Do "partial" Hohmann transfers exist?

I'm doing some research for fiction writing, and I would like to have my plot points comply with known science whenever possible.

Regarding orbital transfers, I know that the fastest way from orbit A to orbit B (provided unlimited delta-V) is practically a straight line, and that the transfer using the least amount of energy is a Hohmann transfer.

I'm wondering about possible in-between transfers, provided a high amount (but finite) of delta-V is available. Could a "half Hohmann" transfer exist, traversing just 90º around the primary? A quarter Hohmann, etc.? Do they have a name? The story I'm writing would ideally have a continuum of orbit transfers, trading speed for energy expenditure.

Is there any open-source or freely online tool to calculate and simulate such transfers?

• "The transfer using the least amount of energy is a Hohmann transfer" This statement is not true. Hohmann transfer's are optimal at certain orbital radii ratios. At large ratios, bi-elliptic transfers may prove to be more optimal from a fuel-expenditure standpoint. Aug 18, 2019 at 20:08
• Thanks for the clarification, @aaastro. I come from a computer science background, and I'm a bit at a loss here :) Aug 19, 2019 at 7:17
• There are infinite numbers of possible transfer between the Hohmann and the straight line, with the straighter transfers using more fuel and less time. Aug 19, 2019 at 12:55
• To further the point by @aaastro, no one has yet found a proof of an optimal transfer given arbitrary start/end orbits. Only for the specific scenario where the orbits are co-planar and within a certain ratio of their radii has it been proven. Aug 19, 2019 at 21:47
• Hi Pablo, sounds quite interesting. A good point to note would be the type of propulsion you use. If you're setting has an ion engine, which have low thrust and impulsive maneuvers are thus rendered weak, then constant thrust maneuvers are the analog and in cases might be more optimal than impulsive transfers subject to efficiency (Isp) due to chemical rocket engines. Look up constant thrust maneuvers for more insight. Aug 22, 2019 at 12:55

Yes this is absolutely a thing. Delta-V can indeed be traded off in a continuous fashion for total flight time (i.e. uses more dV, but lowers transfer times, relative to a Hohmann transfer). Furthermore it's pretty directly analogous to a Hohmann transfer.

I don't know a name for this but the heavily simplified version of this 'partial Hohmann' transfer is as follows:

An impulse pushing a craft in the direction it is travelling raises the other side of the orbit. A Hohmann transfer makes it so this new raised point just clips the orbit of the body you are trying to reach (and then there is another burn to match speed at that intersection). However, if you burn harder, there will still be an intersection and a closer one. It takes more dV for both the initial maneuver and the speed match.

There is indeed literature to discuss this but most it's not usually relevant, for a number of reasons:

• If you are going far gravity assists become the more important time vs dV trade-off.

• dV is very expensive and (for unmanned missions) time spent waiting is relatively inexpensive. However, manned Mars missions are an exception, where this trade-off is directly discussed (though less about the orbital mechanics and more about the cost vs ethics of irradiating astronauts).

Bi-elliptic transfers are also a good example. In some cases they use less dV, but they take longer. This is not a continuum though.

Its worth noting all of this only really applies to journey time, if you are free to choose when to set off. Not "If I set of now, how quickly can I get there?". Launch windows are different, but still apply.

There is still a trade-off that can be made in flight, but this is not really analogous to a Hohmann transfer, and involves a highly inefficient radial burn. This you will likely not see discussed much as it's highly inefficient, and waiting for a launch is basically free.

Good luck with the book, let me know if you want me to elaborate anything further.

• Its probably of note that time spent waiting becomes more critical when in extreme temperature swings. Aug 23, 2019 at 19:43

ANone's answer address how delta-V and trip time trade off with each other, and what to consider when designing a mission.

The other part of the question:

Is there any open-source or freely online tool to calculate and simulate such transfers?

Yes! They are called Lambert solvers. They plot a 3-D graph of delta-V versus trip time and departure date based on starting and ending planets. You can find the delta-V for any trip time you wish, but watch out! Some departure dates can lead to terrible delta-V for a given trip time. I don't know specifically about good solvers for use with our solar system, but here are a couple for Kerbal Space Program that can be modified for use with the real solar system and planets (plus one I found on a quick internet search).

Transfer Calculator -- All GUI'd up and kind of messy, but has our solar system configs.

Launch Window Planner -- For KSP, I think the UI is better and simpler. I'm sure a version for our solar system exists out there.

KSPTOT -- Contains all the bells and whistles for designing interplanetary missions, including a Lambert solver. Also great for gravity assists and many hours wasted on planetary tours. Load up a config file for the real solar system of planets.

It's worth noting that many solvers use the patched conic approximation to solve. This leads to inaccuracies in the closest approach distance. But for story building purposes these tools are probably good enough.

If anyone has other solvers to add to the list, please suggest them and I will try to get them in!

• Thanks! This is perfect. Aug 20, 2019 at 11:03