1. Hohmann Transfers and Plane Changes Daniel Rowe 1

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 2

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. 3

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 r C /r A > 15.58 – If 11.94 < r C /r A < 15.58, the relative efficiency depends on how far out point B is. 4

5. Example: Efficiency Determination 300 km altitude LEO to 35,786 km GEO – r C = 300 + 6,371 = 6,673 km – r A = 35,793 + 6,371 = 42,164 km – r C /r A = 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 5

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 6

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 7

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 8

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12. 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 12

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15. 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.. Analytical Graphics, Inc. Web. 4 Feb. 2011.. 15