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For hyperbolic and parabolic flybys it's common to take advantage of the Oberth effect and get the most delta-v from a propulsive impulse by doing it at the point of maximum velocity.

Question: But what are all of the other classes of spacecraft maneuvers where the Oberth effect can be used to advantage? Are any of the following situations where the Oberth effect can be used for example, or others I couldn't think of? Or special edge cases?

  • plane changes in elliptical orbits?
  • bi-elliptic transfer orbits? this article might say yes but I can't tell for sure.
  • decelerating (retrograde) burns in parabolic/hyperbolic flybys?
  • capture burns? this answer says yes
  • circularization burns that increase semimajor axis?
  • circularization burns that decrease the semimajor axis?
  • escape-to-infinity from elliptical orbits?
  • something else?
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  • $\begingroup$ I want to wager if a plane is flying evenly, at the top of it's trajectory, such that it maintains altitude, it could be seen as a use of the Oberth effect. It may minimize fuel usage, as you can visualize a sub-orbital trajectory as a trajectory around a point mass :)! I think that may be what pilots do for cruising altitude, keep an even and constant thrust at the "apoapsis" of the trajectory. Let me know if you think that isn't correct. Great question! $\endgroup$ – Magic Octopus Urn Sep 30 at 0:26
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The Oberth effect doesn't give you more delta-V. It gives you a larger change in specific orbital energy for the delta-v you decide to expend because of where you decide to expend it. Spending delta-v in a burn parallel to the direction of your velocity when you're moving fastest gives you the largest change in specific orbital energy.

Specific Orbital Energy (and the gravitational parameter of the object being orbited) determine the semimajor axis of your orbit, as well as your hyperbolic excess velocity so the following cases all derive benefit from taking advantage of the Oberth Effect.

  • bi-elliptic transfer orbits
  • decelerating (retrograde) burns in parabolic/hyperbolic flybys
  • capture burns
  • escape-to-infinity from elliptical orbits

A propulsive orbital plane change does not necessarily have an effect on your specific orbital energy, and vector addition is going to bite into your delta-v reserves painfully if your spacecraft is moving fast when you attempt the plane change, so unless you're using it to assist in a bi-elliptic plane change, the Oberth effect does not help here.

For a circularization burn, you don't really have a choice as to where on your current trajectory you do them; If you're going to do it in a single step, you'll have to do it at the distance where the circular orbit intersects your current orbit. At both such points on a Keplerian orbit, you'll have the same speed, and if neither point is at your periapsis or apoapsis, you have to pay the vector addition price for not burning in your direction of travel.

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    $\begingroup$ Thanks for your answer, it's very helpful! $\endgroup$ – uhoh Oct 1 at 3:13

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