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Hohmann Transfers and Plane Changes

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.

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Hohmann Transfers and Plane Changes

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  1. Hohmann Transfers and Plane Changes Daniel Rowe

  2. 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

  3. 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.

  4. 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.

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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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