is more Efficient than a Hohmann
Transfer?
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Answer Yes! Sometimes?
Next Time .. The Bi-elliptic transfer