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Hohmann Transfers and Plane Changes. Daniel Rowe. Hohmann Transfer. In its simplest form, a Hohmann transfer is an elliptical orbit used to transfer between two circular orbits. Most energy efficient transfer technique for the majority of transfer orbit cases. Elliptical Starting Orbits. - PowerPoint PPT Presentation
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Hohmann Transfers and Plane Changes
Daniel Rowe
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Hohmann Transfer
• In its simplest form, a Hohmann transfer is an elliptical orbit used to transfer between two circular orbits.– Most energy efficient
transfer technique for the majority of transfer orbit cases
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Elliptical Starting Orbits
• The most efficient transfer is from perigee A of orbit 1, regardless of whether B or B’ is apogee of orbit 2.
• If orbit 1 is a circle, the target point should be the apogee of orbit 2.
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Bi-Elliptic Transfers
• More efficient than Hohmann transfers when transferring from a very low orbit to a very high orbit– More efficient than
Hohmann if rC/rA > 15.58– If 11.94 < rC/rA < 15.58,
the relative efficiency depends on how far out point B is.
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Example: Efficiency Determination
• 300 km altitude LEO to 35,786 km GEO– rC= 300 + 6,371 = 6,673 km– rA= 35,793 + 6,371 = 42,164 km– rC/rA= 42,164/6,673 = 6.32<11.94• Hohmann transfer is more efficient
• To reach a ratio of 15.58 from a 300 km LEO altitude, one must travel to a radius of 103,965 km
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Important Orbital Parameters
• For the purposes of this tutorial, the most important orbital parameter for every orbit, is Velocity
• For a circular orbit • For an elliptic orbit– Where h is the angular momentum specific to
your orbit can be solved from the formula
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Important Orbital Parameters Cont
• Using the above equations, it is a simple matter to find the ΔV requirement for your entire mission– Simply find the differences between the circular
orbits’ velocities (1 and 3) and the velocity at periapsis and velocity at apoapsis of your elliptic orbit (2)
– Total ΔV is found by adding these two differences
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Simple Plane Changes
• It can be shown that for a plane change accompanied by a speed change
• Without any change in speed, this reduces to
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Simple Plane Changes
• It can be shown that for a plane change accompanied by a speed change
• Without any change in speed, this reduces to
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References
• Curtis, Howard D. Orbital Mechanics for Engineering Students. 1st ed. Amsterdam [u.a.: Elsevier/Butterworth-Heinemann, 2006. Print.
• Tran, Peter. STK for Dummies. Jan.-Feb. 2011. Raw data. Pomona, CA.
• The Astrogator’s Guild. Web. 23 Jan. 2011. <http://www.astrogatorsguild.com/>.
• Analytical Graphics, Inc. Web. 4 Feb. 2011. <http://www.agi.com/default.aspx>.
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